Let the particle of mass m_1 is situateted at the orgin (0.0) and the other particle of mass m_2 is on the x-axis at x distance appart from the first particle. The force of gravitational attraction on the 2nd particle is F(x)=(Gm_1m_2)/x^2
Where G = Gravitational constant.
The work done to displace the 2nd particle infinitesimilly small distance dx towards the first one is given by
dW=F(x)dx
So by integrating in the limit (ootor) we get the gravitational potential energy of the system when they are r distance appart
Hence
W=int_(oo)^rdW=int_(oo)^rF(x)dx
=(Gm_1m_2)int_(oo)^r1/x^2dx
=-(Gm_1m_2)[1/x]_(oo)^r
=-(Gm_1m_2)/r
