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If two bodies are orbiting around a central center of gravity, how does Kepler’s first law (the one regarding the ellipse) apply?

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One has to realize that Kepler's laws are a mere approximation.

The motion of planets around the sun is a two-body problem. In case of such two-body problems, both the bodies revolve around the center of mass. But it turns out that Sun is much much heavier than the planets. So the center of mass of the system is very close to the Sun and Hence it is a good approximation to consider just the planet to be moving around Sun.

To get a detailed idea of this problem, I would suggest you to read http://en.wikipedia.org/wiki/Two-body_problem or a text book on advanced Classical Mechanics.

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