There must be some equations governing these phenomena and perhaps you can solve them to get the answer analytically rather than with iterating?

Astro::Coords - Class for handling astronomical coordinates 

#!/usr/bin/perl 

use strict;
use warnings;
use Time::Piece;
use Astro::Coords;

print qq/Planet\tRight Ascension\t\tDeclination\n/; 

for my $name (qw/Jupiter Saturn/) {

  my $planet = Astro::Coords->new(planet => $name);

  $planet->datetime(Time::Piece->new);

  my $ra  = $planet->ra(format => q/deg/); 
  my $dec = $planet->dec(format => q/deg/); 

  print qq/$name\t$ra\t$dec\n/
}

[download]
Output: 
Planet	Right Ascension		Declination
Jupiter	300.231916167496	-21.0148733591416
Saturn	301.371438440471	-20.6884105467964
One-liner: 
perl -MAstro::Coords -MTime::Piece -Mstrict -e 'print qq/Planet\tRight
+ Ascension\t\tDeclination\n/; for my $name (qw/Jupiter Saturn/) { my 
+$planet = Astro::Coords->new(planet => $name); $planet->datetime(Time
+::Piece->new); my $ra = $planet->ra(format => q/deg/); my $dec = $pla
+net->dec(format => q/deg/); print qq/$name\t$ra\t$dec\n/}'

[download]

In reply to Re^2: calculating planet conjunction with mojo front end by Anonymous Monk
in thread calculating planet conjunction with mojo front end by Aldebaran

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.