shooting yourself down - more physics?

Smitty Two asked:

If you guys aren't tired of arithmetic, I'm wondering if any fighter
pilots have shot themselves down. Probably not, but imagine you're
flying straight and level at 1000 mph and fire a 500 mph projectile at
an enemy that's directly ahead but at a higher altitude. You miss him;
the bullet follows a parabolic path, returning to your altitude just as
you overtake it. Discounting air friction, at what angle was the bullet
fired?

Before you find yourself in the same trap as me, let me ask for some
clarification:

1. Since you stipulate a vacuum, are we flying above the Earth?
2. How high?
3. Are we flying at an absolute altitude, e.g. following an orbital path?
4. Is the plane flying level at the moment of firing with only the gun
pointed up at the target airplane?

Rich "Without a clue" S.