# Orbit of a geostationary satellite

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• Dec 3rd 2008, 06:45 AM
jackiemoon
Orbit of a geostationary satellite
Hi,

Question is: compute the radius of a geostationary satellite's orbit in units of the Earth's radius.

My answer is:

Earth's radius R = 6378.1 km approx
Satellite is 35,786km above ground so radius of the orbit in terms of earth's radius is (35,786/6378.1)R + 1R = 6.61 R

Have I missed anything here or is it just that simple?

Thanks for any advice.
• Dec 3rd 2008, 12:09 PM
mathwimp
Yes, as simple as that ... a better question is:
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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 the same rotation period, would possess exactly the same geostationary orbit radius, and so a different ratio between the two radii ...

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

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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 are no time-dilation effects experienced by the satellite ;-).*

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* O.K - admittedly more advanced Physics than Maths, perhaps, but in this case there is a fundamental relationship between the "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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• Dec 3rd 2008, 02:58 PM
jackiemoon
Hey mathwimp,

thanks for the reply. As I am just 9 weeks into an undergraduate degree after not having studied maths or physics for nearly 12 years, this, at present, is advanced to me.
• Dec 3rd 2008, 04:06 PM
mathwimp
9 weeks into an undergrad degree? That's great.
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Quote:

Originally Posted by jackiemoon
Hey mathwimp,

thanks for the reply. As I am just 9 weeks into an undergraduate degree after not having studied maths or physics for nearly 12 years, this, at present, is advanced to me.

Hey yerself, Jackie,

9 weeks into an undergrad degree? That's great. What subject?

Whatever, it's obviously working; they've already got you proficient at dividing one number into another ...
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