A geostationary satellite orbits the Earth in such a manner that it is always directly above the same point on the equator as the Earth rotates. Assuming that this orbit is circular, what is its radius? (The mass of the Earth is approximately 5.97 × 1024 kg and the gravitational constant G ≈ 6.673 × 10−11 m3kg−1s−2.) Use the same method to estimate the orbital radius of the Moon, again assuming that its orbit is circular and centred on the Earth.

asked by Joe

8 years ago

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1 answer

force gravity=centripetal force
GMem/r^2=mw^2 r

now, w= 1rev/day=2PI/(24*3600) rad/sec

r^3=GMe w^2
solve for r.

answered by bobpursley

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Question

A geostationary satellite orbits the Earth in such a manner that it is always directly above the same point on the equator as the Earth rotates. Assuming that this orbit is circular, what is its radius? (The mass of the Earth is approximately 5.97 × 1024 kg and the gravitational constant G ≈ 6.673 × 10−11 m3kg−1s−2.) Use the same method to estimate the orbital radius of the Moon, again assuming that its orbit is circular and centred on the Earth.

1 answer

force gravity=centripetal force
GMem/r^2=mw^2 r

now, w= 1rev/day=2PI/(24*3600) rad/sec

r^3=GMe w^2
solve for r.

Ask a New Question or answer this question.

bobpursley · Answer

force gravity=centripetal force GMem/r^2=mw^2 r now, w= 1rev/day=2PI/(24*3600) rad/sec r^3=GMe w^2 solve for r.