Shows a a geosynchronous satellite, which is a satellite that goes around the Ea

Question

Shows a a geosynchronous satellite, which is a satellite that goes around the Earth once every 24 hours. 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 cedes the Earth. Use the following values if needed m this problem: The universal gravitational constant G is 6.07 Times 10^-11 N m^2/kgJ. The mass of the earth is 5.98 Times 10^34 The radius of the earth is 6.38 Times 10^6 m. Express your answer numerically In motors to three significant figures.

Explanation / Answer

GMm/R^2 = mv^2/R

GM/R^2 = v^2/R

we know

v = rw

GM/R^2 = (Rw)^2/R

GM/R^2 = Rw^2

GM = R^3 * w^2

R^3 = GM / w^2

w = 2pi/T

T = 86400s

G = 6.67 x 10^-11

M = mass of earth = 5.98 x 10^24 kg

R = 4.23 x 10^7 m

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