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Jumping on the Moon
Name: Michael S.
Status: Educator
Age: 30s
Location: N/A
Country: N/A
Date: February 2004
Question:
Why does Sting's song say "I hope my legs do not break, walking on the moon"? I heard that
there was concern about jumping 20 feet high and breaking your legs on landing due to the fact that
momentum and inertia are a function of mass. Even though on the moon you weigh 1/6, your mass is the
same and you would pick up speed and momentum on the way down and get hurt. Is this true?
Replies:
Michael,
The same equations that Homer Hickam used in the movie "October Sky" where he described the basic
equations of position (s), velocity (v) and acceleration (a) and how the act of differentiating and
integration allow for the transformation of one form of the equation to another.
s = So + Vo* t + 0.5 * a* (t^2)
d/dt (differentiate w/ respect to time)
v = 0 + Vo + ( 1 * a * t )
d/dt (differentiate w/ respect to time)
a = 0 + 0 + a
These equations hold nearly perfectly with the Moon's lack of atmosphere.
Now let me answer your question.
Since your legs are considerably "stronger" given the weaker gravitational pull of the Moon, it is
conceivable that you could squat with both legs, jump as hard and high as you could and reach 40-50
feet high or higher. You are guaranteed to land on your feet, carrying with you all of the momentum
of yourself and space suit) generated from the top of your flight through the entire decent. Now, I
have never been on the Moon but something tells me that you might blow out a femur or two.
-Darin Wagner
I do not know Sting's song, but I do know conservation of energy. That says that if you jump
up leaving the surface of the earth or moon at a certain speed, you will return to the surface
with exactly the same speed. Therefore if you jump 3 feet high on the earth, with the same
effort (so you leave the surface with the same speed) you will jump 18 feet high on the moon,
but you will return to the surface with the same speed.
So the chance of breaking a leg is the same on the moon as on the earth. Except that you are
in flight six times longer. This has advantages and disadvantages, but the main difference,
I would think, is that if you give yourself some angular speed when you push off, you will
rotate six times as much on the moon and so have a rather larger chance of landing on your
head.
So I guess you would be more likely to break your head when jumping on the moon, but no more
likely to break your legs.
Best, Dick Plano...
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