# B Why do objects fall at the same speed in free fall?

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1. Nov 26, 2017

### Staff: Mentor

Yes, this is what I was implying.

If you write out the equations for the evolution of the system as a whole, that does depend on $m_1$. But at any point in the state space the acceleration of $m_1$ does not depend on $m_1$.

All other things being equal, the acceleration of $m_1$ is independent of $m_1$. In the classical two body problem all other things are not kept equal, and that is where the differences come in.

2. Nov 28, 2017

Actually all objects affected by mutual gravitation accelerate towards each other. When you drop a feather the Earth accelerates towards it. However the effect is so small you can't measure it.

So technically it is untrue that unequal masses accelerate (or 'fall') at the same rate, but the difference in acceleration is not observable in practical demonstrations.

3. Nov 28, 2017

"The Sun is going down! " "No, the horizon is moving up!" - Firesign Theatre

4. Nov 28, 2017

### Staff: Mentor

You have to be careful here. The acceleration of object A is not the same thing as the acceleration of A-B. You are talking about the acceleration of A-B. The acceleration of A, at any moment, is independent of the mass of A. The acceleration of A-B depends on the reduced mass of the system.

5. Nov 29, 2017

### Staff: Mentor

It depends on the sum. arel=G(M+m)/R2.

6. Nov 29, 2017

### Staff: Mentor

Oops, yes you are right. The reduced mass gives the equivalent force for a 1 body problem.