A GPS satellite revolves around the earth in a geostationary oribit (it always s
ID: 1392642 • Letter: A
Question
A GPS satellite revolves around the earth in a geostationary oribit (it always seems to be in the same place in the sky)
a) Use Newton's law of graviation to show how the period of roation of any satellite depends upon the distance from the center
B) calculate the distance from the geostationary satellite to the center of the earth, as well as the distance to the surface.
c) Now suppose that we launch a small rocket from the satellite and we want to rise to 100,000,000 meters above the surface of the earth before it stops and returns to earth. What speed must we impart on the rocket?
Explanation / Answer
a) Time period of a satelitte T = 2pi / w
w = 2pi / T
w is the angular speed of satellite
And Gravitational force = centripetal force
GMm / d^2 = m w^2 d
w^2 = GM / d^3
4pi^2 / T^2 = GM / d^3
T = 2pi sqrt[ d^3 / GM ]
b) for earth T = 24 hours = 24 x 3600 sec = 86400 sec
and M = 5.97 x 10^24 kg
86400 = 2 xpi x sqrt[ d^3 / (6.67 x 10^-11 x 5.97 x 10^24)]
d = 42226910.18 m from the centre of earth
from surface = d - R = 35856910.18 m
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