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A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to 2 gRr ( /), where 2 g =9.81 m/s , R = radius of the earth = 6370 km, and r = distance from the center of the earth to the satellite. Assuming that the orbit of the moon is a circle of radius 3 384 10 km, ´ determine the speed of the moon relative to the earth.

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Answer:

3665.46 km/hr

Explanation:

Given that :

R = radius of the earth = 6370 km = (6370 * 10^3)m

Radius from earth center, r = 384 * 10^3 km = (384 * 10^6) m

g = 9.8 m/s²

Using the relation :

V = sqrt(gR² /r)

V² = (9.81 * (6370*10^3)²) / 384 * 10^6

V² = (3.981 * 10^8 *10^6 / 384 * 10^6)

V² = 1.0367 * 10^(12 - 6)

V² = 1.0367 * 10^6

V² = 1036700

V = sqrt(1036700)

V = 1018.1846 m/s

(1018.1846 * 1/1000 * 3600) km/hr

V = 3665.46456 km/hr