Orbits of objects of equal mass

[emergentsystem]

What basic types of stable orbits are there for sets of objects of equal mass?

For example,
with one object it would just be stationary,

with two objects they would rotate at equal speed around a common centre with a constant distance between them (and more complicated stable orbits where the distance oscillates).

What about with three objects and more?

I assume for each set there would be an orbit where each object moves around the common centre of gravity in some fashion, such that from the perspective of each object the movement of the other objects is the same. What other types of basic stable orbits are there?

What would be the best way to generalise all the types of orbits for each number of objects?

Is there a way to visualise these types of orbits?

If anyone can provide any other examples at all, or answer any of these questions, that would be great.

 

[Jano L.]

Orbits of three or more bodies that attract each other via gravitational force may be very complicated.

There are some special cases for which three or more bodies can follows some simple orbits, like the motion of Moon and Earth in the reference frame of the Sun.

Perhaps here you can find some interesting reading on the topic:

https://en.wikipedia.org/wiki/N-body_problem