Without getting into testing, it look very much as if you could simply move the body of the second while loop into the body of the if statement in the first; skip the holder file stuff and rename @firstline* to @mag to match the usage in the first loop.

* Bad name. It's an array not a line and it it used by every line, not just the first??

Untested (no data), but something along these lines should do it.

#!/usr/bin/perl -w
print "What is input file name?: ";
    chomp($input = <STDIN>);
print "What is output file name: ";
    chomp($output = <STDIN>);
print "What is the mininum magnitude?:";
    chomp($min_mag = <STDIN>);
print "What is maximum magnitude?:";
    chomp($max_mag = <STDIN>);

#opening up ngc188cata and putting it into INPUT#
open (INPUT, "$input") || die "died opening input\n";

#opening up ngc188cat2 and setting output of out#
open (STDOUT, ">$output") || die "died opening output\n";

$cfo = "O";
$status = "STATUS=OK";

while ($inline = <INPUT>) {
    #INPUT defined as variable#
    #firstline of array defined by split of white space into variable 
+inline
    @mag = split(/\s+/, $inline); 

    if ($mag[12] >= $min_mag  && $mag[12] <= $max_mag) {
        $hms1 = $mag[2];
        $rah2 = ($hms1 / 15);
        $rah3 = int($rah2);

        $ram1 = ( abs($rah2 - $rah3) )* 60;
        $ram2 = int($ram1);

        $ras1 = abs($ram1 - $ram2) * 60;
        $ras2 = sprintf "%-02.3f", $ras1;

        $hms2 = $mag[3];
        $hh2 = sprintf "%1d", ($hms2);
        $mm2 = sprintf "%02d", (60*( abs($hms2) - abs($hh2) ) );
        $ss2 = sprintf "%-02.2f", 
                 3600*abs($hms2) - 3600*abs($hh2) - 60*abs($mm2);

        $obid = "NGC 188 - $mag[1]";   
        write; #writing to STDOUT
    }
}

close INPUT;
close NEW;


format STDOUT =
@>>> @<<<<<<<<<<<<<<<<<<< @> @> @>>>>>  @< @< @>>>> @  @<<<<<<<<     
$mag[1], $obid, $rah3, $ram2, $ras2, $hh2, $mm2, $ss2, $cfo, $status, 
.
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Use @ARGV, and get the file names, and min/max values as well, from the command line, instead of forcing the user into a dialog with printed prompts and keyboard input via STDIN. You can look at the Getopt::Long and Getopt::Std modules to see how most people do this sort of thing, or you can easily "roll your own" -- something like this:

my $Usage = "Usage: $0 --min MIN --max MAX --in INFILE --out OUTFILE\n
+";

my %args;
while ( @ARGV >= 2 ) {
   if ( $ARGV[0] =~ /^--(min|max|in|out)$/ ) {
      my $opt = substr( shift, 2 );
      $args{$opt} = shift;
   } else {
      last;
   }
}
die $Usage if ( @ARGV or ( keys %args != 4 ));
# all 4 args are mandatory, and only these 4 args are allowed

# now use $args{in} instead of $input, etc...
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There are several reasons for using command-line args in @ARGV instead of a runtime dialog with the user:

• Most command line shells provide a "command history" feature that lets you recall, modify and re-execute prior commands; your program will be a lot easier and quicker to use if it gets everything it needs from the command line.
• Most shells provide pretty good line-editing functions (moving back and forth on the line before executing the command, deleting / cutting / pasting characters or words, etc) whereas the handling of STDIN within a perl script may provide very limited editing abilities (unless you learn about and use a suitable Term module).
• On the command line, you can alter/correct any arg at any time before starting execution; but if you're typing in single answers to questions at runtime and notice a mistake after entering any one of the answers, you just have to quit and start over (very frustrating).
• If the program gets everything it needs from the command line, you can "automate" it -- i.e. run it from some other script; but if you have to carry on a dialog after it starts, running it via some other script becomes a fairly complicated and tricky business.
• (update -- forgot to mention:) Many shells provide "file name completion" on the command line, whereby you simply type the first few characters of a name, hit the tab key or something, and the rest of the file name is filled in for you (or you get a list of files that match what you've typed so far); again, you would only get this feature within a perl script if you learned and used one of the Term modules (which I haven't done yet, because @ARGV handles pretty much everything I ever need).

Note that the ordering of arg flags is flexible: "--min 0" can come before or after "--max 10", and likewise for the file name args; all that matters is that each value comes immediately after its flag.

    chomp($input = <STDIN>);
...
    chomp($output = <STDIN>);
...
open (INPUT, "$input") || die "died opening input\n";#opening up ngc18
+8cata and putting it into INPUT#

open (STDOUT, ">$output") || die "died opening output\n"; #opening up 
+ngc188cat2 and setting output of out#
[download]

  open(INPUT, "<", $input) or die ...
  open(OUTPUT, ">", $output) or die ...
or
  open(INPUT, "< $input") or die ...
  open(OUTPUT, "> $output") or die ...
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