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LiRa [457]
3 years ago
6

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 of the Earth.) Use the following values if needed in this problem: The universal gravitational constant G is 6.67
Physics
1 answer:
noname [10]3 years ago
5 0

Answer:

35870474.30504 m

Explanation:

r = Distance from the surface

T = Time period = 24 h

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of the Earth =  5.98 × 10²⁴ kg

From Kepler's law we have relation

T^2=\frac{4\pi^2r^3}{GM}\\\Rightarrow r=\frac{T^2GM}{4\pi^2}\\\Rightarrow r=\left(\frac{(24\times 3600)^2\times 6.67\times 10^{-11}\times 5.98\times 10^{24}}{4\pi^2}\right)^{\frac{1}{3}}\\\Rightarrow r=42250474.30504\ m

Distance from the center of the Earth would be

42250474.30504-6.38\times 10^6=35870474.30504\ m

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