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, 
.
[download]