# Work done by gravity on a ball & the ball on earth

I have studied today that if a ball was to fall a certain height, then the work done by gravity on the ball would equal the work done by the ball's equal and opposite gravitational pull.

By $W=Fd$, this means that the earth must travel the same distance as the ball.

So if the ball falls 300 meters, the earth would eventually rise 300 meters in the direction of the ball's gravitational pull?

Can you please give me your input on this particular matter because I don't understand it well ?

Just to expand on vaaaaaal's answer, let's simplify this very slightly by assuming that the ball falls at it's average fall velocity $v$ for the whole height $h$ over a time $t$. Obviously, $v = \frac{h}{t}$. Then, we know that total momentum is conserved, so the Earth must fall up with speed $v_{e} = \frac{m}{M_{e}}v$. Thus, over the whole time of falling, the earth moves a distance $d = v_{e}t = \left(\frac{m}{M_{e}}v\right)\frac{h}{v} = h \left(\frac{m}{M_{e}}\right)$. Since the forces are the same, the work done on the earth is smaller by a factor of the ratio of the masses of the ball and the Earth.