Shoot yourself in the back of the head

[bubastis]

What are the physics involved with launching or firing a projectile with such force that it circumnavigates the globe and hits you in the back of the head? Thread inspired by Shaolin Soccer, where a guy kicks a football so hard it flies to the horizon, never seen again. Got me thinking if he put a bit more welly into it, could it hit him in the back of the head.

[Padeye]

If he was on the moon it might be relatively simple. On earth the atmosphere is a problem. The ball cannot have a stable orbit within the atmosphere so it cannot be circular. The best you could do it kick it at an upward trajectory so that it escaped the atmosphere and went into an eccentric orbit so that it came back and hit your head after reentry. You'd need a tough ball because you would have to with enough energy to go into this orbit plus additional energy to account for drag as it leaves the atmosphere. The velocity off your foot have to be much, much higher than has ever been accomplished in the atmosphere. Consider that parts started melting on the X-15 at a fraction of the speed you would need and that happened in the thin upper atmosphere.

[Strinka]

Originally Posted by bubastis

What are the physics involved with launching or firing a projectile with such force that it circumnavigates the globe and hits you in the back of the head? Thread inspired by Shaolin Soccer, where a guy kicks a football so hard it flies to the horizon, never seen again. Got me thinking if he put a bit more welly into it, could it hit him in the back of the head.

They'd be the same as any oribt. Unfortunately, I don't know what those are. But there is a complication that the Earth is not a perfect sphere. You'd have to shoot from the top of Everest to ensure that you don't hit anything else. And of course, the lower the orbit, the faster it has to be going to maintain it. I don't think we have anything that could propel something fast enough for it to maintain such a low orbit.

And, actually, I have no idea how much of that is true. So, more knowledgeable Dopers, refute away.

[RealityChuck]

The bullet would have to travel at orbital velocity. Anything slower, and it falls to the ground.

Jerome Bixby's OTHER famous story deals with this.

SPOILER:

"The Holes Around Mars" His most famous story is "It's a GOOD Life."

[Washoe]

Back when I was in high school I did the calculations necessary to determine whether or not you could shoot yourself in the back if you stood on the summit of the highest mountain on the Moon and fired an AR-15. IIRC, the result I got showed that it couldn’t be done—the bullet would go about three quarters of the way around the Moon before hitting the ground.