Galileo proved at the Tower of Pisa that falling objects fall at the same rate regardless of weight by dropping two differently-weighted objects and noting that they hit the ground at the same time, right?
But don’t the laws of gravity say that more massive bodies attract one another to a greater degree than less massive ones?
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That’s because both objects were falling towards the earth, under the gravitational influence of the earth, so (in a vacuum) they would fall at identical speeds.
On the other hand, if you placed two objects at an equal distance between Earth and the sun, they would fall towards the sun, since the sun has much higher mass than the Earth.
Short answer: Because the Earth is so much more massive than the objects in question that the effective gravitional force is the same.
G ~= m1 + m2 / d^2
The gravitational force between two masses is proportaional to the sum of the masses and inversely proportional to the distance between them squared.
So, if you take two lead weights one of which is 1 lb the other of which is 10 lbs the gravitional force of them is and drop them both from a height of 100 feet
G (1 lb) = Mass of Earth + 1 lb / 100 feet squared
G (10 lbs) = Mass of Earth + 10 lbs / 100 feet
So, although the gravitational force is greater for the 10 lb object the Mass of Earth is such an overwhelming factor that it makes no difference in real life.
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While you have a good question–with all due respect, the story about Galileo and dropping the two objects is apocryphal.
But more to your point, there probably would be some difference in drag, so at some point, one of them would fall faster.
If they were falling without any drag considerations, even a sheet of paper and a block of lead would fall at the same rate. That doesn’t happen in real life, though.
So, the larger ball would theoretically be pulling on the earth harder than the smaller ball, and those two balls are pulling on each other, too–but those attractions are so small that they’re statistically zero.
More massive bodies do indeed have a greater attraction due to gravity, but they also have greater inertia and so greater resistance a change in velocity. The fact that inertial mass equals gravitional mass makes the acceleration due to gravity a constant reguardless of mass (in a vucuum).
Better crack open that textbook again, Glitch. The force of gravity is proportional to the product of the masses. Therefore the force for a 10 kg mass is ten times the force on a 1 kg mass.
Which is what the original poster was asking: if the force is ten times larger, why do they fall at the same speed? The answer is simple. Because the object has ten times the mass, it takes ten times the force to accelerate it at the same rate.
This was discussed at length in Comments on Cecil’s Columns or Comments on Mailbag Answers a while back. I’ll see if I can dig it up. IIRC, the conclusion was that there is a difference based on the products of the masses, but it’s very very very slight.
The Apollo astronauts actually conducted this experiment on the moon with a hammer and a feather. So it happened at least once in real life.
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The Boston Museum of Science has (or had, at least at the time of my last visit sometime in the mid-80s) an exhibit on this. Two plastic tubes ran the height of the building; one had a bowling ball and the other had a feather. The two objects were pulled up to the top and let go; I don’t remember if they did it twice, once at full atmospheric pressure and once in a vacuum, or just in a vacuum - but I do distinctly remember watching the feather plummet at the same speed as the bowling ball in the vacuum.
I can’t find a reference to it quickly, but as I recall, the actual experiment used by Galileo was to roll balls of differing mass down inclined planes and time them over measured distances. A water clock was used, counting the drips, I believe…
I am NOT going to attempt to add to the physics of this!