In response to the intensive ongoing debate recorded in the Comments section of this site, I would like to endorse this clarification from a prominent physicist on the list:
The senior theory (essentially proven) is Newton's inverse square law for gravity. For a simple system, Kepler's Laws are a fallout of what a planetary solution looks like (for the simple case of a single planet circling a massive sun). For a complex situation (like a planet interacting with two suns, several planets, or whatever) you have to go back to Newton's law and solve a many-body problem which takes a computer. In this case Kepler's Laws are only an approximation, since they hold only for the simplest case.
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