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Comment by gnode | Hacker News Reader

> If you shoot a gun on the moon, will it return to your location from the behind, no matter what angle you shoot it?

In most cases no. Although the orbit of the bullet is cyclical (below escape velocity), unless you shoot perfectly level with the surface, its orbit will intersect the moon. Obviously if you shoot slightly down, it'll hit the ground. If you shoot slightly up, it'll hit the ground behind you on its return.

> Is this the velocity required for a bullet to leave orbit no matter what angle you shoot it?

Yes. Although if it hits the moon first, it'll slow down and not escape (unless you were to shoot through the moon).

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- Ah, I see. Does there always exist a velocity `v(theta)` that will make the bullet hit you in the back after one orbit? A slightly different question, but if you shoot a bullet perpendicular to the moon's surface at any speed (as long as it won't hit the ground), it will always hit you in the back after one orbit, right?

- I suppose if you think about it in terms of kinetic energy, this makes sense.

I realize that I made an assumption in my first answer, that the moon is not rotating. A rotation may cause you to move out of the orbital path of the bullet before it gets back to you. If you shot from the poles though, you would remain in the bullet's orbit.

That said, in ideal conditions, even with rotation, the bullet will hit you eventually, but not for a long time on average, given the scale of the moon. In reality it's orbit would probably destabilise due to collisions with dust and perturbations from other gravitational bodies (the Earth, Sun, etc. create an n-body situation which slowly changes the orbit over time).

> Does there always exist a velocity `v(theta)` that will make the bullet hit you in the back after one orbit?

The velocity must be great enough to stay above the surface, and not high enough to escape. Additionally, you must shoot horizontally, like I mentioned before, and not rotate out of the orbit (e.g. by being at the poles, or at the rotational equator, shooting along the equator).

Edit: I was wrong, never mind.

Bullets are sealed. They don't use the atmosphere as an oxidizer. Doesn't mean they fire well in a vacuum, because there are other factors involved. But you could certainly design a firing system to work perfectly fine in a vacuum.

They are capable of being fired underwater.

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