Question

"if the earths mass were double what it is, how would the moons orbit be different?"

Answer 1

The motion of any orbiting object, at least in first approximation, can be defined by Kepler's laws.

The First law:
The orbit of any object can be defined as a conic section. (The simple version of this the orbit of any planet is defined an ellipse with the sun at the focal point

The Second Law:
The area swept out by a planet over equal time periods are always equal. Mathematically: \[\frac{dA_{1}}{dt_{1}}= \frac{dA_{2}}{dt_{2}}\] there are other ways of writting this as well just as \[\frac{d}{dt}\frac{1}{2}r^{2}\dot{\theta}= 0\]

and the Third Law:
This is the one you are most interested in at the current moment. Is that a planets semimajor axis, a^{3}, is proportional to the period, T^{2}. Howeve, the full equation is derived given by:

\[T^{2}=G\frac{4\pi^{2}}{M+m}a^{3}\]

Where m is the mass of the orbiting object(in this case the moon)and M is the central body(the earth). So, if we assuming we want to keep the period of the earth fixed, we wouldn't want to change our moon cycles, we would have to increase the semi-major axis. The new semi-major axis would be found by solving the above equation for a. Please notice that this is under the assumption that the period is kept constant. This is not necessarily true, and in reality it would be more approriate to answer the question in terms of the ratio of T and a. I hope this helped and wans't too complicated. ortherwise send me a chat and I'll walk you through it

Answer 2

did that help?

Answer 3

aka we will all die