Quadibloc wrote:

On May 13, 7:43*pm, Dave Typinski wrote:

You've stumped me, John. *How does changing the orbit inclination
simplify things make the reasoning non-circular?

You're right that we don't need the Earth's mass to know the
acceleration of gravity at the satellite's altitude. But that makes
the Earth's mass - and G - a red herring.

In this case, the mass of the Earth is calculated from big G and the
satellite's orbit parameters. Big G comes from analysis of a torsion
balance experiment and the orbit altitude and period are measured
directly. What's red herringish about that?

If the question is that we don't know whether the Earth's axial
rotation period is 24 hours or 23 hours, 56 minutes, and 4 seconds,
then one satellite in orbit at one altitude would be compatible with
either, given different values of the Earth's mass.

Okay, I think I see your objection now.

The satellite needn't be geostationary or polar. One just has to know
its orbit period and altitude.

You're right, of course: a polar satellite removes the possibly
confusing parameter of Earth's rotation from the orbit period
measurement. It crosses the equator when it crosses and that's that.

Comparing the satellite with the acceleration of gravity on the ground
will settle that. Comparing the periods of satellites at different
heights will settle that, since only in a unique frame of reference
will Kepler's square/cube law be followed.

Yep and yep.

A satellite in polar orbit is a nice case for comparison, because
there is agreement that the Earth does not rotate with a pole
somewhere on the Equator, so the period of such a satellite at a given
altitude would be the same as one in an equatorial orbit relative to a
nonrotating Earth, from which the period of the Earth's rotation is
simple to determine.

Yep.
--
Dave