A satellite revolving in a circular equatorial orbit of radius 
from west to east appears over a certain point at the equator every 
hours. Using these data, calculate the mass of the Earth. The gravitational constant is supposed to be known.
Text Solution
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Sol. We know from the previous problem that a satellite moving west to east at a distance 
from the center of the earth will be revolving round the earth with an angular velocity faster than the earth's diurnal angular velocity. Let
anuglar velocity of the earth. Then
as the relative angular velocity with respect to earth.
Now by Newton's law
So,
Substitution gives
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