- #31
Mark Harder
- 246
- 60
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.
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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