| MadSci Network: Astronomy |
If you have ever seen the vacuum tube experiment with a feather and a penny in a clear glass tube that is almost free of air, you would know the answer to this question: Your teacher is right, both objects will reach the surface of the moon at the same time. The same thing would happen on Earth, but the feather creates more drag than the hammer so the air resistance slows it down.
[The vacuum tube experiment is the analog of a classical (possibly apocryphal) experiment conducted by Galileo. He is said to have taken two (cannon?) balls to the top of the leaning tower of Pisa. The two balls weighed quite different amounts. When he dropped them over the side, they hit the ground at the same instant. The modern demonstration was conducted by astronaut David Scott on the surface of the Moon during the Apollo 15 mission. He dropped a feather and a hammer at the same time; they hit the lunar surface at the same time.
The reason both objects fall at the same rate is that the acceleration due to gravity is the same for all objects, regardless of their mass. Stated in another fashion, the gravitational force between the Earth and the hammer or the feather is
G M m
F = -----
r2
where M is the mass of the Earth, r is the distance
between the Earth and the object (in this case we can take it to be the radius
of the Earth), m is the mass of the object, either the hammer or
the feather, and G is a constant known as Newton's Universal
Gravitation constant. The acceleration produced by a force is
F
a = ---.
m
If we substitute the above expression for F into this expression
for the acceleration, we find that the acceleration is given by
G M
a = ----
r2
or that the acceleration due to gravity that an object feels is independent of
its mass. Moderator]
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