(Figure 1) A satellite that goes around the earth once every 24 hours is called
ID: 1465033 • Letter: #
Question
(Figure 1) A satellite that goes around the earth once every 24 hours is called a geosynchronous satellite. If a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite.
Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:
The universal gravitational constant G is 6.67×1011Nm2/kg2.
The mass of the earth is 5.98×1024kg.
The radius of the earth is 6.38×106m.
Give the orbital radius in meters to three significant digits.
Explanation / Answer
Time periode, T = 24 hours
= 24*60*60
= 86400 s
let r is the radius of orbit.
We know time periode of a stelloite around the earth,
T = 2*pi*r^(3/2)/sqrt(G*M)
T^2 = 4*pi^2*r^3/(G*M)
r^3 = G*M*T^2/(4*pi^2)
r = (G*M*T^2/(4*pi^2))^(1/3)
= (6.67*10^-11*5.98*10^24*86400^2/(4*pi^2))^(1/3)
= 4.23*10^7 m
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