Question

When the Moon orbits Earth, what is the centripetal force?

Answer 1

Gravity.

Explanation:

Any two objects will attract one another gravitationally with a force given by Newton's equation:

`F = G (m_1 m_2) / r^2`

where:

• `G` is the universal gravitational constant, usually referred to as "big G".

• `m_1` and `m_2` are the masses of the objects.

• `r` is the distance between the centres of mass of the two objects.

Notice that the gravitational force decreases in inverse proportion to the square of the distance between the objects.

If there were no force of gravity then the moon would tend to travel in a straight line. With gravity providing a centripetal force, that path is curved towards the Earth, resulting in a roughly circular orbit. In essence the moon is in continuous freefall towards the Earth.

Actually the moon and the Earth orbit around a centre which lies between the centre of the Earth and that of the moon. However, since the Earth is much more massive than the moon, that centre lies within the Earth (at a distance of `4670` km or so from the centre of the Earth).

Answer 2

There is no centripetal force between the Earth and Moon according to General Relativity.

Explanation:

Newton's laws of gravity and motion are a good approximation as long as the masses of the bodies are not too large and they are travelling at speeds significantly slower than the speed of light.

Newton describes gravity as a force when in fact gravity is not a force. In fact it is inaccurate to use the term force of gravity.

Anything with mass causes curvature of 4 dimensional spacetime. The three dimensional analogy is placing a ball on a stretched rubber sheet.

A body moving in the absence of an external force travels in a straight line. In 4 dimensional spacetime this is called a geodesic which is the shortest possible line between two points on a curved surface.

So, gravity is not a force. It is the curvature of spacetime. A geodesic in curved spacetime is not a straight line, it is a curve.

So, there is no force acting between the Earth and the Moon. The shape of the Moon's orbit is the shape of the geodesic of the Moon travelling through the curved spacetime caused by the Earth's mass.