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Since the gravitational attraction between two objects varies with their mass at given distance per the Universal Gravitational Constant, why then do two objects with different masses fall at the same rate as described in the Pisa experiment? Or do they? Is not the combined gravitational force of the heavier object and the gravitational force of the Earth greater than the forces of the lighter object and the Earth? And if the force is greater why wouldn't the two objects both accelerate toward each other faster and come into contact quicker than the lighter object and the Earth?
- dleemoon (age 64)
Apple Valley, CA, USA
Yes they do fall at the same accelerated rate. You are correct in stating that the gravitational force is proportional to the masses of both the earth and that of the body. However, as the force is proportional to the gravitational attraction, the acceleration is inversely proportional to the mass itself. Do the division: the mass of the body cancels out.
This is actually a very fundamental physics question. Many sophisticated experiments have been carried out since Galileo's time and they all come out to the same conclusion. These go under the name of "Equivalence of gravitational and inertial mass". See:http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_experiment
for some detailed information.
p.s. Of course we're assuming other forces, like air friction, aren't important here. Mike W.
(published on 05/02/10)
Follow-Up #1: light and gravity
as you have explained in the previous answer....mass does not effect how fast a body is falling towards the Earth.......
and if mass does not really cause any change to the speed then a body of rest mass = 0 should also be attracted towards the earth in the form of acceleration.....
is this seen when we are talking about something like light???
if the particles of light are to accelerate they must undergo change in speed and this is against the observations .......
well if earth can accelerate a light particle then what will be the extent of acceleration produced by a black hole??
i thought that since time has to slow down and gravity is providing an extra amount of energy can we say that its frequency increases .......
thus that would mean the light we receive even on earth has different frequency from the original ......
is it really so??
- apurva (age 17)
I'll take your last question first. Yes, it really is so that the light we receive has a different frequency than at the source, shifted by gravity. The gravitational frequency shift was first measured in 1960 by comparing accurate clocks at the top and bottom of a tower. It's been measured in a variety of ways many times since.
Usually the light sources are big stars so the net shift is to lower frequency, from leaving the star. The increase on approaching the earth is small.
If it seems hard to understand how light behaves in a gravitational field, that's because you can't get a good picture in standard Euclidean space-time. That sort of picture gets the curvature wrong by a factor of two. Space is not flat when gravity is present.
(published on 05/04/10)
Follow-up on this answer.