# Central force motion

w3390

## Homework Statement

Sketch the elliptical and hyperbolic orbits two objects make around each other if their masses are equal. Next to each, sketch the equivalent one-body orbit.

## The Attempt at a Solution

For the elliptical orbit, I just drew two ellipses that overlap in a venn diagram sort of fashion where the center of mass is midway between the two objects.

I am confused about the equivalent one-body orbit. The system can be reduced to a single object of reduced mass $$\mu$$ but I don't understand how to figure out its path.

For the hyperbolic orbit, wouldn't it just look the same as the elliptical orbit except with a higher eccentricity?

I have the same confusion when trying to deal with the path of the reduced mass in this one too.

If anyone can help clarify to me how I can visualize the sketches, I would greatly appreciate it.