Determine the magnitude and direction of the gravitational force exerted (a) on the moon by earth and (b) on earth by moon.
Earth's mass: 5.98 x 10^24 kg Moon's mass: 7.35 x 10^22 kg Distance between the Earth and the Moon: 384,999 km.
Any two bodies with a mass attract each other due to the gravitational force. The force exerted by each body on the other is towards its center of mass. In the case of spherical bodies the center of mass lies at the geometric center.
The force by which each of them is attracted towards the other is the same.
It is given by the Newton's law of universal gravitation as F = G*M1*M2/r^2, where G is a constant equal to 6.674*10^-11 N m^2/kg^2, M1 and M2 are the mass of the two bodies and r is the distance between them.
Here the mass of the Earth is 5.98*10^24 kg, the mass of the Moon is 7.35*10^22 kg and the distance between the Earth and the Moon is 384,399 km.
The force of attraction is: 1.985*10^20 N.
The Earth attracts the moon by a force equal to 1.985*10^22 N towards its center and the Moon does the same in the opposite direction.