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A geostationary orbit is a circular orbit above the earth`s equator. An object in such an orbit has an orbital period equal to the earth`s rotational period, and therefore appears motionless in the sky relative to ground observers. This is useful for communication and weather satellites since antennas on earth do not have to track them and instead are pointed in a permanent direction at the orbiting satellites. Using Newton`s Law of Gravitational Attraction, a mass of earth equal to 5.9736 x 1024 kg, and an orbital period of 23 hours, 56 minutes, 4.0916 seconds, calculate the radius R of a geostationary orbit around the earth

A geostationary orbit is a circular orbit above the earth`s equator. An object in such an orbit has an orbital period equal to the earth`s rotational period, and therefore appears motionless in the sky relative to ground observers. This is useful for communication and weather satellites since antennas on earth do not have to track them and instead are pointed in a permanent direction at the orbiting satellites.

Using Newton`s Law of Gravitational Attraction, a mass of earth equal to 5.9736 x 1024 kg, and an orbital period of 23 hours, 56 minutes, 4.0916 seconds, calculate the radius R of a geostationary orbit around the earth

Grade:12

1 Answers

Nirmal Singh.
askIITians Faculty 44 Points
10 years ago
if Radius R is the geostationary orbit then we know that v = 2*pie*R / T
and also we know v= sqrt (GM /R)
equating both equation
sqrt (GM/R) = 2 * pie* R /T
on squaring and calculating T^2 = [4*pie^2 / (GM)] * R1/3
R = [GMT2 / 4*pie2]1/3
putting all value we can calculate
G = 6.67x10^-11 Nm^2/kg^2
M = 5.936 x 10^24 Kg
T = 23 hr 56 min 4.0916 sec
R = 4.2 x 10^4 km
Thanks & Regards,
Nirmal Singh
Askiitians faculty

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