system
Given the following post, respond as if you're commenting on Reddit:
human
Would an object with twice the mass (and size) of the moon, situated twice the distance away from Earth that the moon is now, have the same effect on the tides as the moon?

Not sure if this is Astronomy or Planetary Sci. I’ll change if it does not fit.
gpt
First of all, gravity falls off with the square of the distance. So an object twice as far away would only exert one quarter of the gravitational force. So this hypothetical object would have to be four times the mass of the Moon.

But there's more to it. The tidal force is a consequence not of the total gravity from the Moon, but rather the difference in gravity at the side of the Earth closest to the Moon compared to the side that is furthest away.

With a lighter, closer Moon this difference is larger than with a heavier, more distant Moon. This is why the largest contribution to the tidal force on Earth is from our Moon and not from the Sun, even though the force of gravity of the Sun on Earth is greater than that of the Moon.

The exact dependence between distance and tidal force is complicated, but the falloff of the tidal force is closer to the cube of the distance. That means that a hypothetical heavy Moon at the twice the distance would have to be about 8 times as heavy as our current Moon to replicate our current tidal forces.