Calculate the magnitude of the gravitational force between the Earth and an m =

Question

Calculate the magnitude of the gravitational force between the Earth and an m = 4.20 kg mass on the surface of the Earth. The distance to the center of the Earth from the surface is 6.37×103 km and the mass of the Earth is 5.98×1024 kg.

Calculate the magnitude of the gravitational force between the Moon and an m = 4.20 kg mass on the surface of the Earth nearest to the moon. The distance to the center of the Moon from the surface of the Earth is 3.76×105 km and the mass of the Moon is 7.36×1022 kg.

Calculate the ratio of the magnitude of the gravitational force between an m = 4.20 kg mass on the surface of the Earth due to the Sun to that due to the Moon. The mass of the Sun is 1.99×1030 kg and the distance from the center of the Sun to the surface of the Earth is 1.50×108 km.

Explanation / Answer

Gravitational force between two objects of mass m1 and m2 at a distance r is :

F = (Gm1m2)/r2

gravitational force between the Earth and a mass m = (6.67*10-11 * 5.98*1024 * 4.2)/(6.37*103*103)2 = 41.286 N

gravitational force between the Moon and a mass m = (6.67*10-11 * 7.36*1022 * 4.2)/(3.76*105*103)2 = 14.58*10-5 N

gravitational force between the Sun and a mass m = (6.67*10-11 * 1.99*1030 * 4.2)/(1.5*108*103)2 = 24.78*10-3 N

Ratio = (24.78*10-3) /(14.58*10-5) = 169.89

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