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F = ma = GMm/r^2

a = GM/r^2

In the above equation, the small m's cancel out to give a constant acceleration due to gravity from the perspective of big M. I consider a planet and a small moon (little m) a certain distance away from the planet, (assuming small moon is not in motion or in orbit i.e. it will just fall towards the planet).

Normaly we would say the moon would fall towards the Earth with the acceleration defined above, in the same way as an object on the planet, independant of the mass of the object.

But from the small moons perspective we can use the above equation to say it will attract the planet towards it with a certain acceleration derived in the same way (a smaller acceleration).

Is the correct interpretation of this to say the accelerations cancel? or add together ? Both values for the acceleration of the moon towards the planet cannot be true at the same time.

What if the moon is the same size as the planet? then does the moon fall towards the planet whilst the planet towards the moon adding the accelerations?

If the moon is more massive than the planet then surely the planet would fall to the moon.

If i could "hold" the planets apart and they had the same mass/diameter would there be a mid point between them where i could place an object which would be stationary because the forces towards each planet are of equal strength ?

I am very confused about this and do not know how to explain things mathematically

Any help would be greatly appreciated,

Matt