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For two masses; M and m, and distance; r between their centres,

gravitational energy; E

_{p}is:

E

_{p}=GMMr

^{-1}

With this, the further away the masses, the smaller the potential energy the system has

But this does not make sense to me because the further away the masses are,

the more kinetic energy they will collide with (after accelerated for some time due

to gravitational force between the masses).

Other than gravitational potential energy, no other energy can be converted to this

kinetic energy. Hence, the fact that GPE is small for further masses contadicts with

the large KE they will collide with.

Can somebody explain?

more:

The model E

_{p}=GMMr

^{-1}seems not right to me

because if it is derived from:

W=Fd

W=GMMr

^{-2}r

W=GMMr

^{-1}

E

_{p}=GMMr

^{-1}

therefore the gravitational force throughout the acceleration of the two masses

will be constant, whereas in real life it will not be, because the force will

be bigger and bigger as the masses come nearer and nearer.

Please help. Thank you