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What is the approximately height of a geo-stationary satellite from the earth's surface?
Wiki User
∙ 10y ago
Before you begin, you need to know that a geosynchronous orbit completes one orbit every day.
Step 1
F= N/T= 1/1 day= 1/86400 seconds
T= 1/F= 86400 seconds
Step 2
The formulas we will use are:
v= square root of (Gme/r)
v= 2(3.14...)r/T * This is derived from the formula v=d/t, since the satellite is circling a sphere (circumference/time it takes to complete one orbit)
We already know the following information:
G= 6.67x10-11 N*m2/kg2
rE= 6.38x106 m
me= 5.98x1024 kg
v= square root of (Gme/r)
2(3.14...)r/T= square root of (Gme/r)
(2(3.14...)r/T)2= Gme/r
4(3.14...)2r2/T2= Gme/r
* cross out an r from each side and rearrange the formula:
r3= GmeT2/4(3.14...)2
r= cubed root of (GmeT2/4(3.14...)2)
r= cubed root of (6.67x10-11*5.98x1024*864002)/4(3.14)2
r= 4.22x107 m
Step 3
r= rE+ height above earth's surface
4.22x107= 6.38x106+ height above earth's surface
Therefore, the altitude of the satellite's orbit above the earth's surface is 3.59x107 m
Wiki User
∙ 13y ago
Wiki User
∙ 10y ago24000 km
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