What Would Happen to the Orbit of the Moon if it Were Twice as Massive?

Question:  If the Moon was twice more massive and if it had the same orbital speed, would its orbit change?  Further from Earth (because of the centrifugal force), or closer to Earth (because of the gravitational force) or the same (because of the same orbital speed)?  Thank you in advance.  — Chris

Answer:  Newton’s law of universal gravitation tells us that the force between to masses is given by:

Fg = GMm/r^2

…where G is the universal gravitation constant and in our case M is the mass of the Earth, m is the mass of the Moon, and r is the distance between the Earth and Moon.  The Moon orbits the Earth without falling into the Earth (thus succumbing to Newton’s universal law of gravity) by counteracting this gravitational force with an equal an opposite centripetal force:

Fc = mv^2/r

If we set Fg = Fc we get:

GMm/r^2 = mv^2/r

Solving for v, the orbital velocity of the Moon, we get:

v^2 = GM/r

So, as you can see, the mass of the Moon (m) does not come into play.  The orbit would not change.

Jeff Mangum

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