An orbiting space station is observed to remain always vertically above the same point on the earth. Where on earth is the observer? Describe the orbit of the space station as completely as possible.
Text Solution
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Sol. The observer must be on the equator of the earth. The orbit of the space station is a large circle in the equatorial plane with center at the center of the earth. The radius of the orbit can be figured out using the orbiting period of 24 hours as follows. Let the radius of the orbit be R and that of the earth be R 0 .
We have 
= 
,
Where v is the speed of the space station, G is the universal constant of gravitation, m and M are the masses of the space station and the earth respectively, giving
v 2 = 
,
As mg = 
,
We have GM = 
.
Hence v 2 = 
.
For circular motion with constant speed v, the orbiting period is
T = 
.
Hence 
= 
And R = 
= 4.2 × 10 4 km.
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