Equal Energy Exchange in Gravitationally Attracted Objects?

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Gravitationally attracted objects do not exchange equal energy due to their differing masses. When a ball is dropped from a height, it accelerates towards the Earth, gaining kinetic energy, while the Earth experiences an imperceptible change in velocity. The energy transferred to the ball is significantly greater than that transferred to the Earth, resulting in the ball having most of the system's kinetic energy. The Earth’s minuscule acceleration leads to an almost negligible velocity change. Overall, the potential energy lost by the system primarily converts into the ball's kinetic energy.
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Hey all. I was reading a post and a question popped into my head.

Do objects that are gravitationally attracted to each other give each other the same energy, but in opposite directions, no matter the difference in masses? Like if I drop a ball from 100 ft, does the ball give the Earth the same amount of energy that the Earth gives the ball, but just in the opposite direction? I'm assuming this cancels out any net gain or loss in energy overall. Is that correct?
 
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Drakkith said:
same energy, but in opposite directions

Erm. Energy is a scalar quantity, it has no direction associated with it...
 
Nabeshin said:
Erm. Energy is a scalar quantity, it has no direction associated with it...

Ok. Energy resulting in velocity, but in opposite directions. Or however the correct way of saying it is.
 
Drakkith said:
Hey all. I was reading a post and a question popped into my head.

Do objects that are gravitationally attracted to each other give each other the same energy, but in opposite directions, no matter the difference in masses? Like if I drop a ball from 100 ft, does the ball give the Earth the same amount of energy that the Earth gives the ball, but just in the opposite direction? I'm assuming this cancels out any net gain or loss in energy overall. Is that correct?

I really don't think that they end up with the same energy. I get a result that it takes about 2.49 s for a ball dropped from that height to reach the ground, at which point it has a speed of about 24.45 m/s. If I use the miniscule acceleration experienced by the Earth (assuming a 1 kg ball) to figure out what Earth's velocity would be after 2.49 s, I get something like 4x10-24 m/s.

The net result seems to be that essentially ALL of the potential energy lost by the Earth-ball system ends up as kinetic energy of the ball.
 

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