# Orbits, ellipitical, circular, or ?

1. Sep 17, 2011

### flyingpig

In our solar system, it is ellpitical because we have one sun.

In a different solar system, could orbits go like an ellipsoid? How would the orbit change if there are more than one stars? If a star is purple light (hottest) and a red one is beside it (least hot), does thta mean that red star can orbit around that purple one?

2. Sep 17, 2011

### xts

??? Orbit must be (per definition) a 1-dim line, while ellipsoid is a 2-dim surface...

They could have very strange shapes, or even do not exist (i.e. the planet trajectory wouldn't be a closed line, or the planet would be finally shot out of the solar system)

Only simplest cases may be solved analytically, especially Euler's 3-body case, where two stars orbit around their centre of mass on circular orbit, then orbit of small planet moving in the same plane may be computed (http://en.wikipedia.org/wiki/Euler's_three-body_problem)

Other well-known simple case is a Lagrange solution to a system, where one star is much heavier than second (so the second only slightly perturbates the movement of planet in the field of the first, heavy one), and the orbit of a planet is synchronous with orbit of lighter star.

There are no general solution to other such systems, even for those cases where two stars orbit their centre of mass over elonged ellipse.

Colour (or temperature) of stars makes no difference. Only masses of the stars. They always orbit their common centre of mass - you may say that one orbit another only in case when one is much heavier than second.

3. Sep 17, 2011

### Janus

Staff Emeritus
As an example, here's what the orbit of such a planet might look like. The yellow dot is a sun-sized star, the red circle the orbit of a small red dwarf (~.05 solar mass) orbiting it, and the blue line the orbit of the planet.

Notice how the planet's orbit waves in and out due to the perturbing effect of the Red Dwarf.

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