REM Elaboration

REM Mass or Dimensions?

It’s the mass that counts, not the dimensions

If the mass of a planet is computed only from its orbit, then a measurement of its ”acceleration of gravity” should give a different mass from that determined only from its radius in its local frame of reference. Has this comparison been done for the moon?

If a universal radius based acceleration constant, A_r, could be calculated from the radius of the earth, R_e , and g at the surface:
R_e = 6,371 km
A_rR_e = g = 9.81 m/sec²
A_r = (9.81 m/sec²)/6,371 km = 1.54 x 10^-6 /sec²

Then for a planet of radius R the surface acceleration outward would be
a_r = A_rR = 1.54 x 10^-6/sec² x R

For the moon, R = 1,737 km this gives
g_m = 1.54 x 10^-6/sec² x 1,737 km = 2.67 m/sec² for the radius based case.

But the official moon gravity is, g_m = g x m_m/m_e
where
Earth mass = m_e 5.972 x 10^24 kg
moon mass = m_m 7.347 x 10^22 kg
g_m = 9.81 m/sec² x m_m/m_e = 1.11 m/sec²

In the famous hammer and feather drop video by Apollo 15 astronaut, David Scott, on the moon they both take close to t = 1.3 seconds (from frame accurate video measurement) to fall about d = 1.2m (4 ft).

d = ½g_mt²
so
g_m would have to be = 2d/t² ≈ 1.42 m/sec²

d would have to be ~2.25 m (~7.4 ft) for g_m = 2.67 m/sec². No good! It must be the mass, not the dimensions, as I originally thought, that determines the radial acceleration, and thus conforms to general relativity. So the moon gravity test falsifies expansion by dimensions.

However, calculating A_r is a lot harder than this, and needs to be done in the quantum realm. Any takers?