## Gravatational Force between earth and moon

I was wondering, if the moon losses its mass at a constant rate and the earth gains mass at this constant rate (so the sum of there masses is equal), the force between them would stay the same would it not?

F = GMm/d²

What happens to the moon?

Does the moon move away, stay the same or come closer to the earth. Also would the effect of the moon losing mass mean that the tides of the sea seize to exist?

Thanks :)
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 I haven't done the math, but the better way to say it is the product of the masses is equal. Classically viewing it, the centripetal acceleration of the moon is dependent on the earth's mass, in which as the earth gets bigger, the needed acceleration would increase. The moon's orbit would get smaller and closer to the earth.
 Recognitions: Science Advisor The force obviously changes as the Newton equation shows. The moon probably comes closer. The tidal effect is complicated, since the loss of moon's mass and the decrease in d have opposite effects.

## Gravatational Force between earth and moon

Would the product of the masses decrease (while the sum stays the same). Therefore the force decreases thus the distance increases? Therefore the moon moves out of orbit?

Not sure that is right, but could you show me your reasoning for the moon to move closer. Is that because the earth exerts a greater force on the moon.

Thanks :)

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 Quote by thomas49th Would the product of the masses decrease (while the sum stays the same). Therefore the force decreases thus the distance increases? Therefore the moon moves out of orbit? Not sure that is right, but could you show me your reasoning for the moon to move closer. Is that because the earth exerts a greater force on the moon. Thanks :)
The force does decrease, as the product of the masses decreases as mass is moved from the smaller mass to the larger mass. The distance also decreases, as the speed needed fro orbit a a given distance (taking the mass of both bodies into account is found by:

$$V_o = \sqrt{\frac{GM^2}{r(M+m)}}$$

where M would be the mass of the Earth while m is the mass of the Moon. Note that while M+m remains constant, M increases as mass moves from M to m. Since we have to assume that the speed of m does not change, it would be less than the new speed needed to maintain that orbit and it will fall into a lower one.
 Hi, I'm not sure I fully understand it: "Since we have to assume that the speed of m does not change, it would be less than the new speed needed to maintain that orbit and it will fall into a lower one" are you saying the orbit speed of m around M is the same? also when you said: "M increases as mass moves from M to m" do you mean when the mass moves from m to M

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