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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

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