Two particles moving in a central potential

[Fibo112]

Homework Statement

Two particles move in a central potential. The potential has the form V(r1, r2)=-a/(/r1-r2/^1.5)...

Homework Equations

The Attempt at a Solution

I am having trouble understanding what it means for two particles to move in a central potential. From what I understand a central potential is a force field whose force on any given particle points in the direction of a specific point and whose magnitude only depends on the distance r from that point. Does V(r1,r2) mean the sum of the potential energies of the two particles? This doesn't seem to make much sense based on the definition of V(r1,r2).

 

[TSny]

Homework Statement

Two particles move in a central potential. The potential has the form V(r1, r2)=-a/(/r1-r2/^1.5)...

Just to be clear, do the / 's inside the parentheses represent absolute value? Do r1 and r2 represent position vectors?

I am having trouble understanding what it means for two particles to move in a central potential. From what I understand a central potential is a force field whose force on any given particle points in the direction of a specific point and whose magnitude only depends on the distance r from that point.

In this problem, "central force" means that each particle experiences a force from the other particle directed along the line connecting the particles (either attractive or repulsive). The magnitude of the force depends only on the distance of separation $| \vec r_1 -\vec r_2|$

Does V(r1, r2) mean the sum of the potential energies of the two particles? This doesn't seem to make much sense based on the definition of V(r1,r2).

$V(\vec r_1, \vec r_2)$ is the potential energy of the 2-particle system. It is not the sum of two potential energies.