Theoretical Orbits of Planets in Binary Star Systems
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In the next diagram, the planet has an orbit around just one of the stars (its parent star). The distance between the planet and its parent star is very small relative to the distance between the two stars. At this relative proximity the gravitational field affecting the planet is almost the same as it would be if its parent star were a single star. So the planet has a simple elliptical orbit (circular in this example). The orbital period p = 0.042. We've shown a retrograde orbit. At relatively small distances like this, retrograde and prograde orbits are both viable.
However, as we examine relatively larger internal planet orbits, prograde orbits become increasingly unstable. The following orbits, which are stable in the retrograde direction, would all be impossible in the prograde direction.
In the next diagram, the planet has a retrograde internal orbit at a distance of approx d = 0.5 from its parent star.
In the next diagram, the planet has an internal orbit at a distance of approx d = 0.67 from its parent star.
The next two diagrams show a planet orbiting its parent star with a period p = 1. The orbit is quasi-circular around star A, but star A is moving in its own orbit too. The combination of these two motions with exactly the same period results in an ice-cream-spoon shaped orbit for the planet. As shown in the second diagram, the planet sometimes approaches the other star closer than it ever gets to its parent star.
java animation of the above orbit
In the next diagram we examine the shape of internal quasi-circular orbits by 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).
If we relax any of the conditions specified in the introduction, even more complex internal orbits arise.
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Copyright 2001 S.Edgeworth