- #1
Alexander350
- 36
- 1
If you had two masses, [itex]m_{1}[/itex] and [itex]m_{2}[/itex], and you released them in space infinitely far apart, their kinetic energies would satisfy [itex]\frac{1}{2}m_{1}v_{1}^2+\frac{1}{2}m_{2}v_{2}^2=\frac{Gm_{1}m_{2}}{r}[/itex] if they met with a distance r between their centres of mass. This equation therefore tells you the velocities needed for the two bodies to escape the gravitational pull of each other, i.e. the escape velocities. So, why does the formula for the escape velocity of an object on Earth only include the kinetic energy of the object, and not the Earth itself? Is the kinetic energy of the Earth just negligibly small (because the conservation of momentum means its velocity is pretty much zero) and can therefore be ignored? Would it only be necessary if the two objects had similar mass?