There’s a question about the moon’s gravity that I’ve had for some time now: Given that the moon’s gravity is only a small percentage of the Earth’s, if I were to jump off a cliff on the moon, would I get hurt? My guess is that the landing would be slightly rough, but not enough to hurt me. Any ideas?
It all depends on how high the cliff is.
Since gravity on the moon’s surface is about 1/6th of that on Earth, at the bottom of a 60 foot cliff on the moon you’d be going as fast as you would if you jumped off a 10 foot cliff on the Earth. (Maybe a little faster on the moon, because there is no air to slow you down)
Of course, if you jump off a small cliff on the moon, stumble upon landing and tear a hole in spacesuit, you’re pretty much doomed.
Now, would this be after all your friends jumped off a cliff on the moon?
Interestingly enough, falling off of a cliff on the moon can be more dangerous than on the Earth. This is because the moon has no atmosphere to slow your fall, and thus you have no terminal velocity. Still, for small cliffs you probably be better off on the moon (assuming your space suit doesn’t rip, which it probably would).
I don’t know about you, but I’d certainly want some Guinea P… ahem I mean “friends” to go first.
It’s pretty simple physics
time of fall = √(height/gravity)
velocity at landing = time of fall * gravity
energy of impact = mass* velocity[sup]2[/sup]/2
The gravitational field at the surface of the Earth is about 9.8 m/sec[sup]2[/sup]
The gravitational field on the surface of the Moon is about 1.6 m/sec[sup]2[/sup]
Work in metric units (meters, kg, seconds, joules) and you’ll have no problem.
Strictly speaking, this isn’t entirely true. You can’t ever freefall faster than the escape velocity of the body you are falling towards. Of course, with the Moon’s 2.37 km/s escape velocity, that would still make for a mighty painful impact.
QED:
Please explain your confusing remark.
If a body is accelerating towards another body; with no other external forces acting on it, it will increase in velocity until it hits the body. If the earth had no atmosphere and I jumped from a ladder 10 miles high, I’m going to be speeding up all the way to the ground.
Are you trying to describe some other phenomenon, like jumping out of a spaceship half-way to the moon?
Sorry but you got mixed up. The fact that the velocity will not exceed escape velocity does not mean it will not keep increasing until you hit the surface. there is no terminal velocity which is a velocity which does not increase any more. Think about it.
If you’re falling fast enough or far enough for air resistance to make a difference, I’d think you’d be dead anyway.
Sailor, Q.E.D. is entirely correct, assuming that the falling object starts off at rest with respect to the Moon.
BwanaBob, the Moon’s escape velocity is the initial velocity an object would have to have to rise to an infinite distance from the Moon before falling back again. In practical terms, such an object is said to have “escaped” the Moon’s gravitational pull. An object initially at rest with respect to the Moon, then, cannot reach a greater speed than the escape velocity as it falls toward the Moon, since no object can be farther than an infinite distance away.
[sub]God, I miss teaching physics! :([/sub]
robby/Q.E.D:
Well, yeah, but that’s not the same thing as terminal velocity. What Donut was saying is that, while falling, you will never come to a point where you stop accelerating (until, of course, you hit the ground), which is what the definition of terminal velocity is.
If you shoot yourself straight downward from a cannon at 2.37 km/s into a deep hole on the moon, you’ll still accelerate. If you shoot yourself from a cannon on Earth at terminal velocity into the Grand Canyon, you won’t accelerate.
I strongly side with BwanaBob’s questioning of Q.E.D.'s point. The latter is really not at all relevant.
Escape velocity is only a terminal velocity in the sense that it is the fastest one can go* when you go splat on the Moon’s surface. Terminal in this meaning is completely different from it’s meaning on Earth.
In the Earth’s atmosphere, if you start off going faster than terminal velocity, you will slow down until you reach it. Not so on the moon. Also, terminal velocity varies based on mass and aerodynamic shapes. A feather has a low one, a bullet a high one. It also varies based on height due to the air being less dense higher up. And then there’s this …
Since the Moon, like the Earth is hollow with openings at the poles (big smirk), if you fall into the North pole hole on the Moon, you will continue to accelerate until you reach the center, far faster than the escape velocity at surface.
(It’s strange, but one can quite clearly hear the groan “Oh no, not another ‘falling thru the Earth’ thread!” over a Cat5 cable.)
*The issue of one going faster at start is quite significant. What if your lunar rocket pack does a 180 and you start hurtling toward the surface. You can turn it off, but you will still accelerate more. With an atmosphere, once you have the rocket pack turned off, you can hope to slow down some and hit the surface a tad more gently.
Nope, no sir. He is mistaken and, furthermore, whether the object starts out at rest or not is completely irrelevant.
Terminal velocity is the speed at which friction with the atmosphere causes and upward force equivalent to the force of gravity and therefore speed no longer increases but remains constant.
This does not happen in a body with no atmosphere and the speed is increasing until the body hits the body. There is no such thing as terminal velocity. The fact that the velocity does not exceed a certain number is irrelevant. That is not the definition of “terminal velocity”
You guys are correct. :smack:
I was overly focused on Q.E.D.'s statement that “You can’t ever freefall faster than the escape velocity of the body you are falling towards,” which is a true statement (assuming the freefalling object is initially at rest with respect to the body it is falling towards) that had never occurred to me before.
This indeed has nothing whatsoever to do with the concept of “terminal velocity.”
So what’s the answer? Would I get hurt? 
-Adam
In my country, moon cliffs jump off you.
The answer is yes, but getting hurt would involve jumping off a somewhat higher cliff than on Earth (ignoring the fact that merely tripping over a rock could damage your suit and kill you).
Per the equations I gave (and E = mgh, which I left out) “somewhat higher” is misleading. For the same energy, velocity, or momentum at impact, the lunar cliff would have to be (9.8/1.6) or ~6x as high., as zimaane correctly said in the first reply.
All you need to do is jump off Earth cliffs until you get hurt, and multiply by 6 to get your personal lunar threshold. Ready? Begin…
The reason I used ‘somewhat’ was to take into consideration all the variables other than gravity; chiefly lack of air resistance, but it would probably also be fair to consider inappropriate reflex timing, balance problems etc… as well.
Six times as high? So if I jumped off a 24-foot cliff I’d be fine? And assume that I’m wearing an untearable spacesuit. 