I have a trivial question about a satellite if it is in Geosynchronous Orbit?

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MatthewRosenfeld

New member
These orbits have to be circular. Calculate how high above the earth's surface a satellite in a geosynchronous orbit has to be. The only information needed is the mass of the earth (-6.4 x 10^24kg) and the radius of the earth (-6.4 x 10^6m) It is not good enough to give just the answer (35.8m) Actually show how you reached the answer
 
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tOhmtMistressBekki

New member
A geostationary orbit is circular. A geosynchronous orbit (any orbit with a 24 period) can be elliptical. In reality ANY orbit is going to have some eccentricity, so even the ground tracks of comm satellites do little figure 8s.

But anyway...
Centripetal acceleration on the satellite
= omega^2 r = (2 pi / T)^2 r
=
Acceleration due to gravity
= G M / r^2

Solve for the orbital radius:
r = cubert (G M T^2 / (4 pi^2) )

Then subtract the radius of the earth (given) from that to get your altitude. They give you the mass, M. You'll have to look up newton's big G. And of course the period, T, is one day, which you will want to convert to seconds. Then plugnchug.
 
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