I know Pete and also know that he is knowledgeable in physics. Why would you even require him to provide such a derivation? If you think you know more then why not just post it?

I was merely commenting that he claimed to have explained why the orbits are ellipses, when in fact all he said was effectively "because Kepler said so". The OP might or might not be satisfied with that, and the tone of your post suggests that you think it is sufficient. If that is the expected level of explanation here, then I'm sorry to waste everybody's time, but I personally don't think it's satisfactory without the mathematical derivation (which I assumed would automatically be given somewhere).

As I mentioned in a post above which nobody appears to have read, the orbital motion of a planet is determined by the law of conservation of angular momentum. This is all nicely explained in the link you give above, or

http://farside.ph.utexas.edu/teaching/301/lectures/node155.htmlhere [nofollow]. (c.f. formula 582)

Because the force on the planet is always directed to one point, the centre of the sun, the angular momentum of the planet is constant. This alone determines that the orbit is a conic section, and despite PmbPhy's claim that I am ignorant of the laws of gravitation, I do know that the actual size of this force is not important in determining that. He also took me to task for suggesting that a planet could have a straight line trajectory. Whether this qualifies as an orbit or not, the fact is that in the hypothetical instance of a planet being introduced with zero angular momentum, the trajectory would be a straight line into the sun. I mentioned this for the sake of completeness to show that theoretically all conic sections are possible for orbital motion, that's all.