The moon (7.35 x 10^22 kg) is 3.85 x 10^8 m from the earth and orbits around it in a circle. a) if the period of the moon is 27.3 days, how fast is it moving in m/s? b) find the centripetal force that the earth exerts on the moon. c) identify the type of force that is the centripetal force.

a) Speed of the Moon: 1025 m/s

The speed of the moon is equal to the ratio between the circumference of its orbit and the orbital period:

where

is the radius of the orbit of the Moon

is the orbital period

Substituting into the formula, we find

b) Centripetal force:

The centripetal force acting on the Moon is given by:

where

is the mass of the Moon

is its orbital speed

is the radius of the orbit

Substituting into the formula, we find

c) Gravitational force

The only relevant force that acts on the Moon, and that keeps the Moon in circular motion around the Earth, is the gravitational force exerted by the Earth on the Moon. In fact, this force "pulls" the Moon towards the Earth, so towards the centre of the orbit of the Moon, therefore it acts as source of centripetal force for the Moon.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach