Mass of Earth/Sun: Comparing in Different Frames

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Discussion Overview

The discussion revolves around the mass of the Earth and the Sun as perceived from different inertial frames in a two-body system. Participants explore the implications of frame dependence on mass measurements, the nature of orbital speed, and the challenges of defining mass without an external reference. The conversation touches on theoretical concepts from general relativity and Mach's principle.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants suggest that in a frame at rest with respect to the Sun, the Earth has an orbital speed v, while in a frame at rest with respect to the Earth, the Sun has the same speed v, leading to potential contradictions in mass definitions.
  • Others argue that without a third body for reference, it is impossible to distinguish between the two frames or define orbital speed, thus complicating mass measurements.
  • A participant mentions the Sagnac effect as a means to determine angular velocity but questions its applicability to defining the center of mass in this context.
  • Some contributions reference Einstein's Machian thought-experiment, suggesting that the paradox may depend on assumptions about the Machian nature of gravity.
  • There are discussions about the necessity of a third reference point to define a bounded system and the implications for mass definitions in a two-body gravitational interaction.
  • Participants express uncertainty about whether mass can be uniquely defined in a two-body system with gravity as the only interaction.

Areas of Agreement / Disagreement

Participants generally disagree on the implications of frame dependence for mass definitions and the necessity of a third body for establishing a reference frame. The discussion remains unresolved, with multiple competing views presented.

Contextual Notes

Limitations include the lack of a third body for reference, which affects the ability to define orbital speed and mass in a two-body system. The discussion also highlights the complexity of applying general relativity concepts to this scenario.

  • #31
PeterDonis said:
Even though the density and curvature are infinite there?

Yes.
 
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  • #32
bcrowell said:
Yes.

Hmm...okay, at least I'm clear about your position. I don't think it's a very common position to take (as I understand it, the "standard" position in GR is that singularities, such as the initial singularity of the FRW models and the r = 0 singularity of the Schwarzschild interior, are a sign that the theory breaks down, and a better theory is needed to cover such cases--presumably some kind of quantum gravity theory), but in the absence of any actual experimental evidence concerning singularities, I can't say it's ruled out.
 

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