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Yes, as simple as that ...

the geostationary orbit pretty much depends only on the (polar) rotation rate of a (any) planet (also almost incidentally in this case, the mass M of the planet), so there is no fundamental relationship between the geostationary orbit radius and the planet's radius: for example, a less dense planet of equal mass to the Earth, but by dint of it being less dense having a larger radius, with thesamerotation period, would possess exactly the same geostationary orbit radius, and so adifferentratio between the two radii ...

As such this isn't really an"topic ... is it?AdvancedApplied Maths"

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... a better question is:

*compute the radius of a satellite's orbit;-).in units of the Earth's radius, such that there arenotime-dilation effects experienced by the satellite*

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*O.K - admittedly more advanced Physics than Maths, perhaps, but in this case thereaisbetween thefundamental relationship"zero time-dilation orbit radius"and the planet's radius - and, to me, at least, an astonishingly simple one.

I do have the answer and the working for it, in case you give up ;-)

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