Gravitational Potential Energy - Further=Smaller?

[wavingerwin]

I recently looked at wikipedia for gravitational potential energy

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^-2r
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

 

[Doc Al]

I recently looked at wikipedia for gravitational potential energy

For two masses; M and m, and distance; r between their centres,
gravitational energy; E_p is:

E_p=GMMr^-1

You left out an all-important minus sign:
GPE = -GMm/r.

GPE increases as they separate to a maximum value of 0 at infinity.

 

[wavingerwin]

You left out an all-important minus sign:
GPE = -GMm/r.

GPE increases as they separate to a maximum value of 0 at infinity.

Ah, i see :shy:

So, if there are two masses, 5E+6 kg and 10E+5 kg, separated at 50 m at their centres
hence: GPE of the system is -6.67 Joules

does this mean to move from r=infinity to r=50m it has lost 6.67Joules of potential energy
converted to EK?

 

[cjl]

That is correct (I didn't do the calculation to check though, so I'm assuming you got the value right).