Question

The mass of Earth is 5.97 × 1024 kg, the mass of the Moon is 7.35 × 1022 kg, and the mean distance of the Moon from the center of Earth is 3.84 × 105 km. Use these data to calculate the magnitude of the gravitational force exerted by Earth on the Moon.

Answer 1

Mass of the Earth, ME = 5.97 X 10²⁴ kg

Mass of the Moon, MM = 7.35 X 10²² kg

Distance between the Earth and the Moon, d = 3.84 X 10⁵ km = 3.84 X10⁸ m

The magnitude of the gravitational force exerted by Earth on the Moon,

F = G M_E M_M / d² where G = Gravitation constant = 6.67 X 10 ^-11 m³ kg^-1s^-2

= (6.67 X 10 ^-11 m³ kg^-1s^-2 )X (5.97 X 10²⁴ kg ) X ( 7.35 X 10²² kg ) / (3.84 X10⁸ m)²

= 1.9848 X 10²⁰ N (Ans)