Believe this was featured in a paper that recently used trig to prove the Pythagorean theorem (previously thought to be a circular definition). I think some highschoolers cracked it as part of a mathematics challenge or something.

Gyrojet ammunition has entered the chat.

Major concern here for LEO engagements is that any shots that miss are a liability coming back to hit the gunner.

Basically once a bullet’s fired, a new orbit is defined for that bullet, a new elipse can be drawn. That now elipse is constrained by the position and direction of that bullet the moment it’s fired. Unfortunately that means that one bullet orbit later the bullet is going to be in the exact same position with the exact same velocity. The gunner had better hope that orbit phases are misaligned.

Shooting at targets in the retrograde direction might be safest, they’re more likely to dip into the edge of the atmosphere and start to lose a bit of velocity ensuring they never come back.

But actually, if you had no gravity acting to change the velocity vector, the bullet would continue in a straight line. If you shot at the horizon it would be like drawing a straight line tangent to a circle. The bullet’s not going to end up going in the shooters azimuthal direction, but it sure is going to gain altitude as the curvature of the body peels down way away from the straight line it’s flying,