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On the way to the moon, the Apollo astronauts reach a pointwhere the Moon\'s gra

ID: 1754011 • Letter: O

Question

On the way to the moon, the Apollo astronauts reach a pointwhere the Moon's gravitational pull is stronger than that ofEarth's. Find the distance of this point from the center of theEarth. The masses of the Earth and the Moon are 5.98 x1024 kg and 7.36 x 1022 kg, respectively, andthe distance from the Earth to the Moon is 3.84 x 108m.
Ans. in units of m. On the way to the moon, the Apollo astronauts reach a pointwhere the Moon's gravitational pull is stronger than that ofEarth's. Find the distance of this point from the center of theEarth. The masses of the Earth and the Moon are 5.98 x1024 kg and 7.36 x 1022 kg, respectively, andthe distance from the Earth to the Moon is 3.84 x 108m.
Ans. in units of m.

Explanation / Answer

F = G m1m2/r² G = 6.67e-11 m³/kgs² m1 and m2 are the masses of the two objects in kg r is the distance in meters between their centers (center ofmass) earth mass 5.98e24 kg moon mass 7.36e22 kg F1 from earth = G m 5.97e24/(x)² F2 from moon = G m 7.35e22/(3.844e8 –x)² set them equal, G and m cancel 5.98e24/(x)² = 7.36e22/(3.844e8 –x)² cross multiply and solve for x

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