Thanks, hippo, I knew I got it backwards 60 seconds after I posted. With your help, my script for determining when jupiter and venus conjoin is shaping up:

#! /usr/bin/perl
use warnings;
use strict;
use 5.010;
use WWW::Mechanize::GZip;
use HTML::TableExtract qw(tree);
use open ':std', OUT => ':utf8';
use Prompt::Timeout;
use constant TIMEOUT => 3;
use constant MAXTRIES => 8;

my $site = 'http://www.fourmilab.ch/yoursky/cities.html';
my $mech = 'WWW::Mechanize::GZip'->new;
$mech->get($site);
$mech->follow_link( text => 'Portland OR' );
my $lub = 2457204.63659;    #least upper bound
my $glb = 2457207.63659;    #greatest lower bound
$mech->set_fields(qw'date 2');
my $guess = median( $lub, $glb );
say "guess is $guess";
$mech->set_fields( jd => $guess );
$mech->click_button( value => "Update" );
my $te = 'HTML::TableExtract'->new;
$te->parse( $mech->content );
my $table      = ( $te->tables )[3];
my $table_tree = $table->tree;
my $venus      = $table_tree->cell( 4, 1 )->as_text;
say "say venus is *$venus*";
my $jupiter = $table_tree->cell( 7, 1 )->as_text;
$te->delete;
say "say jupiter is *$jupiter*";
my $vstr = string_to_second($venus);
my $jstr = string_to_second($jupiter);
say "vstr is $vstr";
say "jstr is $jstr";
my $upper = $lub;
my $lower = $glb;
my $equal;
my $equal_sec;
my $now_string = localtime;
my $filename   = 'planet1.txt';
open( my $jh, '>>', $filename ) or warn "Could not open file '$filenam
+e' $!";
say $jh " venus jupiter jd  $now_string";
my $attempts = 1;

while ( ( abs( $jstr - $vstr ) gt 0 ) ) {

  #wait 5 secs
  my $default = (($attempts ge MAXTRIES)) ? 'N' : 'Y';
  my $answer = prompt( "Make query number $attempts?", $default, TIMEO
+UT );
  exit if $answer =~ /^N/i;

  $guess = median( $upper, $lower );
  say "guess is $guess";
  $mech->set_fields( jd => $guess );
  $mech->click_button( value => "Update" );
  #say $mech->dump_forms;
  $te = 'HTML::TableExtract'->new;
  $te->parse( $mech->content );
  $table      = ( $te->tables )[3];
  $table_tree = $table->tree;
  $venus      = $table_tree->cell( 4, 1 )->as_text;
  say "say venus is *$venus*";
  $jupiter = $table_tree->cell( 7, 1 )->as_text;
  say "say jupiter is *$jupiter*";
  $vstr = string_to_second($venus);
  say "vstr is $vstr";
  $jstr = string_to_second($jupiter);
  say "jstr is $jstr";
  say $jh " $vstr $jstr $guess ";

  if ( $jstr gt $vstr ) {
    $upper = $guess;
  }
  elsif ( $vstr gt $jstr ) {
    $lower = $guess;
  }
  else {
    $equal = $guess;
    say "equal, while condition should fail $equal";
    $equal_sec = $vstr;

  }
  $te->delete;
  $attempts++;
}

my $equal_ra = second_to_string($equal_sec);
say "equal_ra is $equal_ra";
say $jh "equal seconds is $equal_sec and equal ra is $equal_ra";

sub median {
  my ( $upper, $lower ) = @_;
  my $return = ( $upper + $lower ) / 2.0;
  return $return;
}

sub string_to_second {
  my $string = shift;
  my $return = 9000;
  if ( my $success = $string =~ /^(\d*)h\s+(\d*)m\s+(\d*)s$/ ) {

    #say "success is $success";
    say " $1 $2 $3";
    $return = 3600 * $1 + 60 * $2 + $3;
  }
  else {
    say "string was misformed";
  }
  return $return;
}

sub second_to_string {
  my $seconds = shift;
  say "seconds are $seconds";
  my $hours = int( $seconds / 3600 );
  say "hours are $hours";
  my $remainder = $seconds % 3600;
  say "remainder is $remainder";
  my $minutes = int( $remainder / 60 );
  say "minutes are $minutes";
  my $sec = $remainder % 60;

  my $return = join( '', $hours, 'h ', $minutes, 'm ', $sec, 's' );
  return $return;
}
[download]

Output to planet1.txt:

 venus jupiter jd  Sat Jun 20 17:16:37 2015
 34790 34686 2457206.13659 
 34682 34653 2457205.38659 
 34628 34636 2457205.01159 
 34655 34644 2457205.19909 
 34641 34640 2457205.10534 
 34634 34638 2457205.058465 
 34638 34639 2457205.0819025 
 34640 34640 2457205.09362125 
equal seconds is 34640 and equal ra is 9h 37m 20s
[download]

Always fishing for criticism on form and style.