Theoretical Orbits of Planets in Binary Star Systems
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In the next diagram, a planet has a retrograde orbit with a period p = 0.6. It is interesting that the planet completes an orbit in less time than the two stars take to complete their orbits. The planet's distance from the star system centre varies between d = 0.84 and d = 0.74.
The typical shape of the quasi-circular orbit is easy to see here. It comprises regular fluctuations to either side of a truly circular path. These fluctuations are synchronous with the alignment of the planet and the two stars.
When the planet and both stars are in conjunction, i.e. lined up in a straight line, the planet is at its maximum distance from the star system's centre.
When the planet is equidistant from both stars, the planet is at its minimum distance from the star system's centre.
In the next diagram, a planet has a retrograde orbit with a period p = 0.42. The planet's distance from the star system centre varies between d = 0.70 and d = 0.55. The variation in distance is much greater than in the previous example, because the gravitational field of the star system fluctuates more at this proximity.
In the next diagram, a planet has a retrograde orbit with a period p = 1. The orbit shape is a rounded square because the planet experiences exactly 4 conjunctions per orbit.
java animation
of the above orbit
In the next diagram, a planet has a quasi-circular orbit with a period p = 0.5. The orbit shape is a rounded triangle because the planet experiences exactly 3 conjunctions per orbit.
java
animation of the above orbit
In the next diagram, a planet has a quasi-circular orbit with a period p = 0.33. Note that even though the planet has an external orbit, it sometimes comes closer to the centre of the star system than does either star.
The minimum possible period for a planet with an external quasi-circular orbit will be determined by the actual physical sizes of the stars and planet. As we simulate orbits which take the planet closer and closer to the stars, eventually instability will occur because of tidal effects.
In the next diagram we re-examine the shape of some of the above external quasi-circular orbits, using a viewing frame which rotates with the star system, so that the stars appear to not move.
The numbers in the diagram state the period of each planet's orbit (relative to the period of the star system).
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Copyright 2001 S.Edgeworth