Question

If the earth's mass were doubled what it is in what ways would the moon's orbit be different

Answer 1

The moons orbit would be faster or further away. As if mass is doubled, its gravitational force would also double.. So it has to be further away to keep its orbit.

Answer 2

One equation that gives us information about how a satellite moves around an object is the following one:

v^2 = (G*M)/R

Where V is the velocity of the satellite, G is the gravitational constant, M is the mass of the Earth in this case, and R is the distance between the satellite and the Earth.

If you double M, there are a range of probabilities, where the extremes are:

The velocity of the moon does not change:

In this situation we have:

v^2 = (G*2M)/R'

where R' is the new distance, if we want to restore the previous equation, here we must have R' = 2R, this means that the distance between the Earth and the moon is also doubled.

The other extreme is that the distance is not changed:

(v')^2 = (G*2M)/R = 2*v^2

where v' is the new velocity

Then we have that v' = √2*v will be the new velocity of the moon.

And there are the possibilities where both velocity and distance changes, which are a lot more.