Strategy for drawing equipotentials

[etotheipi]

Homework Statement

Two equal masses M are separated by a distance of 6r. Sketch the following equipotentials: -10GM/3r, -2GM/3r, -GM/3r

Relevant Equations

$$V=-\frac{GM}{r}$$

The only one that I can see is for the potential $$V=-\frac{2GM}{3r}$$ since the midpoint of the two masses satisfies this equation. The only other useful inference I can make is that the most negative potentials closes to the surface of either planet, and the lowest potentials will be far away from the system.

What is the general technique you would use to do this question? One strategy I thought of was to notice the second equipotential contains the middle point, so the first equipotential actually consists of two loops within this 'dumbbell' and the second is entirely around the dumbbell equipotential. This isn't too rigorous, so I was wondering if there was a more systematic way of going about this? Thanks

 

[haruspex]

Homework Statement: Two equal masses M are separated by a distance of 6r. Sketch the following equipotentials: -10GM/3r, -2GM/3r, -GM/3r
Homework Equations: $$V=-\frac{GM}{r}$$

The only one that I can see is for the potential $$V=-\frac{2GM}{3r}$$ since the midpoint of the two masses satisfies this equation. The only other useful inference I can make is that the most negative potentials closes to the surface of either planet, and the lowest potentials will be far away from the system.

What is the general technique you would use to do this question? One strategy I thought of was to notice the second equipotential contains the middle point, so the first equipotential actually consists of two loops within this 'dumbbell' and the second is entirely around the dumbbell equipotential. This isn't too rigorous, so I was wondering if there was a more systematic way of going about this? Thanks

That looks like a good basis for a sketch. You could also identify the points where the curves cross the line of centres.