Theoretical Orbits of Planets in Binary Star Systems
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So far we have looked at planets orbiting a simple binary star system (which satisfies the conditions defined near the beginning of this article). Can planets survive in more complex binary star systems?
In the next diagram we look at just one rather extreme example. It's a binary star system in which the stars have unequal masses, and eccentric orbits around each other. The planet has an eccentric retrograde external orbit. Moreover the planet has a significant mass. The ratio of masses of the planet and the two stars is 1:10:20. This orbit is more complicated than the previous examples, because the gravitational field is more complicated. However, the orbit is stable.
The planet perturbs the orbits of the stars with several effects. The centre of mass of the binary star pair orbits around the centre of mass of the entire trinary system. The orbital motions of the two stars around each other are not exactly elliptical. And the orbits of the stars experience apsidal advance.
The smallest ellipse is the orbit of the more massive star. The medium-size ellipse is the orbit of the less massive star. The large ellipse is the orbit of the planet.
Orbits in which a planet passes close enough to a star for tidal effects to be large will tend to be unstable.
Inclination of a planet's orbit relative to the orbits of the stars around each other would introduce a further complexity in a planet's orbit. This is beyond the scope of this article, except to say that this extra complexity is not necessarily destabilizing.
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Copyright 2001 S.Edgeworth