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

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.

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.