Calculate the magnitude of thegravitational force between the Earth and an m = 3

Question

Calculate the magnitude of thegravitational force between the Earth and an m = 3.10 kg mass onthe surface of the Earth. The distance to the center of the Earthfrom the surface is 6.37×103 km and the mass ofthe Earth is 5.98×1024 kg. Calculate the magnitude of the gravitational force between theMoon and an m = 3.10 kg mass on the surface of the Earth nearest tothe moon. The distance to the center of the Moon from the surfaceof the Earth is 3.76×105 km and the mass of theMoon is 7.36×1022 kg.
Calculate the ratio of the magnitude of the gravitationalforce between an m = 3.10 kg mass on the surface of the Earth dueto the Sun to that due to the Moon. The mass of the Sun is1.99×1030 kg and the distance from the center ofthe Sun to the surface of the Earth is 1.50×108km. Calculate the magnitude of thegravitational force between the Earth and an m = 3.10 kg mass onthe surface of the Earth. The distance to the center of the Earthfrom the surface is 6.37×103 km and the mass ofthe Earth is 5.98×1024 kg. Calculate the magnitude of the gravitational force between theMoon and an m = 3.10 kg mass on the surface of the Earth nearest tothe moon. The distance to the center of the Moon from the surfaceof the Earth is 3.76×105 km and the mass of theMoon is 7.36×1022 kg.
Calculate the ratio of the magnitude of the gravitationalforce between an m = 3.10 kg mass on the surface of the Earth dueto the Sun to that due to the Moon. The mass of the Sun is1.99×1030 kg and the distance from the center ofthe Sun to the surface of the Earth is 1.50×108km.

Explanation / Answer

Mass m = 3.1 kg

Mass of earth M = 5.98 * 10 ^ 24 kg

Distance of the center of the earth from the surface r =6.37 * 10 ^ 6 m

Gravitational force F = GMm / r ^ 2

Where G = Gravitational constant = 6.67 * 10 ^ -11 N m^2 /kg^ 2

Distanc eof the center of the moon from the surface of theearth r ‘ = 3.76 * 10 ^ 8 m

Mass of moon M ‘ = 7.36 * 10 ^ 22 kg

Gravitational force of moon F ‘ = GM ‘ m / r‘ ^ 2

Plug the values weget  F ‘ = 1.076*10^-4 N

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