- #31
TurtleMeister
- 897
- 90
Yes, I agree with Morberticus and Dave. You're basically saying the same thing I said in post #17. I don't even think the OP was even considering anything more than a two body problem. Using more than two bodies only serves to complicate the understanding of the universality of free fall and the equivalence principle. The EP has not been mentioned in this thread. But I think it is important to bring it up because the UFF and EP go hand in hand. I will use the following illustration:
The dot located between m1 and m2 is the CoM. Notice that it is in the center an equal distance from m1 and m2. This tells us that the mass of m1 and m2 are equal. I cannot do animation here so you'll have to visualize the following.
Lets increase the mass of m2. Two things will happen. 1)The increase in inertial mass of m2 will cause the CoM to move to a position closer to m2. 2)The increase in gravitational mass of m2 will cause the relative acceleration of m1 and m2 toward each other to increase. Now, the equivalence principle tells us that gravitational mass is proportionally equal to inertial mass. So the shorter distance that m2 has to travel to reach the CoM (as a result of the increase in inertial mass of m2) exactly offsets the increase in acceleration (as a result of the increase in gravitational mass of m2). So the acceleration of m2 relative to the CoM remains constant, and the time that it takes to reach the CoM decreases. The only way to change the acceleration of m2 relative to CoM is to change the mass of m1.
The dot located between m1 and m2 is the CoM. Notice that it is in the center an equal distance from m1 and m2. This tells us that the mass of m1 and m2 are equal. I cannot do animation here so you'll have to visualize the following.
Lets increase the mass of m2. Two things will happen. 1)The increase in inertial mass of m2 will cause the CoM to move to a position closer to m2. 2)The increase in gravitational mass of m2 will cause the relative acceleration of m1 and m2 toward each other to increase. Now, the equivalence principle tells us that gravitational mass is proportionally equal to inertial mass. So the shorter distance that m2 has to travel to reach the CoM (as a result of the increase in inertial mass of m2) exactly offsets the increase in acceleration (as a result of the increase in gravitational mass of m2). So the acceleration of m2 relative to the CoM remains constant, and the time that it takes to reach the CoM decreases. The only way to change the acceleration of m2 relative to CoM is to change the mass of m1.
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