Question

How far apart would two Earth sized planets have to be to have the same effect as the Moon on the Earth?

Answer 1

Two Earth sized planets would need to be 3,466,000 km apart to have the same tidal effect as the Moon.

Explanation:

Using Newton's equations of gravity, the gravitational force between two bodies is given by:

`F=(GMm)/r_2`

Where `G` is the gravitational constant, `M` is the mass of the Earth and `m` is the mass of the Moon.

So, for two earth sized planets to have the same gravitational effect as the Moon, the force between then need to be the same as that between Earth and Moon.

The Earth is `81.3` times the mass of the Moon. So, the square of the distance between the planets must be `81.3` times the distance between the Earth and the Moon. The Moon's semi major axis distance is 384,400km.

So the distance between the planets to give the same effect as the Moon is:

`r=384,000 * sqrt(81.3)=3,466,000 km`