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Do heavier objects actually fall a TINY bit faster?

Bellator 243

If F=G(m1*m2)/r2 then the force between the earth an object will be greater the more massive the object. My interpretation of this is that the earth will accelerate towards the object slightly faster than it would towards a less massive object, resulting in the heavier object falling quicker.

Am I missing something or is the difference so tiny we could never even measure it?

Edit: I am seeing a lot of people bring up drag and also say that the mass of the object cancels out when solving for the acceleration of the object. Let me add some assumptions to this question to get to what I’m really asking:

1: Assume there is no drag
2: By “fall faster” I mean the two object will meet quicker
3: The object in question did not come from earth i.e. we did not make the earth less massive by lifting the object
4. They are not dropped at the same time

Ans By Shadydentist

You are correct, heavier things will accelerate the earth more than light things. The acceleration of earth is equal to G*m2/r2. For a 1000 kg mass on the earth’s surface (~6 x 106 m), this translates into an acceleration of about 2 x 10-21 meters per second2 .

The very best accelerometers can measure things on the order of 10-9 m/s2 , so you’re also right in that we cannot measure this.