Hello. According to link. http://einstein.stanford.edu/MISSION/mission1.html we have 0.000011 degrees/year due frame dragging and 0.0018 degrees/year due geodetical effect. Could you estimate how these numbers would change if radius of the Earth would decrease lets say 10 times? I mean everything else (masses, velocities, orbits) stays the same, only decrease the radius of the Earth (the Earth becomes denser).
Re: ProbeB The moment of inertia I, of a sphere is 2/5 m R^{2}, so if the radius decreases and the mass does not, the angular momentum Iω will be smaller unless the rate of rotation increases. The magnitude of the frame dragging depends on the angular momentum. The geodetic effect depends on the mass and the orbital radius, so I guess for a given radius it won't change.
Re: ProbeB There is another question about geodetical effect. How smooth it effects the precession during 1 rotation of the satellite around the Earth. I mean: lets divide 1 rotation to lets say 4 parts. Lets say by one revolution around the Earth we have got precession = 1. Is it accumulates smoothly like 0.25 + 0.25 + 0.25 + 0.25 = 1 Or maybe some other way like 1.5 + 1.5 – 1 – 1 = 1 or 1.5 – 1 + 1.5 – 1 = 1 Is here some variations of the angle during 1 revolution around the Earth? (by theory and by real data)