Instead of drawing $red and then drawing $green, you need to find out which of the two is in the back, and draw that one first.

For example, do it like this:

# Define the two planets
my @large= ($red,   200,200,50,50 );
my @small= ($green, $xc, $yc, 25, 25 );

my( $front, $back );

if( $red_is_in_front_of_green ) {
    $front= \@large;
    $back= \@small;
} else {
    $front= \@small;
    $back= \@large;
};

# Just in case we ever go beyond two objects
my @objects_to_draw= ($back, $front);

for my $item (@objects_to_draw) {
    my( $color, @position )= @$item;
    $ima->filledEllipse( @position, $color );
};
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