Equal Energy Exchange in Gravitationally Attracted Objects?

[Drakkith]

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?

 

[Nabeshin]

same energy, but in opposite directions

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

 

[Drakkith]

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.

 

[cepheid]

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.