# A change in the mass of the moon [closed]

Would a change in the mass or radius of the moon have any effect on its speed?

When asked this question in an assignment, I stated that it did not. My reasoning being that a change in the mass or radius of the moon would in no way change the acceleration or velocity of the moon. The moon would travel along the same path, the only difference being that the gravitational force being exerted by/on the Earth and Moon would be of a lesser magnitude. As the mass of the Moon decreases by ½, does the gravitational force.

F=ma

½F=½m*a

The original gravitational force being exerted is double that of the new gravitational force

2(G MiMii/r2)=G Mi(1/2Mii)/r2

I got this answer wrong and I am unsure why. Was I wrong in my approach? Are there other forces that I should have taken into account when coming to my conclusion?

Edit:The mass of the moon simply vanishes.

## closed as off-topic by Peter Shor , Brandon Enright, tpg2114♦, Qmechanic♦Dec 3 '13 at 0:58

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• Because mass is conserved, there is no physical way to change the mass of the moon without removing part of it. And if you remove part of it, whether the speed changes depends on how you remove part of it. So you're asking about an impossible scenario. On the other hand, a change in the radius would not have any effect on its speed. – Peter Shor Dec 2 '13 at 21:30