Gravity and Length Contraction

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Discussion Overview

The discussion explores the relationship between gravitational force and relativistic effects, specifically whether an observer moving close to the speed of light would perceive an increase in the Earth's gravitational force due to length contraction and changes in density. The scope includes concepts from both special and general relativity.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether passing the Earth at relativistic speeds would result in a larger perceived gravitational force due to length contraction affecting density.
  • Another participant agrees with the initial claim, suggesting that the energy of the Earth increases, which could imply an increase in effective gravitational mass.
  • A different participant challenges the idea, stating that the reasoning based on special relativity is incorrect and that general relativity should be considered, where gravitational force is described in terms of geodesics.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between relativistic effects and gravitational force, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion involves assumptions about the applicability of special versus general relativity and the interpretation of gravitational effects, which are not fully resolved.

Charlie G
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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?
 
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Charlie G said:
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! :smile:

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

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