I think I have an answer for the following problem, but I'm not sure if it (or the assumptions used to get it) are correct:(adsbygoogle = window.adsbygoogle || []).push({});

Consider a 540 kg synchronous satellite in a circular orbit in the same plane as our equator. Find the height H of the satellite above the Earth's equator.

What I got:

msat - mass of satellite = 540 kg

mearth - mass of earth = 5.98 x 10^24 kg

r = radius = distance between earth's center and the satellite = r

G = 6.67 x 10^-11 (N m^2 / kg^2)

v = velocity of the satellite

a = acceleration for uniform circular motion

radius earth = 6380 km

F = ma

a = v^2 / r

G (msat * mearth) / r^2 = msat ( v^2 / r )

v = (2*pi*r) / T

T = 1 day = 86,400 seconds

substituting...and cancelling msat on both sides

G (mearth / r^2 ) = (2*pi*r)^2 / (r T^2 )

Re-arranging...

r^3 = ( G*mearth*T^2 ) / (4*pi^2)

r^3 = 7.54 x 10^22 meters cubed.

r = 4.23 X 10^7 meters or 42,300 km

total radius - earth radius = height above the earth's surface

42,300 km - 6,380 km = 35,920 km or 35,920,000 meters above the earth's surface

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# Homework Help: Satellite orbit question: does mass affect this problem?

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