GRAVITATIONAL MOTION OF TWO BODIES

                Here I shows the advance of theoretical calculation over experimental calculation using a simple event.
All you know the experiment of Galileo, to show that all bodies of different masses will fall simultaneously without depends the mass.
          But it doesn't true the heavier mass reach at ground first. This argument cannot prove using experiment.
Consider two  bodies of mass M & m separated withe distance of 'd'. According to the Newton's gravitational law two bodies approaching to their center of mass of system.

The acceleration of mass M,                                              

             g₁ = (1/M) [G (Mm)/r²];

The acceleration of mass m,

             g₂ =- (1/m) [G (Mm)/r²];

the resultant acceleration is g = g₁-g₂ = {(1/m)+(1/M)} [G (mM)/r²]
                                         g = [G (m+M)/r²]

From the above equation you can find the gravitational acceleration depends the masses of the body.
consider two masses m, m'. If the mass of earth is M then,
                                        g = [G (m+M)/r²];
                                  g’  = [G (m’+M)/r²) 

 ^{if  m'> m then g'>g, ie. m' attain faster than m.}

^{This give that acceleration of two bodies depends their mass.} 

^{Then how we can say Galileo's experiment is true.}