# How would the transfer of mass from the Moon to Earth change the rotation, orbit and speed of the Moon and Earth?

I've read the creation of dams in Earth can change the speed of rotation of the planet because they reallocate the mass over the planet.

Let's suppose humans find a valuable mineral in the Moon and they start to transfer it in huge amounts to the Earth. How would the massive transfer of mass from the Moon to Earth, change the rotation, orbit and speed of the Moon and Earth.

Ok, so since possible repliers have been how much mass it would transfers, let's suppose I want to know the effects from any point between 0 to 1/10 to the mass of the moon. Since the effects would be different when 1% was transfered to the point to when 10% was transfered

• What is "massive" for you? This is quite important if the question is to be answered quantitatively. A thousand tons, a million tons, a billion tons, ten thousand trillion tons? If the last value seems "massive" to you, please be aware that it represents just a little more than 0.01% of the mass of the Moon... – AlexP Oct 3 '18 at 12:23
• I think you need to be more specific about how you plan to move this mass to the earth from the moon. This is important so that we can talk about where the energy comes from as well as where it goes. – Mathaddict Oct 3 '18 at 22:41
• @Mathaddict: Energy is not a conserved quantity in mechanics. On the other hand, momentum is... – AlexP Oct 4 '18 at 10:34
• @AlexP, is it your assertion then that energy cannot affect momentum? – Mathaddict Oct 4 '18 at 13:51
• @Mathaddict: Energy can obviously affect momentum, or else engines won't turn... – AlexP Oct 4 '18 at 14:19

## 1 Answer

Well, the lower the mass of the moon the closer it needed to be in order for it to be held by a null-sum of centripetal force and gravitational pull. But you might think that if the earth is heavier by that ammount obv the gravitational pull is the same again and nothing changes. Two objects attract each other with an equal ammount of gravitational force. Always. Gx((M1xM2)/(d^2)) shows us that that is not true. if both masses are 100 the product is 10 000, if you take 10 from one to the other its 90*110 which is a tad bit lighter. So while the moon would have to come slightly closer to still be in orbit it might just happen that it would fly of into space.

If you have a good PC try "Universe Sandbox". It's a fun game and you can try out all of stuff like that. What if the moon was lighter or the earth heavier and the sun would shrink or whatever. It will give u the answer and its a fun simulation of the universe

edit: or it needed to slow down for the centripetal force to be smaller

• This is handwaving. Handwaving has its uses, but elementary Newtonian mechanics is much too elementary to call for handwaving. Wait until the querent comes back and specifies how much mass is to be moved from the Moon to the Earth, and then we can easily compute the effects on the orbit of the Moon and on the rotation speed of the Earth. – AlexP Oct 4 '18 at 10:32
• @AlexP I don't think he wants it that precise or he would have asked precisely. I gave him an answer as precise as his question allowes it – Maritn Ge Oct 4 '18 at 11:11
• I updated the question. – Pablo Oct 4 '18 at 13:59