|  line  | 
 stmt  | 
 bran  | 
 cond  | 
 sub  | 
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 # -*- encoding: utf-8; indent-tabs-mode: nil -*-  | 
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 #  | 
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 #     Perl extension for computing the sunrise/sunset on a given day  | 
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 #     Copyright (C) 1999-2003, 2013, 2015, 2017, 2019, 2021 Ron Hill and Jean Forget  | 
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 #  | 
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 #     See the license in the embedded documentation below.  | 
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 #  | 
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 package Astro::Sunrise;  | 
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1041908
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 use strict;  | 
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 use warnings;  | 
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 use POSIX qw(floor);  | 
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13931
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12219
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 use Math::Trig;  | 
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151342
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1431
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 use Carp;  | 
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108
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 use vars qw( $VERSION @ISA @EXPORT @EXPORT_OK %EXPORT_TAGS $RADEG $DEGRAD );  | 
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11
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 require Exporter;  | 
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 @ISA       = qw( Exporter );  | 
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20
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 @EXPORT    = qw( sunrise sun_rise sun_set );  | 
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21
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 @EXPORT_OK = qw( DEFAULT CIVIL NAUTICAL AMATEUR ASTRONOMICAL sind cosd tand asind acosd atand atan2d equal );  | 
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22
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 %EXPORT_TAGS = (  | 
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         constants => [ qw/DEFAULT CIVIL NAUTICAL AMATEUR ASTRONOMICAL/ ],  | 
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24
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         trig      => [ qw/sind cosd tand asind acosd atand atan2d equal/ ],  | 
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         );  | 
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 $VERSION =  '0.99';  | 
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 $RADEG   = ( 180 / pi );  | 
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 $DEGRAD  = ( pi / 180 );  | 
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 my $INV360     = ( 1.0 / 360.0 );  | 
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 sub sun_rise {  | 
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11
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1
  
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4024
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   my ($sun_rise, undef) = sun_rise_sun_set(@_);  | 
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8
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   return $sun_rise;  | 
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 }  | 
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 sub sun_set {  | 
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8
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2104
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   my (undef, $sun_set) = sun_rise_sun_set(@_);  | 
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8
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   return $sun_set;  | 
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 }  | 
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 sub sun_rise_sun_set {  | 
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0
  
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   my %arg;  | 
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19
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100
  
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   if (ref($_[0]) eq 'HASH') {  | 
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11
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     %arg = %{$_[0]};  | 
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   else {  | 
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     @arg{ qw/lon lat alt offset/ } = @_;  | 
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   # This trick aims to fulfill two antagonistic purposes:  | 
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51
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   # -- do not load DateTime if the only function called is "sunrise"  | 
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   # -- load DateTime implicitly if the user calls "sun_rise" or "sun_set". This is to be backward  | 
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   # compatible with 0.92 or earlier, when Astro::Sunrise would load DateTime and thus, allow  | 
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   # the user to remove this line from his script.  | 
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19
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 50
  
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49
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   unless ($INC{DateTime}) {  | 
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1103
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     eval "use DateTime";  | 
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2
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11
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1
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6
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5
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2
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1
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11
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57
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19
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55
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     croak $@  | 
| 
58
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       if $@;  | 
| 
59
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| 
60
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| 
61
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19
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47
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   my ($longitude, $latitude) = @arg{ qw/lon lat/ };  | 
| 
62
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19
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100
  
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43
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   my $alt       = defined($arg{alt}      ) ?     $arg{alt}       : -0.833;  | 
| 
63
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19
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100
  
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40
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   my $offset    = defined($arg{offset}   ) ? int($arg{offset})   : 0 ;  | 
| 
64
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19
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100
  
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49
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   my $tz        = defined($arg{time_zone}) ?     $arg{time_zone} : 'local';  | 
| 
65
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19
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 50
  
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73
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   $arg{precise}    ||= 0;  | 
| 
66
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19
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 50
  
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60
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   $arg{upper_limb} ||= 0;  | 
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67
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19
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100
  
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63
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   $arg{polar}      ||= 'warn';  | 
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68
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19
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 50
  
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59
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   $arg{trace}      ||= 0;  | 
| 
69
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19
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100
  
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131
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   croak "Longitude parameter (keyword: 'lon') is mandatory"  | 
| 
70
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     unless defined $longitude;  | 
| 
71
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18
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100
  
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111
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   croak "Latitude parameter (keyword: 'lat') is mandatory"  | 
| 
72
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     unless defined $latitude;  | 
| 
73
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   croak "Wrong value of the 'polar' argument: should be either 'warn' or 'retval'"  | 
| 
74
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17
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100
  
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 66
  
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130
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     if $arg{polar} ne 'warn' and $arg{polar} ne 'retval';  | 
| 
75
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| 
76
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16
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51
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   my $today = DateTime->today(time_zone => $tz);  | 
| 
77
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16
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30208
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   $today->set( hour => 12 );  | 
| 
78
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16
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6915
 | 
   $today->add( days => $offset );  | 
| 
79
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| 
80
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   my( $sun_rise, $sun_set ) = sunrise( { year  => $today->year,  | 
| 
81
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                                          month => $today->mon,  | 
| 
82
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                                          day   => $today->mday,  | 
| 
83
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                                          lon   => $longitude,  | 
| 
84
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                                          lat   => $latitude,  | 
| 
85
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                                          tz    => ( $today->offset / 3600 ),  | 
| 
86
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                                          #  | 
| 
87
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                                          # DST is always 0 because DateTime  | 
| 
88
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                                          # currently (v 0.16) adds one to the  | 
| 
89
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                                          # offset during DST hours  | 
| 
90
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                                          isdst      => 0,  | 
| 
91
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                                          alt        => $alt,  | 
| 
92
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                                          precise    => $arg{precise},  | 
| 
93
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                                          upper_limb => $arg{upper_limb},  | 
| 
94
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                                          polar      => $arg{polar},  | 
| 
95
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                                          trace      => $arg{trace},  | 
| 
96
 | 
16
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2202
 | 
                                       } );  | 
| 
97
 | 
16
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 | 
114
 | 
   return ($sun_rise, $sun_set);  | 
| 
98
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 }  | 
| 
99
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    | 
| 
100
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub sunrise  {  | 
| 
101
 | 
790
 | 
 
 | 
 
 | 
  
790
  
 | 
  
1
  
 | 
719797
 | 
   my %arg;  | 
| 
102
 | 
790
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1966
 | 
   if (ref($_[0]) eq 'HASH') {  | 
| 
103
 | 
672
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1262
 | 
     %arg = %{$_[0]};  | 
| 
 
 | 
672
 | 
 
 | 
 
 | 
 
 | 
 
 | 
3442
 | 
    | 
| 
104
 | 
 
 | 
 
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 | 
 
 | 
   }  | 
| 
105
 | 
 
 | 
 
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 | 
 
 | 
   else {  | 
| 
106
 | 
118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
493
 | 
     @arg{ qw/year month day lon lat tz isdst alt precise/ } = @_;  | 
| 
107
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
   }  | 
| 
108
 | 
 
 | 
 
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 | 
   my (        $year, $month, $day, $lon, $lat, $TZ, $isdst, $trace)  | 
| 
109
 | 
790
 | 
 
 | 
 
 | 
 
 | 
 
 | 
2650
 | 
     = @arg{ qw/year   month   day   lon   lat   tz   isdst   trace/ };  | 
| 
110
 | 
790
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1717
 | 
   my $altit     = defined($arg{alt}    ) ? $arg{alt}     : -0.833;  | 
| 
111
 | 
790
 | 
 
 | 
  
100
  
 | 
 
 | 
 
 | 
2915
 | 
   $arg{precise}    ||= 0;  | 
| 
112
 | 
790
 | 
 
 | 
  
100
  
 | 
 
 | 
 
 | 
2211
 | 
   $arg{upper_limb} ||= 0;  | 
| 
113
 | 
790
 | 
 
 | 
  
100
  
 | 
 
 | 
 
 | 
2295
 | 
   $arg{polar}      ||= 'warn';  | 
| 
114
 | 
790
 | 
 
 | 
  
 50
  
 | 
 
 | 
 
 | 
2261
 | 
   $trace           ||= 0;  | 
| 
115
 | 
790
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1363
 | 
   croak "Year parameter is mandatory"  | 
| 
116
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     unless defined $year;  | 
| 
117
 | 
789
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1253
 | 
   croak "Month parameter is mandatory"  | 
| 
118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     unless defined $month;  | 
| 
119
 | 
788
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1299
 | 
   croak "Day parameter is mandatory"  | 
| 
120
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     unless defined $day;  | 
| 
121
 | 
787
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1362
 | 
   croak "Longitude parameter (keyword: 'lon') is mandatory"  | 
| 
122
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     unless defined $lon;  | 
| 
123
 | 
786
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1257
 | 
   croak "Latitude parameter (keyword: 'lat') is mandatory"  | 
| 
124
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     unless defined $lat;  | 
| 
125
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   croak "Wrong value of the 'polar' argument: should be either 'warn' or 'retval'"  | 
| 
126
 | 
785
 | 
  
100
  
 | 
  
100
  
 | 
 
 | 
 
 | 
2326
 | 
       if $arg{polar} ne 'warn' and $arg{polar} ne 'retval';  | 
| 
127
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
128
 | 
784
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1318
 | 
   if (! $arg{precise})   {  | 
| 
129
 | 
602
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1072
 | 
     my $revsub = \&rev180; # normalizing angles around 0 degrees  | 
| 
130
 | 
602
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1072
 | 
     if ($trace) {  | 
| 
131
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       printf $trace "\nBasic computation for %04d-%02d-%02d, lon %.3f, lat %.3f, altitude %.3f, upper limb %d\n"  | 
| 
132
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                            , $year, $month, $day  | 
| 
133
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                            , $lon  | 
| 
134
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                            , $lat  | 
| 
135
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                            , $altit  | 
| 
136
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
                                            , $arg{upper_limb};  | 
| 
137
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
138
 | 
602
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1214
 | 
     my $d = days_since_2000_Jan_0( $year, $month, $day ) + 0.5 - $lon / 360.0;  | 
| 
139
 | 
602
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1436
 | 
     my ($h1, $h2) = sun_rise_set($d, $lon, $lat, $altit, 15.0, $arg{upper_limb}, $arg{polar}, $trace, $revsub);  | 
| 
140
 | 
602
 | 
  
 50
  
 | 
  
100
  
 | 
 
 | 
 
 | 
5214
 | 
     if ($h1 eq 'day' or $h1 eq 'night' or $h2 eq 'day' or $h2 eq 'night') {  | 
| 
 
 | 
 
 | 
 
 | 
  
 66
  
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
 
 | 
 
 | 
 
 | 
  
 66
  
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
141
 | 
150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
859
 | 
       return ($h1, $h2);  | 
| 
142
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
143
 | 
452
 | 
 
 | 
 
 | 
 
 | 
 
 | 
880
 | 
     return convert_hour($h1, $h2, $TZ, $isdst);  | 
| 
144
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
145
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   else {  | 
| 
146
 | 
182
 | 
 
 | 
 
 | 
  
516
  
 | 
 
 | 
655
 | 
     my $revsub = sub { _rev_lon($_[0], $lon) }; # normalizing angles around the local longitude  | 
| 
 
 | 
516
 | 
 
 | 
 
 | 
 
 | 
 
 | 
719
 | 
    | 
| 
147
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
247
 | 
     my $ang_speed = 15.0;  | 
| 
148
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
149
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # This is the initial start  | 
| 
150
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
324
 | 
     my $d = days_since_2000_Jan_0($year, $month, $day) - $lon / 360.0;  | 
| 
151
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
152
 | 
182
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
312
 | 
     if ($trace) {  | 
| 
153
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       printf $trace "\nPrecise sunrise computation for %04d-%02d-%02d, lon %.3f, lat %.3f, altitude %.3f, upper limb %d angular speed %.5f\n"  | 
| 
154
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $year, $month, $day  | 
| 
155
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $lon,  | 
| 
156
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $lat,  | 
| 
157
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $altit  | 
| 
158
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $arg{upper_limb}  | 
| 
159
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
                    , $ang_speed;  | 
| 
160
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
161
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
200
 | 
     my $h1_lmt = 12; # LMT decimal hours, noon then the successive values of sunrise  | 
| 
162
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
207
 | 
     my $h1_utc;      # UTC decimal hours, noon LMT then the successive values of sunrise  | 
| 
163
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
310
 | 
     for my $counter (1..9) {  | 
| 
164
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       # 9 is a failsafe precaution against a possibly runaway loop  | 
| 
165
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       # but hopefully, we will leave the loop long before, with "last"  | 
| 
166
 | 
269
 | 
 
 | 
 
 | 
 
 | 
 
 | 
290
 | 
       my $h2_utc;  | 
| 
167
 | 
269
 | 
 
 | 
 
 | 
 
 | 
 
 | 
608
 | 
       ($h2_utc, undef) = sun_rise_set($d + $h1_lmt / 24, $lon, $lat, $altit, $ang_speed, $arg{upper_limb}, $arg{polar}, $trace, $revsub);  | 
| 
168
 | 
269
 | 
  
100
  
 | 
  
100
  
 | 
 
 | 
 
 | 
999
 | 
       if ($h2_utc eq 'day' or $h2_utc eq 'night') {  | 
| 
169
 | 
150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
184
 | 
         $h1_utc = $h2_utc;  | 
| 
170
 | 
150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
199
 | 
         last;  | 
| 
171
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
172
 | 
119
 | 
 
 | 
 
 | 
 
 | 
 
 | 
169
 | 
       $h1_utc = $h1_lmt - $lon / 15;  | 
| 
173
 | 
119
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
165
 | 
       if (equal($h1_utc, $h2_utc, 5)) {  | 
| 
174
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         # equal within 1e-5 hour, a little less than a second  | 
| 
175
 | 
32
 | 
 
 | 
 
 | 
 
 | 
 
 | 
42
 | 
         $h1_utc = $h2_utc;  | 
| 
176
 | 
32
 | 
 
 | 
 
 | 
 
 | 
 
 | 
59
 | 
         last;  | 
| 
177
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
178
 | 
87
 | 
 
 | 
 
 | 
 
 | 
 
 | 
133
 | 
       $h1_utc = $h2_utc;  | 
| 
179
 | 
87
 | 
 
 | 
 
 | 
 
 | 
 
 | 
120
 | 
       $h1_lmt = $h1_utc + $lon / 15;  | 
| 
180
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
181
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
182
 | 
182
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
261
 | 
     if ($trace) {  | 
| 
183
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       printf $trace "\nPrecise sunset computation for %04d-%02d-%02d, lon %.3f, lat %.3f, altitude %.3f, upper limb %d angular speed %.5f\n"  | 
| 
184
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $year, $month, $day  | 
| 
185
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $lon,  | 
| 
186
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $lat,  | 
| 
187
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $altit  | 
| 
188
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    , $arg{upper_limb}  | 
| 
189
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
                    , $ang_speed;  | 
| 
190
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
191
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
221
 | 
     my $h3_lmt = 12; # LMT decimal hours, noon then the successive values of sunset  | 
| 
192
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
217
 | 
     my $h3_utc;      # UTC decimal hours, noon LMT then the successive values of sunset  | 
| 
193
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
284
 | 
     for my $counter (1..9) {  | 
| 
194
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       # 9 is a failsafe precaution against a possibly runaway loop  | 
| 
195
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       # but hopefully, we will leave the loop long before, with "last"  | 
| 
196
 | 
247
 | 
 
 | 
 
 | 
 
 | 
 
 | 
254
 | 
       my $h4_utc;  | 
| 
197
 | 
247
 | 
 
 | 
 
 | 
 
 | 
 
 | 
505
 | 
       (undef, $h4_utc) = sun_rise_set($d + $h3_lmt / 24, $lon, $lat, $altit, $ang_speed, $arg{upper_limb}, $arg{polar}, $trace, $revsub);  | 
| 
198
 | 
247
 | 
  
100
  
 | 
  
100
  
 | 
 
 | 
 
 | 
970
 | 
       if ($h4_utc eq 'day' or $h4_utc eq 'night') {  | 
| 
199
 | 
150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
159
 | 
         $h3_utc = $h4_utc;  | 
| 
200
 | 
150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
180
 | 
         last;  | 
| 
201
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
202
 | 
97
 | 
 
 | 
 
 | 
 
 | 
 
 | 
414
 | 
       $h3_utc = $h3_lmt - $lon / 15;  | 
| 
203
 | 
97
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
123
 | 
       if (equal($h3_utc, $h4_utc, 5)) {  | 
| 
204
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         # equal within 1e-5 hour, a little less than a second  | 
| 
205
 | 
32
 | 
 
 | 
 
 | 
 
 | 
 
 | 
40
 | 
         $h3_utc = $h4_utc;  | 
| 
206
 | 
32
 | 
 
 | 
 
 | 
 
 | 
 
 | 
50
 | 
         last;  | 
| 
207
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
208
 | 
65
 | 
 
 | 
 
 | 
 
 | 
 
 | 
94
 | 
       $h3_utc = $h4_utc;  | 
| 
209
 | 
65
 | 
 
 | 
 
 | 
 
 | 
 
 | 
91
 | 
       $h3_lmt = $h3_utc + $lon / 15;  | 
| 
210
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
211
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
212
 | 
182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
302
 | 
     return convert_hour($h1_utc, $h3_utc, $TZ, $isdst);  | 
| 
213
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
214
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
215
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
216
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #######################################################################################  | 
| 
217
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # end sunrise  | 
| 
218
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 ###################################################################################  | 
| 
219
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
220
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
221
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
222
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for days_since_2000_Jan_0  | 
| 
223
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
224
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
225
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # year, month, day  | 
| 
226
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
227
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
228
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
229
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # process the year month and day (counted in days)  | 
| 
230
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Day 0.0 is at Jan 1 2000 0.0 UT  | 
| 
231
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Note that ALL divisions here should be INTEGER divisions  | 
| 
232
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
233
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
234
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
235
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # day number  | 
| 
236
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
237
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub days_since_2000_Jan_0 {  | 
| 
238
 | 
11
 | 
 
 | 
 
 | 
  
11
  
 | 
 
 | 
5558
 | 
     use integer;  | 
| 
 
 | 
11
 | 
 
 | 
 
 | 
 
 | 
 
 | 
138
 | 
    | 
| 
 
 | 
11
 | 
 
 | 
 
 | 
 
 | 
 
 | 
57
 | 
    | 
| 
239
 | 
784
 | 
 
 | 
 
 | 
  
784
  
 | 
  
0
  
 | 
1294
 | 
     my ( $year, $month, $day ) = @_;  | 
| 
240
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
241
 | 
784
 | 
 
 | 
 
 | 
 
 | 
 
 | 
2366
 | 
     my $d =   367 * $year  | 
| 
242
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             - int( ( 7 * ( $year + ( ($month + 9) / 12 ) ) ) / 4 )  | 
| 
243
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             + int( (275 * $month) / 9 )  | 
| 
244
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             + $day - 730530;  | 
| 
245
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
246
 | 
784
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1850
 | 
     return $d;  | 
| 
247
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
248
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
249
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
250
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
251
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
252
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for convert_hour  | 
| 
253
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
254
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
255
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Hour_rise, Hour_set, Time zone offset, DST setting  | 
| 
256
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # hours are in UT  | 
| 
257
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
258
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
259
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
260
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # convert to local time  | 
| 
261
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
262
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
263
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
264
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
265
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # hour:min rise and set  | 
| 
266
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
267
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
268
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub convert_hour {  | 
| 
269
 | 
634
 | 
 
 | 
 
 | 
  
634
  
 | 
  
0
  
 | 
990
 | 
   my ($hour_rise_ut, $hour_set_ut, $TZ, $isdst) = @_;  | 
| 
270
 | 
634
 | 
 
 | 
 
 | 
 
 | 
 
 | 
939
 | 
   return (convert_1_hour($hour_rise_ut, $TZ, $isdst),  | 
| 
271
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
           convert_1_hour($hour_set_ut,  $TZ, $isdst));  | 
| 
272
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
273
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
274
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
275
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for convert_1_hour  | 
| 
276
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
277
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
278
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Hour, Time zone offset, DST setting  | 
| 
279
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # hours are in UT  | 
| 
280
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
281
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
282
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
283
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # convert to local time  | 
| 
284
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
285
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
286
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
287
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
288
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # hour:min  | 
| 
289
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
290
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
291
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub convert_1_hour {  | 
| 
292
 | 
1268
 | 
 
 | 
 
 | 
  
1268
  
 | 
  
0
  
 | 
1761
 | 
   my ($hour_ut, $TZ, $isdst) = @_;  | 
| 
293
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
294
 | 
1268
 | 
  
100
  
 | 
  
100
  
 | 
 
 | 
 
 | 
4865
 | 
   if ($hour_ut eq 'day' or $hour_ut eq 'night') {  | 
| 
295
 | 
300
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1213
 | 
     return $hour_ut;  | 
| 
296
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
297
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
298
 | 
968
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1284
 | 
   my $hour_local = $hour_ut + $TZ;  | 
| 
299
 | 
968
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1321
 | 
   if ($isdst) {  | 
| 
300
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $hour_local ++;  | 
| 
301
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
302
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
303
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   # The hour should be between 0 and 24;  | 
| 
304
 | 
968
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1781
 | 
   if ($hour_local < 0) {  | 
| 
 
 | 
 
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
305
 | 
2
 | 
 
 | 
 
 | 
 
 | 
 
 | 
3
 | 
     $hour_local += 24;  | 
| 
306
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
307
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   elsif ($hour_local > 24) {  | 
| 
308
 | 
20
 | 
 
 | 
 
 | 
 
 | 
 
 | 
24
 | 
     $hour_local -= 24;  | 
| 
309
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
310
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
311
 | 
968
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1185
 | 
   my $hour =  int ($hour_local);  | 
| 
312
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
313
 | 
968
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1776
 | 
   my $min  = floor(($hour_local - $hour) * 60 + 0.5);  | 
| 
314
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
315
 | 
968
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1624
 | 
   if ($min >= 60) {  | 
| 
316
 | 
7
 | 
 
 | 
 
 | 
 
 | 
 
 | 
12
 | 
     $min -= 60;  | 
| 
317
 | 
7
 | 
 
 | 
 
 | 
 
 | 
 
 | 
13
 | 
     $hour++;  | 
| 
318
 | 
7
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
15
 | 
     $hour -= 24 if $hour >= 24;  | 
| 
319
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
320
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
321
 | 
968
 | 
 
 | 
 
 | 
 
 | 
 
 | 
4422
 | 
   return sprintf("%02d:%02d", $hour, $min);  | 
| 
322
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
323
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
324
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
325
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub sun_rise_set {  | 
| 
326
 | 
1118
 | 
 
 | 
 
 | 
  
1118
  
 | 
  
0
  
 | 
2440
 | 
     my ($d, $lon, $lat, $altit, $ang_spd, $upper_limb, $polar, $trace, $revsub) = @_;  | 
| 
327
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
328
 | 
1118
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1788
 | 
     if ($trace) {  | 
| 
329
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "\n";  | 
| 
330
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
331
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
332
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute local sidereal time of this moment  | 
| 
333
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1659
 | 
     my $gmst0   = GMST0($d);  | 
| 
334
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1692
 | 
     my $sidtime = revolution( $gmst0 + 180.0 );  | 
| 
335
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
336
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute Sun's RA + Decl + distance at this moment  | 
| 
337
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1881
 | 
     my ( $sRA, $sdec, $sr ) = sun_RA_dec($d, $lon, $trace);  | 
| 
338
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
339
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute time when Sun is at south - in hours (LMT then UTC)  | 
| 
340
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
2024
 | 
     my $tsouth_lmt  = 12.0 - $revsub->( $sidtime - $sRA ) / 15;  | 
| 
341
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1728
 | 
     my $tsouth      = $tsouth_lmt - $lon / 15;  | 
| 
342
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
343
 | 
1118
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1715
 | 
     if ($trace) {  | 
| 
344
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), GMST0 $gmst0 %s %s\n",            _fmt_hr(24 * ($d - int($d)), $lon, 0), _fmt_angle($gmst0  ), _fmt_dur($gmst0   / 15);  | 
| 
345
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), sidereal time $sidtime, %s %s\n", _fmt_hr(24 * ($d - int($d)), $lon, 0), _fmt_angle($sidtime), _fmt_dur($sidtime / 15);  | 
| 
346
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), right asc $sRA %s %s\n",          _fmt_hr(24 * ($d - int($d)), $lon, 0), _fmt_angle($sRA    ), _fmt_dur($sRA     / 15);  | 
| 
347
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), declination $sdec %s %s\n",       _fmt_hr(24 * ($d - int($d)), $lon, 0), _fmt_angle($sdec   ), _fmt_dur($sdec    / 15);  | 
| 
348
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), solar noon at $tsouth (%s)\n",    _fmt_hr(24 * ($d - int($d)), $lon, 0), _fmt_hr($tsouth, $lon, 0);  | 
| 
349
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
350
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
351
 | 
1118
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
1701
 | 
     if ($upper_limb) {  | 
| 
352
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         # Compute the Sun's apparent radius, degrees  | 
| 
353
 | 
485
 | 
 
 | 
 
 | 
 
 | 
 
 | 
682
 | 
         my $sradius = 0.2666 / $sr;  | 
| 
354
 | 
485
 | 
 
 | 
 
 | 
 
 | 
 
 | 
948
 | 
         $altit -= $sradius;  | 
| 
355
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
356
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
357
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute the diurnal arc that the Sun traverses to reach  | 
| 
358
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # the specified altitude altit:  | 
| 
359
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1459
 | 
     my $cost =   ( sind($altit) - sind($lat) * sind($sdec) )  | 
| 
360
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                / ( cosd($lat) * cosd($sdec) );  | 
| 
361
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
362
 | 
1118
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1976
 | 
     if ($trace) {  | 
| 
363
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       print $trace "altit = $altit, sind(altit) = ", sind($altit), ", lat = $lat, sind(lat) = ", sind($lat), "\n";  | 
| 
364
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       print $trace "sdec = $sdec, sind(sdec) = ", sind($sdec), ", lat = $lat, cosd(lat) = ", cosd($lat), "\n";  | 
| 
365
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       print $trace "sdec = $sdec, cosd(sdec) = ", cosd($sdec), ", cost = $cost\n";  | 
| 
366
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
367
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
368
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1240
 | 
     my $t;  | 
| 
369
 | 
1118
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
2304
 | 
     if ( $cost >= 1.0 ) {  | 
| 
 
 | 
 
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
370
 | 
142
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
258
 | 
       if ($polar eq 'retval') {  | 
| 
371
 | 
138
 | 
 
 | 
 
 | 
 
 | 
 
 | 
360
 | 
         return ('night', 'night');  | 
| 
372
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
373
 | 
4
 | 
 
 | 
 
 | 
 
 | 
 
 | 
595
 | 
       carp "Sun never rises!!\n";  | 
| 
374
 | 
4
 | 
 
 | 
 
 | 
 
 | 
 
 | 
228
 | 
       $t = 0.0;    # Sun always below altit  | 
| 
375
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
376
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     elsif ( $cost <= -1.0 ) {  | 
| 
377
 | 
320
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
638
 | 
       if ($polar eq 'retval') {  | 
| 
378
 | 
312
 | 
 
 | 
 
 | 
 
 | 
 
 | 
858
 | 
         return ('day', 'day');  | 
| 
379
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
380
 | 
8
 | 
 
 | 
 
 | 
 
 | 
 
 | 
944
 | 
       carp "Sun never sets!!\n";  | 
| 
381
 | 
8
 | 
 
 | 
 
 | 
 
 | 
 
 | 
437
 | 
       $t = 12.0;    # Sun always above altit  | 
| 
382
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
383
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     else {  | 
| 
384
 | 
656
 | 
 
 | 
 
 | 
 
 | 
 
 | 
903
 | 
       my $arc = acosd($cost);    # The diurnal arc  | 
| 
385
 | 
656
 | 
 
 | 
 
 | 
 
 | 
 
 | 
3548
 | 
       $t = $arc / $ang_spd;      # Time to traverse the diurnal arc, hours  | 
| 
386
 | 
656
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1038
 | 
       if ($trace) {  | 
| 
387
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
         printf $trace "Diurnal arc $arc -> $t hours (%s)\n", _fmt_dur($t);  | 
| 
388
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       }  | 
| 
389
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
390
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
391
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Store rise and set times - in hours UT  | 
| 
392
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
393
 | 
668
 | 
 
 | 
 
 | 
 
 | 
 
 | 
838
 | 
     my $hour_rise_ut = $tsouth - $t;  | 
| 
394
 | 
668
 | 
 
 | 
 
 | 
 
 | 
 
 | 
837
 | 
     my $hour_set_ut  = $tsouth + $t;  | 
| 
395
 | 
668
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
925
 | 
     if ($trace) {  | 
| 
396
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), sunrise at $hour_rise_ut (%s)\n", _fmt_hr(24 * ($d - int($d)), $lon),  | 
| 
397
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    _fmt_hr($hour_rise_ut, $lon);  | 
| 
398
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), sunset  at $hour_set_ut (%s)\n",  _fmt_hr(24 * ($d - int($d)), $lon),  | 
| 
399
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                    _fmt_hr($hour_set_ut , $lon);  | 
| 
400
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
401
 | 
668
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1292
 | 
     return($hour_rise_ut, $hour_set_ut);  | 
| 
402
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
403
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
404
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #########################################################################################################  | 
| 
405
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
406
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
407
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for GMST0  | 
| 
408
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
409
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
410
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Day number  | 
| 
411
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
412
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
413
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
414
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # computes GMST0, the Greenwich Mean Sidereal Time  | 
| 
415
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # at 0h UT (i.e. the sidereal time at the Greenwich meridian at  | 
| 
416
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # 0h UT).  GMST is then the sidereal time at Greenwich at any  | 
| 
417
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # time of the day..  | 
| 
418
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
419
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
420
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
421
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
422
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Sidtime  | 
| 
423
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
424
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub GMST0 {  | 
| 
425
 | 
1118
 | 
 
 | 
 
 | 
  
1118
  
 | 
  
0
  
 | 
1515
 | 
     my ($d) = @_;  | 
| 
426
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
427
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1992
 | 
     my $sidtim0 = revolution(   ( 180.0 + 356.0470 + 282.9404 )  | 
| 
428
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                               + ( 0.9856002585 + 4.70935E-5 ) * $d );  | 
| 
429
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1519
 | 
     return $sidtim0;  | 
| 
430
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
431
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
432
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
433
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
434
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
435
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for sun_RA_dec  | 
| 
436
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
437
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
438
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # day number, $r and $lon (from sunpos)  | 
| 
439
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
440
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
441
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
442
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # compute RA and dec  | 
| 
443
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
444
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
445
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
446
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
447
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Sun's Right Ascension (RA), Declination (dec) and distance (r)  | 
| 
448
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
449
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
450
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub sun_RA_dec {  | 
| 
451
 | 
1118
 | 
 
 | 
 
 | 
  
1118
  
 | 
  
0
  
 | 
1695
 | 
     my ($d, $lon_noon, $trace) = @_;  | 
| 
452
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
453
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute Sun's ecliptical coordinates  | 
| 
454
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1655
 | 
     my ( $r, $lon ) = sunpos($d);  | 
| 
455
 | 
1118
 | 
  
 50
  
 | 
 
 | 
 
 | 
 
 | 
1774
 | 
     if ($trace) {  | 
| 
456
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
       printf $trace "For day $d (%s), solar noon at ecliptic longitude $lon %s\n", _fmt_hr(24 * ($d - int($d)), $lon_noon), _fmt_angle($lon);  | 
| 
457
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
458
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
459
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute ecliptic rectangular coordinates (z=0)  | 
| 
460
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1508
 | 
     my $x = $r * cosd($lon);  | 
| 
461
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1467
 | 
     my $y = $r * sind($lon);  | 
| 
462
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
463
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute obliquity of ecliptic (inclination of Earth's axis)  | 
| 
464
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1489
 | 
     my $obl_ecl = 23.4393 - 3.563E-7 * $d;  | 
| 
465
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
466
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Convert to equatorial rectangular coordinates - x is unchanged  | 
| 
467
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1434
 | 
     my $z = $y * sind($obl_ecl);  | 
| 
468
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1433
 | 
     $y    = $y * cosd($obl_ecl);  | 
| 
469
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
470
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Convert to spherical coordinates  | 
| 
471
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1537
 | 
     my $RA  = atan2d( $y, $x );  | 
| 
472
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1818
 | 
     my $dec = atan2d( $z, sqrt( $x * $x + $y * $y ) );  | 
| 
473
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
474
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
2127
 | 
     return ( $RA, $dec, $r );  | 
| 
475
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
476
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }    # sun_RA_dec  | 
| 
477
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
478
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
479
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
480
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
481
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for sunpos  | 
| 
482
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
483
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
484
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  day number  | 
| 
485
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
486
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
487
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
488
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Computes the Sun's ecliptic longitude and distance  | 
| 
489
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # at an instant given in d, number of days since  | 
| 
490
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # 2000 Jan 0.0.  | 
| 
491
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
492
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
493
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
494
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
495
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # ecliptic longitude and distance  | 
| 
496
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # ie. $True_solar_longitude, $Solar_distance  | 
| 
497
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
498
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub sunpos {  | 
| 
499
 | 
1118
 | 
 
 | 
 
 | 
  
1118
  
 | 
  
0
  
 | 
1487
 | 
     my ($d) = @_;  | 
| 
500
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
501
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                       Mean anomaly of the Sun  | 
| 
502
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                       Mean longitude of perihelion  | 
| 
503
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                         Note: Sun's mean longitude = M + w  | 
| 
504
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                       Eccentricity of Earth's orbit  | 
| 
505
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                       Eccentric anomaly  | 
| 
506
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                       x, y coordinates in orbit  | 
| 
507
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     #                       True anomaly  | 
| 
508
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
509
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute mean elements  | 
| 
510
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1690
 | 
     my $Mean_anomaly_of_sun = revolution( 356.0470 + 0.9856002585 * $d );  | 
| 
511
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1534
 | 
     my $Mean_longitude_of_perihelion = 282.9404 + 4.70935E-5 * $d;  | 
| 
512
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1345
 | 
     my $Eccentricity_of_Earth_orbit  = 0.016709 - 1.151E-9 * $d;  | 
| 
513
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
514
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     # Compute true longitude and radius vector  | 
| 
515
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1781
 | 
     my $Eccentric_anomaly =   $Mean_anomaly_of_sun  | 
| 
516
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                             + $Eccentricity_of_Earth_orbit * $RADEG  | 
| 
517
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                * sind($Mean_anomaly_of_sun)  | 
| 
518
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                * ( 1.0 + $Eccentricity_of_Earth_orbit * cosd($Mean_anomaly_of_sun) );  | 
| 
519
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
520
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1583
 | 
     my $x = cosd($Eccentric_anomaly) - $Eccentricity_of_Earth_orbit;  | 
| 
521
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
522
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1672
 | 
     my $y = sqrt( 1.0 - $Eccentricity_of_Earth_orbit * $Eccentricity_of_Earth_orbit )  | 
| 
523
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             * sind($Eccentric_anomaly);  | 
| 
524
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
525
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1483
 | 
     my $Solar_distance = sqrt( $x * $x + $y * $y );    # Solar distance  | 
| 
526
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1562
 | 
     my $True_anomaly = atan2d( $y, $x );               # True anomaly  | 
| 
527
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
528
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1397
 | 
     my $True_solar_longitude = $True_anomaly + $Mean_longitude_of_perihelion;    # True solar longitude  | 
| 
529
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
530
 | 
1118
 | 
  
100
  
 | 
 
 | 
 
 | 
 
 | 
2074
 | 
     if ( $True_solar_longitude >= 360.0 ) {  | 
| 
531
 | 
447
 | 
 
 | 
 
 | 
 
 | 
 
 | 
555
 | 
       $True_solar_longitude -= 360.0;    # Make it 0..360 degrees  | 
| 
532
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
533
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
534
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
2080
 | 
     return ( $Solar_distance, $True_solar_longitude );  | 
| 
535
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
536
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
537
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
538
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
539
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub sind {  | 
| 
540
 | 
7832
 | 
 
 | 
 
 | 
  
7832
  
 | 
  
1
  
 | 
15193
 | 
     sin( ( $_[0] ) * $DEGRAD );  | 
| 
541
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
542
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
543
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub cosd {  | 
| 
544
 | 
6714
 | 
 
 | 
 
 | 
  
6714
  
 | 
  
1
  
 | 
9791
 | 
     cos( ( $_[0] ) * $DEGRAD );  | 
| 
545
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
546
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
547
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub tand {  | 
| 
548
 | 
6
 | 
 
 | 
 
 | 
  
6
  
 | 
  
1
  
 | 
41
 | 
     tan( ( $_[0] ) * $DEGRAD );  | 
| 
549
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
550
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
551
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub atand {  | 
| 
552
 | 
6
 | 
 
 | 
 
 | 
  
6
  
 | 
  
1
  
 | 
20
 | 
     ( $RADEG * atan( $_[0] ) );  | 
| 
553
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
554
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
555
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub asind {  | 
| 
556
 | 
6
 | 
 
 | 
 
 | 
  
6
  
 | 
  
1
  
 | 
17
 | 
     ( $RADEG * asin( $_[0] ) );  | 
| 
557
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
558
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
559
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub acosd {  | 
| 
560
 | 
662
 | 
 
 | 
 
 | 
  
662
  
 | 
  
1
  
 | 
1688
 | 
     ( $RADEG * acos( $_[0] ) );  | 
| 
561
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
562
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
563
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub atan2d {  | 
| 
564
 | 
3361
 | 
 
 | 
 
 | 
  
3361
  
 | 
  
1
  
 | 
7343
 | 
     ( $RADEG * atan2( $_[0], $_[1] ) );  | 
| 
565
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
566
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
567
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
568
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
569
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for revolution  | 
| 
570
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
571
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
572
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # any angle  | 
| 
573
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
574
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
575
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
576
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # reduces any angle to within the first revolution  | 
| 
577
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # by subtracting or adding even multiples of 360.0  | 
| 
578
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
579
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
580
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
581
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
582
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # the value of the input is >= 0.0 and < 360.0  | 
| 
583
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
584
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
585
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub revolution {  | 
| 
586
 | 
3354
 | 
 
 | 
 
 | 
  
3354
  
 | 
  
0
  
 | 
3651
 | 
     my $x = $_[0];  | 
| 
587
 | 
3354
 | 
 
 | 
 
 | 
 
 | 
 
 | 
6722
 | 
     return ( $x - 360.0 * floor( $x * $INV360 ) );  | 
| 
588
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
589
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
590
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
591
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for _rev_lon  | 
| 
592
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
593
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
594
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
595
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # two angles in degrees, the variable angle and the reference angle (longitude)  | 
| 
596
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
597
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
598
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
599
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Reduce input variable angle  to within reference-180 .. reference+180 degrees  | 
| 
600
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
601
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
602
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
603
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
604
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # angle that was reduced  | 
| 
605
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
606
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub _rev_lon {  | 
| 
607
 | 
516
 | 
 
 | 
 
 | 
  
516
  
 | 
 
 | 
744
 | 
     my ($x, $lon) = @_;  | 
| 
608
 | 
516
 | 
 
 | 
 
 | 
 
 | 
 
 | 
753
 | 
     return $lon + rev180($x - $lon);  | 
| 
609
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
610
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
611
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
612
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
613
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # FUNCTIONAL SEQUENCE for rev180  | 
| 
614
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
615
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _GIVEN  | 
| 
616
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
617
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # any angle  | 
| 
618
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
619
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _THEN  | 
| 
620
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
621
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Reduce input to within -180..+180 degrees  | 
| 
622
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
623
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
624
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # _RETURN  | 
| 
625
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
626
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # angle that was reduced  | 
| 
627
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #  | 
| 
628
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub rev180 {  | 
| 
629
 | 
1118
 | 
 
 | 
 
 | 
  
1118
  
 | 
  
0
  
 | 
1404
 | 
     my ($x) = @_;  | 
| 
630
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
631
 | 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
2810
 | 
     return ( $x - 360.0 * floor( $x * $INV360 + 0.5 ) );  | 
| 
632
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
633
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
634
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub equal {  | 
| 
635
 | 
259
 | 
 
 | 
 
 | 
  
259
  
 | 
  
1
  
 | 
886
 | 
     my ($A, $B, $dp) = @_;  | 
| 
636
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
637
 | 
259
 | 
 
 | 
 
 | 
 
 | 
 
 | 
1342
 | 
     return sprintf("%.${dp}g", $A) eq sprintf("%.${dp}g", $B);  | 
| 
638
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
639
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
640
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub _fmt_hr {  | 
| 
641
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
 
 | 
0
 | 
   my ($hr, $lon, $is_lmt) = @_;  | 
| 
642
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my ($lmt, $utc);  | 
| 
643
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   if ($is_lmt) {  | 
| 
644
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $lmt = $hr;  | 
| 
645
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $utc = $lmt - $lon / 15;  | 
| 
646
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
647
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   else {  | 
| 
648
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $utc = $hr;  | 
| 
649
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $lmt = $utc + $lon / 15;  | 
| 
650
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
651
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $hr_h_utc = $utc;         my $hr_h_lmt = $lmt;  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
652
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $hr_d_utc = $utc / 24;    my $hr_d_lmt = $lmt / 24;  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
653
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $hr_utc   = floor($utc);  my $hr_lmt   = floor($lmt);  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
654
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $utc        -= $hr_utc;      $lmt        -= $hr_lmt;  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
655
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $utc        *= 60;           $lmt        *= 60;  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
656
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $mn_utc   = floor($utc);  my $mn_lmt   = floor($lmt);  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
657
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $utc        -= $mn_utc;      $lmt        -= $mn_lmt;  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
658
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $utc        *= 60;           $lmt        *= 60;  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
659
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $sc_utc   = floor($utc);  my $sc_lmt   = floor($lmt);  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
    | 
| 
660
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   return sprintf("UTC: %02d:%02d:%02d %f h %f d, LMT: %02d:%02d:%02d %f h %f d", $hr_utc, $mn_utc, $sc_utc, $hr_h_utc, $hr_d_utc  | 
| 
661
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                                                                , $hr_lmt, $mn_lmt, $sc_lmt, $hr_h_lmt, $hr_d_lmt);  | 
| 
662
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
663
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
664
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub _fmt_dur {  | 
| 
665
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
 
 | 
0
 | 
   my ($dur) = @_;  | 
| 
666
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $sign = '';  | 
| 
667
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   if ($dur < 0) {  | 
| 
668
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $sign = '-';  | 
| 
669
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $dur *= -1;  | 
| 
670
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
671
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $hr = floor($dur);  | 
| 
672
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $dur  -= $hr;  | 
| 
673
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $dur  *= 60;  | 
| 
674
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $mn = floor($dur);  | 
| 
675
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $dur  -= $mn;  | 
| 
676
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $dur  *= 60;  | 
| 
677
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $sc = floor($dur);  | 
| 
678
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   return sprintf("%s%02d h %02d mn %02d s", $sign, $hr, $mn, $sc);  | 
| 
679
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
680
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
681
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub _fmt_angle {  | 
| 
682
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
 
 | 
0
 | 
   my ($angle) = @_;  | 
| 
683
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $sign = '';  | 
| 
684
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   if ($angle < 0) {  | 
| 
685
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $sign = '-';  | 
| 
686
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
     $angle *= -1;  | 
| 
687
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
688
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $hr = floor($angle);  | 
| 
689
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $angle  -= $hr;  | 
| 
690
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $angle  *= 60;  | 
| 
691
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $mn = floor($angle);  | 
| 
692
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $angle  -= $mn;  | 
| 
693
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   $angle  *= 60;  | 
| 
694
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   my $sc = floor($angle);  | 
| 
695
 | 
0
 | 
 
 | 
 
 | 
 
 | 
 
 | 
0
 | 
   return sprintf(q<%s%02d°%02d'%02d">, $sign, $hr, $mn, $sc);  | 
| 
696
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
697
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
698
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub DEFAULT      () { -0.833 }  | 
| 
699
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub CIVIL        () { - 6 }  | 
| 
700
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub NAUTICAL     () { -12 }  | 
| 
701
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub AMATEUR      () { -15 }  | 
| 
702
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub ASTRONOMICAL () { -18 }  | 
| 
703
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
704
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Ending a module with whatever, which risks to be zero, is wrong.  | 
| 
705
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Ending a module with 1 is boring. So, let us end it with:  | 
| 
706
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 1950;  | 
| 
707
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 # Hint: directed by BW, with GS, WH and EVS  | 
| 
708
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
709
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 __END__  | 
| 
710
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
711
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =encoding utf8  | 
| 
712
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
713
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 NAME  | 
| 
714
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
715
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Astro::Sunrise - Perl extension for computing the sunrise/sunset on a given day  | 
| 
716
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
717
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 VERSION  | 
| 
718
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
719
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This documentation refers to C<Astro::Sunrise> version 0.99.  | 
| 
720
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
721
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 SYNOPSIS  | 
| 
722
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
723
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   # When did the sun rise on YAPC::Europe 2015?  | 
| 
724
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   use Astro::Sunrise;  | 
| 
725
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   my ($sunrise, $sunset) = sunrise( { year => 2015, month => 9, day => 2, # YAPC::EU starts on 2nd September 2015  | 
| 
726
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                       lon  => -3.6, lat   => 37.17,       # Granada is 37°10'N, 3°36'W  | 
| 
727
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                       tz   => 1,    isdst => 1 } );       # This is still summer, therefore DST  | 
| 
728
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
729
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   # When does the sun rise today in Salt Lake City (home to YAPC::NA 2015)?  | 
| 
730
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   use Astro::Sunrise;  | 
| 
731
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   use DateTime;  | 
| 
732
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sunrise_today = sun_rise( { lon => -111.88, lat => 40.75 } ); # 40°45'N, 111°53'W  | 
| 
733
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
734
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   # And when does it set tomorrow at Salt Lake City?  | 
| 
735
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   use Astro::Sunrise;  | 
| 
736
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   use DateTime;  | 
| 
737
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sunset_tomorrow = sun_set( { lat => 40.75,    # 40°45'N,  | 
| 
738
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                 lon => -111.88,  # 111°53'W  | 
| 
739
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                 alt => -0.833,   # standard value for the sun altitude at sunset  | 
| 
740
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                 offset => 1 } ); # day offset up to tomorrow  | 
| 
741
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
742
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 DESCRIPTION  | 
| 
743
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
744
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This module will return the sunrise and sunset for a given day.  | 
| 
745
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
746
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Months are numbered 1 to 12, in the usual way, not 0 to 11 as in  | 
| 
747
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 C and in Perl's localtime.  | 
| 
748
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
749
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Eastern longitude is entered as a positive number  | 
| 
750
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Western longitude is entered as a negative number  | 
| 
751
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Northern latitude is entered as a positive number  | 
| 
752
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Southern latitude is entered as a negative number  | 
| 
753
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
754
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Please note that, when given as positional parameters, the longitude is specified before the  | 
| 
755
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 latitude.  | 
| 
756
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
757
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The time zone is given as the numeric value of the offset from UTC.  | 
| 
758
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
759
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The C<precise> parameter is set to either 0 or 1.  | 
| 
760
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 If set to 0 no Iteration will occur.  | 
| 
761
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 If set to 1 Iteration will occur, which will give a more precise result.  | 
| 
762
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Default is 0.  | 
| 
763
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
764
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 There are a number of sun altitudes to chose from.  The default is  | 
| 
765
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 -0.833 because this is what most countries use. Feel free to  | 
| 
766
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 specify it if you need to. Here is the list of values to specify  | 
| 
767
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 altitude (ALT) with, including symbolic constants for each.  | 
| 
768
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
769
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over  | 
| 
770
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
771
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<0> degrees  | 
| 
772
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
773
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Center of Sun's disk touches a mathematical horizon  | 
| 
774
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
775
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-0.25> degrees  | 
| 
776
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
777
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Sun's upper limb touches a mathematical horizon  | 
| 
778
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
779
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-0.583> degrees  | 
| 
780
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
781
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Center of Sun's disk touches the horizon; atmospheric refraction accounted for  | 
| 
782
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
783
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-0.833> degrees, DEFAULT  | 
| 
784
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
785
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Sun's upper limb touches the horizon; atmospheric refraction accounted for  | 
| 
786
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
787
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-6> degrees, CIVIL  | 
| 
788
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
789
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Civil twilight (one can no longer read outside without artificial illumination)  | 
| 
790
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
791
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-12> degrees, NAUTICAL  | 
| 
792
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
793
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Nautical twilight (navigation using a sea horizon no longer possible)  | 
| 
794
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
795
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-15> degrees, AMATEUR  | 
| 
796
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
797
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Amateur astronomical twilight (the sky is dark enough for most astronomical observations)  | 
| 
798
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
799
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B<-18> degrees, ASTRONOMICAL  | 
| 
800
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
801
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Astronomical twilight (the sky is completely dark)  | 
| 
802
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
803
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
804
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
805
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 USAGE  | 
| 
806
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
807
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 B<sunrise>  | 
| 
808
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
809
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   ($sunrise, $sunset) = sunrise( { year    => $year,      month      => $month,  | 
| 
810
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                    day     => $day,  | 
| 
811
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                    lon     => $longitude, lat        => $latitude,  | 
| 
812
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                    tz      => $tz_offset, isdst      => $is_dst,  | 
| 
813
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                    alt     => $altitude,  upper_limb => $upper_limb,  | 
| 
814
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                    precise => $precise,   polar      => $action,  | 
| 
815
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                    trace   => $fh } );  | 
| 
816
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
817
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   ($sunrise, $sunset) = sunrise(YYYY,MM,DD,longitude,latitude,Time Zone,DST);  | 
| 
818
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
819
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   ($sunrise, $sunset) = sunrise(YYYY,MM,DD,longitude,latitude,Time Zone,DST,ALT);  | 
| 
820
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
821
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   ($sunrise, $sunset) = sunrise(YYYY,MM,DD,longitude,latitude,Time Zone,DST,ALT,precise);  | 
| 
822
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
823
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the sunrise and sunset times, in HH:MM format.  | 
| 
824
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
825
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The first form uses a hash reference to pass arguments by name.  | 
| 
826
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The other forms are kept for backward compatibility. The arguments are:  | 
| 
827
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
828
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
829
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
830
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item year, month, day  | 
| 
831
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
832
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The three elements of the date for which you want to compute the sunrise and sunset.  | 
| 
833
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Months are numbered 1 to 12, in the usual way, not 0 to 11 as in C and in Perl's localtime.  | 
| 
834
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
835
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Mandatory, can be positional (#1, #2 and #3).  | 
| 
836
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
837
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item lon, lat  | 
| 
838
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
839
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The longitude and latitude of the place for which you want to compute the sunrise and sunset.  | 
| 
840
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 They are given in decimal degrees. For example:  | 
| 
841
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
842
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     lon => -3.6,  #  3° 36' W  | 
| 
843
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     lat => 37.17, # 37° 10' N  | 
| 
844
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
845
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Eastern longitude is entered as a positive number  | 
| 
846
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Western longitude is entered as a negative number  | 
| 
847
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Northern latitude is entered as a positive number  | 
| 
848
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Southern latitude is entered as a negative number  | 
| 
849
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
850
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Mandatory, can be positional (#4 and #5).  | 
| 
851
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
852
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item tz  | 
| 
853
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
854
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Time Zone is the offset from GMT  | 
| 
855
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
856
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Mandatory, can be positional (#6).  | 
| 
857
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
858
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item isdst  | 
| 
859
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
860
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 1 if daylight saving time is in effect, 0 if not.  | 
| 
861
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
862
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Mandatory, can be positional (#7).  | 
| 
863
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
864
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item alt  | 
| 
865
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
866
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Altitude of the sun, in decimal degrees. Usually a negative number,  | 
| 
867
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 because the sun should be I<under> the mathematical horizon.  | 
| 
868
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 But if there is a high mountain range sunward (that is, southward if you  | 
| 
869
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 live in the Northern hemisphere), you may need to enter a positive altitude.  | 
| 
870
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
871
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional. Its default value is -0.833. It can be positional (#8).  | 
| 
872
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
873
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item upper_limb  | 
| 
874
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
875
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 If this parameter set to a true value (usually 1), the algorithm computes  | 
| 
876
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the sun apparent radius and takes it into account when computing the sun  | 
| 
877
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 altitude. This parameter is useful only when the C<alt> parameter is set  | 
| 
878
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 to C<0> or C<-0.583> degrees. When using C<-0.25> or C<-0.833> degrees,  | 
| 
879
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the sun radius is already taken into account. When computing twilights  | 
| 
880
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 (C<-6> to C<-18>), the sun radius is irrelevant.  | 
| 
881
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
882
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Since the default value for the C<alt> parameter is -0.833, the  | 
| 
883
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 default value for C<upper_limb> is 0.  | 
| 
884
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
885
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
886
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
887
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item polar  | 
| 
888
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
889
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 When dealing with a polar location, there may be dates where there is  | 
| 
890
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 a polar night (sun never rises) or a polar day. The default behaviour of  | 
| 
891
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the module is to emit a warning in these cases ("Sun never rises!!"  | 
| 
892
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 or "Sun never sets!!"). But some programmers may find this inconvenient.  | 
| 
893
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 An alternate behaviour is to return special values reflecting the  | 
| 
894
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 situation.  | 
| 
895
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
896
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 So, if the C<polar> parameter is set to C<'warn'>, the module emits  | 
| 
897
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 a warning. If the C<polar> parameter is set to C<'retval'>, the  | 
| 
898
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 module emits no warning, but it returns either C<'day'> or C<'night'>.  | 
| 
899
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
900
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Example:  | 
| 
901
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
902
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   # Loosely based on Alex Gough's activities: scientist and Perl programmer, who spent a year  | 
| 
903
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   # in Halley Base in 2006. Let us suppose he arrived there on 15th January 2006.  | 
| 
904
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   my ($sunrise, $sunset) = sunrise( { year => 2006, month => 1, day => 15,  | 
| 
905
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                       lon => -26.65, lat => -75.58, # Halley Base: 75°35'S 26°39'W  | 
| 
906
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                       tz  => 3, polar => 'retval' } );  | 
| 
907
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   if ($sunrise eq 'day') {  | 
| 
908
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     say "Alex Gough saw the midnight sun the first day he arrived at Halley Base";  | 
| 
909
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
910
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   elsif ($sunrise eq 'night') {  | 
| 
911
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     say "It would be days, maybe weeks, before the sun would rise.";  | 
| 
912
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
913
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   else {  | 
| 
914
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     say "Alex saw his first antarctic sunset at $sunset";  | 
| 
915
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   }  | 
| 
916
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
917
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
918
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
919
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item trace  | 
| 
920
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
921
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter should either be a false value or a filehandle opened for output.  | 
| 
922
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 In the latter case, a few messages are printed to the filehandle, which allows  | 
| 
923
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the programmer to see step by step how the sunrise and the sunset are computed.  | 
| 
924
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
925
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Used for analysis and debugging purposes. You need to read the text  | 
| 
926
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 F<doc/astronomical-notes.pod> to understand what the traced values  | 
| 
927
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 represent.  | 
| 
928
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
929
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
930
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
931
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item precise  | 
| 
932
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
933
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Choice between a precise algorithm and a simpler algorithm.  | 
| 
934
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The default value is 0, that is, the simpler algorithm.  | 
| 
935
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Any true value switches to the precise algorithm.  | 
| 
936
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
937
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The original method only gives an approximate value of the Sun's rise/set times.  | 
| 
938
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The error rarely exceeds one or two minutes, but at high latitudes, when the Midnight Sun  | 
| 
939
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 soon will start or just has ended, the errors may be much larger. If you want higher accuracy,  | 
| 
940
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 you must then use the precise algorithm. This feature is new as of version 0.7. Here is  | 
| 
941
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 what I have tried to accomplish with this.  | 
| 
942
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
943
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 a) Compute sunrise or sunset as always, with one exception: to convert LHA from degrees to hours,  | 
| 
944
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    divide by 15.04107 instead of 15.0 (this accounts for the difference between the solar day  | 
| 
945
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    and the sidereal day).  | 
| 
946
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
947
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 b) Re-do the computation but compute the Sun's RA and Decl, and also GMST0, for the moment  | 
| 
948
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    of sunrise or sunset last computed.  | 
| 
949
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
950
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 c) Iterate b) until the computed sunrise or sunset no longer changes significantly.  | 
| 
951
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    Usually 2 iterations are enough, in rare cases 3 or 4 iterations may be needed.  | 
| 
952
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
953
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional. It can be positional (#9).  | 
| 
954
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
955
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
956
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
957
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head3 I<For Example>  | 
| 
958
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
959
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  ($sunrise, $sunset) = sunrise( 2001, 3, 10, 17.384, 98.625, -5, 0 );  | 
| 
960
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  ($sunrise, $sunset) = sunrise( 2002, 10, 14, -105.181, 41.324, -7, 1, -18);  | 
| 
961
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  ($sunrise, $sunset) = sunrise( 2002, 10, 14, -105.181, 41.324, -7, 1, -18, 1);  | 
| 
962
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
963
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 B<sun_rise>, B<sun_set>  | 
| 
964
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
965
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sun_rise = sun_rise( { lon => $longitude, lat => $latitude,  | 
| 
966
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                           alt => $altitude, upper_limb => $bool,  | 
| 
967
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                           offset  => $day_offset,  | 
| 
968
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                           precise => $bool_precise, polar => $action } );  | 
| 
969
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sun_set  = sun_set ( { lon => $longitude, lat => $latitude,  | 
| 
970
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                           alt => $altitude, upper_limb => $bool,  | 
| 
971
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                           offset  => $day_offset,  | 
| 
972
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                           precise => $bool_precise, polar => $action } );  | 
| 
973
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sun_rise = sun_rise( $longitude, $latitude );  | 
| 
974
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sun_rise = sun_rise( $longitude, $latitude, $alt );  | 
| 
975
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   $sun_rise = sun_rise( $longitude, $latitude, $alt, $day_offset );  | 
| 
976
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
977
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the sun rise time (resp. the sun set time) for the given location  | 
| 
978
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and for today's date (as given by DateTime), plus or minus some offset in days.  | 
| 
979
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The first form use all parameters and transmit them by name. The second form  | 
| 
980
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 uses today's date (from DateTime) and the default altitude.  The third  | 
| 
981
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 form adds specifying a custom altitude.  The fourth form allows for specifying  | 
| 
982
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 an integer day offset from today, either positive or negative.  | 
| 
983
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
984
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The parameters are the same as the parameters for C<sunrise>. There is an additional  | 
| 
985
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 parameter, C<offset>, which allows using a date other than today: C<+1> for  | 
| 
986
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 to-morrow, C<-7> for one week ago, etc.  | 
| 
987
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
988
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The arguments are:  | 
| 
989
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
990
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
991
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
992
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item lon, lat  | 
| 
993
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
994
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The longitude and latitude of the place for which you want to compute the sunrise and sunset.  | 
| 
995
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 They are given in decimal degrees. For example:  | 
| 
996
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
997
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     lon => -3.6,  #  3° 36' W  | 
| 
998
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     lat => 37.17, # 37° 10' N  | 
| 
999
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1000
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Eastern longitude is entered as a positive number  | 
| 
1001
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Western longitude is entered as a negative number  | 
| 
1002
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Northern latitude is entered as a positive number  | 
| 
1003
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  Southern latitude is entered as a negative number  | 
| 
1004
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1005
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Mandatory, can be positional (#1 and #2).  | 
| 
1006
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1007
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item alt  | 
| 
1008
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1009
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Altitude of the sun, in decimal degrees. Usually a negative number,  | 
| 
1010
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 because the sun should be I<under> the mathematical horizon.  | 
| 
1011
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 But if there is a high mountain range sunward (that is, southward if you  | 
| 
1012
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 live in the Northern hemisphere), you may need to enter a positive altitude.  | 
| 
1013
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1014
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional. Its default value is -0.833. It can be positional (#3).  | 
| 
1015
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1016
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item offset  | 
| 
1017
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1018
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 By default, C<sun_rise> and C<sun_set> use the current day. If you need another  | 
| 
1019
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 day, you give an offset relative to the current day. For example, C<+7> means  | 
| 
1020
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 next week, while C<-365> means last year.  | 
| 
1021
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1022
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter has nothing to do with timezones.  | 
| 
1023
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1024
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Optional, 0 by default, can be positional (#4).  | 
| 
1025
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1026
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item time_zone  | 
| 
1027
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1028
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Time Zone is the Olson name for a timezone. By default, the functions  | 
| 
1029
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 C<sun_rise> and C<sun_set> will try to use the C<local> timezone.  | 
| 
1030
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1031
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
1032
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1033
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item upper_limb  | 
| 
1034
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1035
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 If this parameter set to a true value (usually 1), the algorithm computes  | 
| 
1036
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the sun apparent radius and takes it into account when computing the sun  | 
| 
1037
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 altitude. This parameter is useful only when the C<alt> parameter is set  | 
| 
1038
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 to C<0> or C<-0.583> degrees. When using C<-0.25> or C<-0.833> degrees,  | 
| 
1039
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the sun radius is already taken into account. When computing twilights  | 
| 
1040
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 (C<-6> to C<-18>), the sun radius is irrelevant.  | 
| 
1041
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1042
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Since the default value for the C<alt> parameter is -0.833, the  | 
| 
1043
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 default value for C<upper_limb> is 0.  | 
| 
1044
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1045
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
1046
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1047
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item polar  | 
| 
1048
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1049
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 When dealing with a polar location, there may be dates where there is  | 
| 
1050
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 a polar night (sun never rises) or a polar day. The default behaviour of  | 
| 
1051
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the module is to emit a warning in these cases ("Sun never rises!!"  | 
| 
1052
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 or "Sun never sets!!"). But some programmers may find this inconvenient.  | 
| 
1053
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 An alternate behaviour is to return special values reflecting the  | 
| 
1054
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 situation.  | 
| 
1055
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1056
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 So, if the C<polar> parameter is set to C<'warn'>, the module emits  | 
| 
1057
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 a warning. If the C<polar> parameter is set to C<'retval'>, the  | 
| 
1058
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 module emits no warning, but it returns either C<'day'> or C<'night'>.  | 
| 
1059
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1060
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
1061
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1062
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item trace  | 
| 
1063
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1064
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter should either be a false value or a filehandle opened for output.  | 
| 
1065
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 In the latter case, a few messages are printed to the filehandle, which allows  | 
| 
1066
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the programmer to see step by step how the sunrise and the sunset are computed.  | 
| 
1067
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1068
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Used for analysis and debugging purposes.  | 
| 
1069
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1070
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
1071
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1072
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item precise  | 
| 
1073
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1074
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Choice between a precise algorithm and a simpler algorithm.  | 
| 
1075
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The default value is 0, that is, the simpler algorithm.  | 
| 
1076
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Any true value switches to the precise algorithm.  | 
| 
1077
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1078
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 For more documentation, see the corresponding parameter  | 
| 
1079
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for the C<sunrise> function.  | 
| 
1080
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1081
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This parameter is optional and it can be specified only by keyword.  | 
| 
1082
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1083
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
1084
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1085
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head3 For Example  | 
| 
1086
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1087
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $sunrise = sun_rise( -105.181, 41.324 );  | 
| 
1088
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $sunrise = sun_rise( -105.181, 41.324, -15 );  | 
| 
1089
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $sunrise = sun_rise( -105.181, 41.324, -12, +3 );  | 
| 
1090
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $sunrise = sun_rise( -105.181, 41.324, undef, -12);  | 
| 
1091
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1092
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 Trigonometric functions using degrees  | 
| 
1093
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1094
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Since the module use trigonometry with degrees, the corresponding functions  | 
| 
1095
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 are available to the module user, free of charge. Just mention the  | 
| 
1096
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 tag C<:trig> in the C<use> statement. These functions are:  | 
| 
1097
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1098
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
1099
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1100
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item sind, cosd, tand  | 
| 
1101
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1102
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The direct functions, that is, sine, cosine and tangent functions, respectively.  | 
| 
1103
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Each one receives one parameter, in degrees, and returns the trigonometric value.  | 
| 
1104
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1105
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item asind, acosd, atand  | 
| 
1106
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1107
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The reverse functions, that is, arc-sine, arc-cosine, and arc-tangent.  | 
| 
1108
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Each one receives one parameter, the trigonometric value, and returns the corresponding  | 
| 
1109
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 angle in degrees.  | 
| 
1110
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1111
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item atan2d  | 
| 
1112
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1113
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Arc-tangent. This function receives two parameters: the numerator and the denominator  | 
| 
1114
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 of a fraction equal to the tangent. Use this function instead of C<atand> when you  | 
| 
1115
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 are not sure the denominator is not zero. E.g.:  | 
| 
1116
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1117
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   use Astro::Sunrise qw(:trig);  | 
| 
1118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   say atan2d(1, 2) # prints 26,5  | 
| 
1119
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   say atan2d(1, 0) # prints 90, without triggering a "division by zero" error  | 
| 
1120
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1121
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item equal  | 
| 
1122
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1123
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Not really a trigonometrical function, but still useful at some times. This function  | 
| 
1124
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 receives two floating values and an integer value. It compares the floating numbers,  | 
| 
1125
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and returns "1" if their most significant digits are equal. The integer value  | 
| 
1126
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 specifies how many digits are kept. E.g.  | 
| 
1127
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1128
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   say equal(22/7, 355/113, 3) # prints 1, because :  22/7   = 3.14285715286 rounded to 3.14  | 
| 
1129
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                               #                     355/113 = 3.14159292035 rounded to 3.14  | 
| 
1130
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
   say equal(22/7, 355/113, 4) # prints 0, because :  22/7   = 3.14285715286 rounded to 3.143  | 
| 
1131
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                               #                     355/113 = 3.14159292035 rounded to 3.142  | 
| 
1132
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1133
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
1134
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1135
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 EXPORTS  | 
| 
1136
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1137
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 By default, the functions C<sunrise>, C<sun_rise> and C<sun_set> are exported.  | 
| 
1138
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1139
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The constants C<DEFAULT>, C<CIVIL>, C<NAUTICAL>, C<AMATEUR> and C<ASTRONOMICAL> are  | 
| 
1140
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 exported on request with the tag C<:constants>.  | 
| 
1141
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1142
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The functions C<sind>, C<cosd>, C<tand>, C<asind>, C<acosd>, C<atand>, C<atan2d> and C<equal>  | 
| 
1143
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 exported on request with the tag C<:trig>.  | 
| 
1144
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1145
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 DEPENDENCIES  | 
| 
1146
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1147
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This module requires only core modules: L<POSIX>, L<Math::Trig> and L<Carp>.  | 
| 
1148
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1149
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 If you use the C<sun_rise> and C<sun_set> functions, you will need also L<DateTime>.  | 
| 
1150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1151
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 BUGS AND ISSUES  | 
| 
1152
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1153
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Before reporting a bug, please read the text  | 
| 
1154
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 F<doc/astronomical-notes.pod> because the strange behavior you observed  | 
| 
1155
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 may be a correct one, or it may be a corner case already known and  | 
| 
1156
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 already mentioned in the text.  | 
| 
1157
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1158
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Nevertheless, patches and (justified) bug reports are welcome.  | 
| 
1159
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1160
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 See L<https://github.com/jforget/Astro-Sunrise/issues>  | 
| 
1161
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and L<https://github.com/jforget/Astro-Sunrise/pulls>.  | 
| 
1162
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1163
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 Precise Algorithm  | 
| 
1164
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1165
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The explanations for  the precise algorithm give a  pretty good reason  | 
| 
1166
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for  using  an   angular  speed  of  15.04107  instead   of  15.  Yet,  | 
| 
1167
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 computations with 15.04107 do not  give results conforming to what the  | 
| 
1168
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 NOAA  website and  Stellarium give,  while computations  with 15  give  | 
| 
1169
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 conforming results. The implementation of the precise algorithm should  | 
| 
1170
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 be analysed and checked to find  the reason why 15.04107 does not give  | 
| 
1171
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the proper results.  | 
| 
1172
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1173
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 Kwalitee  | 
| 
1174
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1175
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The CPANTS tools do not recognize the LICENSE POD paragraph. But any  | 
| 
1176
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 human reader will admit that this LICENSE paragraph exists and is valid.  | 
| 
1177
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1178
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 Haiku-OS CPAN Tester  | 
| 
1179
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1180
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The built-in test F<t/06datetime.t> fails on Haiku-OS because there is  | 
| 
1181
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 no way to  extract the timezone name from the  system parameters. This  | 
| 
1182
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 failure does not affect the core functions of L<Astro::Sunrise>.  | 
| 
1183
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1184
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Also reported from a user working on a partially configured FreeBSD machine, see  | 
| 
1185
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 L<https://github.com/jforget/Astro-Sunrise/issues/16>.  | 
| 
1186
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1187
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Hopefully, this will be fixed in the current version.  | 
| 
1188
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1189
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 AUTHOR  | 
| 
1190
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1191
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Ron Hill  | 
| 
1192
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 rkhill@firstlight.net  | 
| 
1193
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1194
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Co-maintainer: Jean Forget (JFORGET at cpan dot org)  | 
| 
1195
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1196
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 SPECIAL THANKS  | 
| 
1197
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1198
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Robert Creager [Astro-Sunrise@LogicalChaos.org]  | 
| 
1199
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for providing help with converting Paul's C code to Perl,  | 
| 
1200
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for providing code for sun_rise, sun_set subs.  | 
| 
1201
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Also adding options for different altitudes.  | 
| 
1202
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1203
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Joshua Hoblitt [jhoblitt@ifa.hawaii.edu]  | 
| 
1204
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for providing the patch to convert to DateTime.  | 
| 
1205
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1206
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Chris Phillips for providing patch for conversion to  | 
| 
1207
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 local time.  | 
| 
1208
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1209
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Brian D Foy for providing patch for constants :)  | 
| 
1210
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1211
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Gabor Szabo for pointing POD mistakes.  | 
| 
1212
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1213
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 People at L<https://geocoder.opencagedata.com/> for noticing an endless  | 
| 
1214
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 loop condition and for fixing it.  | 
| 
1215
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1216
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 CREDITS  | 
| 
1217
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1218
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
1219
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1220
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item  Paul Schlyter, Stockholm, Sweden  | 
| 
1221
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1222
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for his excellent web page on the subject.  | 
| 
1223
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1224
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item Rich Bowen (rbowen@rbowen.com)  | 
| 
1225
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1226
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for suggestions.  | 
| 
1227
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1228
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item Adrian Blockley [adrian.blockley@environ.wa.gov.au]  | 
| 
1229
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1230
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for finding a bug in the conversion to local time.  | 
| 
1231
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1232
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item Slaven Rezić  | 
| 
1233
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1234
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 for finding and fixing a bug with DST.  | 
| 
1235
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1236
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
1237
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1238
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Lightly verified against L<http://aa.usno.navy.mil/data/docs/RS_OneYear.html>  | 
| 
1239
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1240
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 In addition, checked to be compatible with a C implementation of Paul Schlyter's algorithm.  | 
| 
1241
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1242
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 COPYRIGHT and LICENSE  | 
| 
1243
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1244
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 Perl Module  | 
| 
1245
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1246
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Copyright (C)  1999-2003, 2013,  2015, 2017, 2019,  2021 Ron  Hill and  | 
| 
1247
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Jean Forget,  all rights reserved.  This program is  distributed under  | 
| 
1248
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the same terms  as Perl 5.16.3: GNU Public License  version 1 or later  | 
| 
1249
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and Perl Artistic License  | 
| 
1250
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1251
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 You can find the text of the licenses in the F<LICENSE> file or at  | 
| 
1252
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 L<https://dev.perl.org/licenses/artistic.html>  | 
| 
1253
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and L<https://www.gnu.org/licenses/gpl-1.0.html>.  | 
| 
1254
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1255
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Here is the summary of GPL:  | 
| 
1256
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1257
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This program is free software; you can redistribute it and/or modify  | 
| 
1258
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 it under the terms of the GNU General Public License as published by  | 
| 
1259
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the Free Software Foundation; either version 1, or (at your option)  | 
| 
1260
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 any later version.  | 
| 
1261
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1262
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This program is distributed in the hope that it will be useful,  | 
| 
1263
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 but WITHOUT ANY WARRANTY; without even the implied warranty of  | 
| 
1264
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the  | 
| 
1265
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 GNU General Public License for more details.  | 
| 
1266
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1267
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 You should have received a copy of the GNU General Public License  | 
| 
1268
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 along with this program; if not, write to the Free Software Foundation,  | 
| 
1269
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Inc., L<https://www.fsf.org/>.  | 
| 
1270
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1271
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 Original C program  | 
| 
1272
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1273
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Here is the copyright information provided by Paul Schlyter:  | 
| 
1274
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1275
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Written as DAYLEN.C, 1989-08-16  | 
| 
1276
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1277
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Modified to SUNRISET.C, 1992-12-01  | 
| 
1278
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1279
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 (c) Paul Schlyter, 1989, 1992  | 
| 
1280
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1281
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Released to the public domain by Paul Schlyter, December 1992  | 
| 
1282
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1283
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Permission is hereby granted, free of charge, to any person obtaining a  | 
| 
1284
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 copy of this software and associated documentation files (the "Software"),  | 
| 
1285
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 to deal in the Software without restriction, including without limitation  | 
| 
1286
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the rights to use, copy, modify, merge, publish, distribute, sublicense,  | 
| 
1287
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and/or sell copies of the Software, and to permit persons to whom the  | 
| 
1288
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Software is furnished to do so, subject to the following conditions:  | 
| 
1289
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1290
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The above copyright notice and this permission notice shall be included  | 
| 
1291
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 in all copies or substantial portions of the Software.  | 
| 
1292
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1293
 | 
 
 | 
 
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 | 
 
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 | 
 
 | 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR  | 
| 
1294
 | 
 
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 | 
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,  | 
| 
1295
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL  | 
| 
1296
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 THE AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,  | 
| 
1297
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT  | 
| 
1298
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN  | 
| 
1299
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 THE SOFTWARE.  | 
| 
1300
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
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    | 
| 
1301
 | 
 
 | 
 
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 =head1 SEE ALSO  | 
| 
1302
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    | 
| 
1303
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 perl(1).  | 
| 
1304
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    | 
| 
1305
 | 
 
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 | 
 L<DateTime::Event::Sunrise>  | 
| 
1306
 | 
 
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 | 
 
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    | 
| 
1307
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 L<DateTime::Event::Jewish::Sunrise>  | 
| 
1308
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1309
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 The text F<doc/astronomical-notes.pod> (or its original French version  | 
| 
1310
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 F<doc/notes-astronomiques>) in this distribution.  | 
| 
1311
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
1312
 | 
 
 | 
 
 | 
 
 | 
 
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 L<https://stjarnhimlen.se/comp/riset.html>  | 
| 
1313
 | 
 
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    | 
| 
1314
 | 
 
 | 
 
 | 
 
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 | 
 =cut  |