If you fell 200 Miles on the Moon, would you Die?

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I came up with this thought question and wondered the answer. What are your thoughts on this Idea? Will you be stone dead, or will you just be heavily injured?

that's an interesting question. gravity is less, so you'd fall with less force. however with no atmosphere there'd be no air resistance to slow you down. i think you would die.

Since moon gravity is 1/6 that of Earths, falling 200 miles (did you mean meters?) there is like falling 66.6 miles here, which would make you dead.

Without atmosphere it would be worse that on Earth beside the lower gravity.

Falling 200 miles on the moon would do a lot more than kill you, it would pulverise you. They would be scraping you from the debris of your spacesuit (forgive the imagery). When falling on Earth you reach terminal velocity (about 122 mph) after about 15 seconds, then you stop accelerating. On the moon there is no atmosphere and so no air resistance and nothing to slow you down. Acceleration due to gravity on the moon is about 1.63 m/s/s, and you would be falling 321869m (200 miles to the nearest metre)

If my math is correct (and it's very possible it's not, it's been a while) you would be falling, and constantly accelerating, for a bit under 10.5 minutes, and would hit the ground at a little over 1024 m/s, or over 2290 miles per hour. That is 0.636 of a mile per second. You would definitely be dead.

As a side note, if you were falling 200 miles onto the earth you probably wouldn't even make it to the ground. You would first suffocate as the atmosphere only starts around 65-75 miles above the earth, then as you enter the atmosphere you would burn up due to all the air resistance. I'm not sure but it would probably be enough to turn you into ash. 200 miles is a really long way to fall.

Newton's law of gravitation for the gravitational field at some point r from the center of mass of an object is:

g=(GM)/r^2

Where G is the gravitational constant and M is the mass of the object. As you move farther away from the center of mass of the object, g gets smaller, meaning the gravitational field gets weaker. As you move closer, g gets bigger, meaning the gravitational field gets stronger.

The point is, the "acceleration of gravity" is not actually a constant. In most "near Earth" scenarios we only treat it as such. The moon is small enough, and your distance of 200 miles is great enough, that the variability of the gravitational field shouldn't be ignored.

Before we continue, let's look at kinetic energy involved in impacts here on Earth if you were a 160lbs man jumping off of things.

A 1 meter (about 3 feet) box: 712.5984 Joules
6 feet: 1296.929088 Joules
20 feet: 4275.5904 Joules
100 feet: 21662.99136 Joules

Now back to the moon.

I've used Excel to approximate the velocity you would have right before impact. It's somewhere around 939m/s, which is somewhere between the velocity when calculated using the gravitational field 200 miles out, and the gravitational field at the surface.

You would have a kinetic energy of 3.2X10^7 joules
That's 32,000,000 joules.

That's like falling from 27.8 miles here on Earth with no wind resistance to slow you down....if I've not made any mistakes.

If you had zero velocity w.r.t. the moon then, as others have shown, you'd be very dead. But, since you didn't specify an initial velocity you could have escape velocity where you'd never hit the moon.

Or, you could have a velocity vector that is close to tangent to the moon's surface and less than escape velocity but great enough to put you into an orbit (that doesn't intersect the surface).

And, actually, that's how Newton figured out the math that's involved with orbits. He imagined a cannon shooting a cannonball parallel to the Earth's surface further and further out. The further the cannonballs went the more the surface of the Earth curved away from them. Newton realized that eventually a cannonball would "fall" all the way around the Earth without ever touching the surface.

And the thing about the math (2nd order differential equation) is that you have to specify 2 things in order to have a solution -- the initial position and initial velocity.

You'd be very dead on impact or become a tiny (dead) satellite orbiting the moon.
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