General relativity and tidal forces

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Discussion Overview

The discussion revolves around the relationship between general relativity (GR) and tidal forces, exploring how tides can be understood within the framework of GR compared to Newtonian gravity. Participants examine the implications of geodesics, fictitious forces, and the Riemann curvature tensor in the context of tidal interactions, particularly in strong gravitational fields and rotating bodies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that tides on Earth are traditionally described using Newton's theory, but relativistic effects may become significant in strong gravitational fields, potentially doubling the predicted tidal strength.
  • There is a discussion about how GR calculates tidal forces, with one participant suggesting that different parts of a body traveling different geodesics could lead to the body tearing apart over time.
  • Another viewpoint proposes that the fictitious forces experienced by different parts of a body, which tend to pull it apart, are what constitute tidal forces in GR.
  • One participant mentions that tidal forces can be identified as components of the Riemann curvature tensor, and that under most circumstances, Newtonian approximations are valid for measuring tidal forces.
  • Concerns are raised about the implications of different parts of a body needing to travel at different velocities, particularly in the context of tidal locking, which could lead to shearing forces not accounted for by gravitational theories.
  • Another participant emphasizes that centrifugal forces due to rotation do not contribute to the Riemann curvature tensor, suggesting a need to separate these effects when analyzing tidal forces.
  • References to modern techniques for measuring the gravity tensor are provided, indicating ongoing research and practical applications in the field.

Areas of Agreement / Disagreement

Participants express differing views on the role of fictitious forces, the implications of geodesics, and the effects of rotation on tidal forces. The discussion remains unresolved with multiple competing perspectives on how GR and Newtonian gravity relate to tidal phenomena.

Contextual Notes

Participants highlight limitations in the treatment of tidal forces in GR, particularly regarding the assumptions made about rigid bodies and the effects of rotation. The discussion also touches on the complexity of measuring gravitational effects and the need for careful consideration of various forces at play.

  • #61
Nugatory said:
The relativistic effects that matter across a light-year (about 1016 meters) are completely irrelevant at the diameter of the moon (less than 107 meters. There are simply no relativistic phenomena involved in understanding the tidal lock of these systems (yes, you CAN solve them using the methods of the GR gravitational theory... but the first step in that solution is to apply the weak-field approximation and that gives you the same results as Newtonian gravity).

Bandersnatch is correct. If no torque is applied to the non-relativistic rotating rod it will be straight (although if has been elastically deformed by an applied torque it will take a moment for the deformation to relax and the rod to regain that undeformed straight shape). The only reason for the outer edge to lag would be drag, atmospheric or otherwise.

I was not talking about relativistic effects, i was talking about deformation due to torque. I think the point of our misunderstanding is that you consider that the torque is not constant, but if the force from gravity is constant, so is the torque. And this force is always greater on the near side. Think of it this way: the law of inertia states the if there are no forces on a body, it will remain in its rest state, either traveling at a constant linear velocity or standing still (which are the same thing). To maintain a stable curved path, like an orbit, the centripetal acceleration must be constant. This constant force generates a constant torque, like in a mery go round. If you don't hold on to something, you will fly off at the tangent. This must mean a constant centripetal force, and if the body is not falling towards the central mass, but orbiting, there is a constant force holding it in its curved path. This constant force is gravity, and it generates a constant torque. Why do you believe the torque ceases?
 
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  • #62
altergnostic said:
I agree, but you are considering the body after it is in tidal lock. The point is that there is a torque for the body to reach tidal lock, and my argument is that the body will reach tidal lock but will suffer shearing.
You're argument is wrong, and has gone on far too long.

I haven't seen tide lock explained by heat the way you state, could give me a reference?
This is old, old stuff, some going back to George Darwin and A.E.H. Love. More recently, but still old stuff,

Goldreich P. and Soter S. (1966). Q in the Solar System. Icarus 5, 375-389.
MacDonald, G.J.F (1964). Tidal Friction, Rev. Geophsys 2, 467-541.

You don't even understand the basics, and you are trying to argue? Thread locked.
 

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