The spacecraft moves in a circular orbit around the Earth in the plane of the Moon's orbit with an angular velocity equal to the angular velocity of the Moon's rotation around the Earth. While moving, the ship is between the Earth and the Moon on a straight line connecting their centers. The distance from the ship to the Earth is such that the gravitational forces acting on the ship from the Earth and the Moon are equal to each other. Are the ship's engines working? What is the weight of the astronaut on the ship? The mass of the astronaut is 70 kg, the period of revolution of the Moon around the Earth is 27.3 days. The mass of the Earth is 81 times the mass of the Moon, and the distance from the Earth to the Moon is 60 Earth radii. The radius of the Earth is taken to be 6400 km.
Detailed solution. Format jpg
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