Understanding Tidal Forces on a Sphere: Do They Also Act Horizontally?

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Discussion Overview

The discussion centers on the nature of tidal forces acting on a sphere composed of test particles, particularly whether these forces also induce horizontal squashing in addition to the vertical effects typically associated with gravitational gradients. Participants explore the implications of these forces in the context of both theoretical models and real-world phenomena, such as ocean tides influenced by the moon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the mechanism behind horizontal squashing of a sphere of test particles, noting that the gradient of gravitational force is primarily vertical and asking if it also acts horizontally.
  • Another participant reiterates the point about the gravitational gradient being mainly vertical, referencing classical Newtonian gravity to support their view.
  • Concerns are raised about the differences in behavior between interconnected water in oceans and non-interacting test particles, suggesting that water must flow in response to tidal forces in both vertical and horizontal directions.
  • A later reply asserts that the calculations of gravitational force changes do not depend on whether the subject is water or test particles, indicating that the fundamental forces remain unchanged regardless of the medium.
  • One participant acknowledges the difference in how oceans, as incompressible fluids, respond to tidal forces compared to free non-interacting particles, while maintaining that the forces themselves are not different.

Areas of Agreement / Disagreement

Participants express differing views on the implications of tidal forces on interconnected versus non-interacting systems. While there is some agreement that the forces themselves remain unchanged, the discussion reflects unresolved questions about the mechanisms and responses of different materials to these forces.

Contextual Notes

Participants note that the discussion is framed within classical gravity, and there are unresolved aspects regarding the assumptions made about the behavior of fluids versus test particles in response to tidal forces.

exponent137
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In http://arxiv.org/pdf/gr-qc/0103044v5.pdf in page 6 it is written about a tidal forces on a sphere built up from test particles.
It is written that ball also starts to being squashed in the horizontal directions. I do not understand this. Because gradient of gravitational force is mainly in vertical direction. Is it also in horizontal direction?
What is mechanism for squashing in horizontal direction?

Is here at this ball of test particles any distinction to the tide on Earth caused by moon?
 
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exponent137 said:
Because gradient of gravitational force is mainly in vertical direction. Is it also in horizontal direction?

This is already true for Newtonian Gravity:

tide_fig2.gif


https://web.njit.edu/~gary/320/Lecture12.html
 
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Water in oceans is connected, Baez's test particles are not. Thus water must flow from elsewhere on vertical direction and it should flow elsewhere from horizontal direction. Earth gives backbone to water.
Is here any special difference to calculation because of these two reasons, or is this neglected?
 
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exponent137 said:
Water in oceans is connected, Baez's test particles are not. Thus water must flow from elsewhere on vertical direction and it should flow elsewhere from horizontal direction. Earth gives backbone to water.
Is here any special difference to calculation because of these two reasons, or is this neglected?

There is no difference. We're calculating the changes in the magnitude and direction of the gravitational force at various points and those don't care whether they're acting on water or a cloud of test particles.

(As A.T. has already pointed out, this is not a relativity question - it's just classical gravity).
 
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There is a difference is how the oceans respond to those tidal forces, as a more or less incompressible fluid constrained in its motion as you noted, instead of free non-interacting particles - though as Nugatory said, not in the forces themselves.
 
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