Calculate the ratio of the magnitude of the gravitational force between an m = 4

Question

Calculate the ratio of the magnitude of the gravitational force between an m = 4.10 kg mass on the surface of the Earth due to the Sun to that due to the Moon. The mass of the Sun is 1.99×10^30 kg and the distance from the center of the Sun to the surface of the Earth is 1.50×10^8 km. The mass of the Earth is 5.98×10^24 kg. The distance to the center of the Earth from the surface is 6.37×10^3 km. The distance to the center of the Moon from the surface of the Earth is 3.76×10^5 km and the mass of the Moon is 7.36×10^22 kg.

Explanation / Answer

The Ratio is given by (M/R2)sun/(M/R2)moon

(M/R2)sun = 1.99×10^30/( 1.50×10^11 )^2 = 8.844x10^7

(M/R2)moon = 7.36×10^22 /( 3.76×10^8)^2 = 5.206x10^5

Therefore, answer = 169.88

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