Why is gravitational acceleration independent of test masses?

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Discussion Overview

The discussion centers on the question of why gravitational acceleration is independent of the mass of the objects involved, exploring both Newtonian gravity and General Relativity. Participants examine the implications of these theories on the behavior of freely falling bodies and the nature of gravitational and inertial mass.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that according to Newtonian gravity, all objects fall at the same rate due to the equality of inertial and gravitational mass, but this is described as a coincidence.
  • Others argue that in General Relativity, the equivalence of gravitational and inertial mass is a fundamental postulate, suggesting that gravity is an inertial force and that objects follow geodesics in curved spacetime.
  • A participant mentions that freely-falling bodies experience the same acceleration, leading to the conclusion that mass does not affect the rate of fall, provided air resistance is ignored.
  • Some participants express confusion about how objects can behave similarly if gravity is not considered a force, questioning the nature of motion in curved spacetime.
  • There is a discussion about the implications of Newton's first law and how it relates to motion in the absence of forces, with references to the differences between Newtonian mechanics and General Relativity.
  • Participants discuss hypothetical scenarios involving "Unobtanium" to illustrate the differences in predictions between Newtonian gravity and General Relativity.

Areas of Agreement / Disagreement

Participants express differing views on the nature of gravitational acceleration and the explanations provided by Newtonian gravity versus General Relativity. No consensus is reached regarding the interpretation of these theories or the implications of their principles.

Contextual Notes

Some statements rely on assumptions about definitions of mass and force, and there are unresolved questions regarding the implications of curved spacetime on motion. The discussion also highlights the limitations of Newtonian mechanics in explaining certain phenomena observed in nature.

  • #31
F1 / m1 = g. (Inertial masses and forces).
F2 / m2 = G M/r2. (Gravitational masses and forces).
The quantities on the rh sides of both equations are all measurable quantities that don't depend on any assumptions about gravitational and inertial forces and masses. So we can equate the lh sides of both equations and we get F1 / m1 = F2 / m2 . Assuming that inertial mass = gravitational mass, i.e. m1 = m2 the m's cancel leaving the forces equal. So we can equate the rh sides of the first 2 equations:
g = G M/r 2,
which means that gravitational acceleration is independent of the test masses.
 
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