Gravity and Length Contraction

[Charlie G]

I was wondering whether or not the Earth would have a larger gravitational force, relative to me, if I passed the Earth at close to the speed of light?

The reason I ask is if I pass the Earth by then it appears to be flatened, but only in the direction of its motion. So, if its length decreases but its width stays the same, then wouldn't I measure a drastically greater density than an observer at rest relative to the Earth, and therefore more gravity?

 

[tiny-tim]

I was wondering whether or not the Earth would have a larger gravitational force, relative to me, if I passed the Earth at close to the speed of light?

The reason I ask is if I pass the Earth by then it appears to be flatened, but only in the direction of its motion. So, if its length decreases but its width stays the same, then wouldn't I measure a drastically greater density than an observer at rest relative to the Earth, and therefore more gravity?

Hi Charlie G!

Yes, that's right …

we normally say that the energy of the Earth has increased, and energy is mass, with the same gravitational effect as matter, so the effective gravitational mass has increased (by the same factor as the "length" has contracted) …

but your way works also (and shows that everything in relativity fits together! )

 

[luxxio]

I was wondering whether or not the Earth would have a larger gravitational force, relative to me, if I passed the Earth at close to the speed of light?

The reason I ask is if I pass the Earth by then it appears to be flatened, but only in the direction of its motion. So, if its length decreases but its width stays the same, then wouldn't I measure a drastically greater density than an observer at rest relative to the Earth, and therefore more gravity?

I think that this is noy true. You are thinking in terms of special relativity. In term of general relativity the gravitational force is expressed in terms of geodesics.

 

[Charlie G]

Thx for all the replies:) It is pretty cool how all of relativity's stuff falls into place so well.