Originally Posted by **assaftolko** in the solution they say that the potential gravitational energy of this system at the beginning is -Gm*m/r0. |

Right - the system consists of two stars, and both together have this PE.

Originally Posted by **assaftolko** this is the potential energy of each one of the stars, so isn't this suppose to be doubled for the whole system? |

No - the PE of each star is not GM^2/R separately. The mistake in thinking that both stars start with PE = Gm^2/r0 is that the derivation of that equation is based on the energy required to separate one object from the other a distance r0. Imagine that you hold star 1 steady wh1le moving star 2 away from it - let's call this case 1. Energy is force times distance, so star 2 requires energy to move it distance r0 while star 1 is stationary (and hence star 2 doesn't gain or lose PE). The total change in PE

__for the system__ is GM^2/r_0.

Alternatively consider case 2 - suppose the two stars begin life touching, and then you move them apart by having each move a distance ro/2 in opposite directions. If we define x as the distance each has moved, then the gravitational force betwen them at any point is GM^2/(2x)^2, and the energy required to move each to r0/2 is (1/2)GM^2/r0. Hence each gains half the PE of case 1, but the total change in PE for the system is the same.

One thing to remember is that PE is not an absolute number - unlike KE there really is no place where PE=0. What we must be careful to talk about is the

__change__ in PE from one state to another, not an absolute value for PE in either state. It's a subtle distinction, but it's one reason why you can't "add" the PE of two different objects unless you know that they both have the same starting reference point.