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Over thousands of years, the eccentricity of the Earth's orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets

Newton is credited with understanding that the second law is not special to the inverse square law of gravitation, being a consequence just of the radial nature of that law; while the other laws do depend on the inverse square form of the attraction. Carl Runge and Wilhelm Lenz much later identified a symmetry principle in the phase space of planetary motion (the orthogonal group O(4) acting) which accounts for the first and third laws in the case of Newtonian gravitation, as conservation of angular momentum does via rotational symmetry for the second law.

Just bumping this to the top; are we agreed that the correct explanation for the elliptical shape of the planetary orbits in our solar system is owing to gravitational interactions between the orbiting bodies?

If the solar system was created from rotating gas that became the sun and planets then the orbits should be round.

Why do planets have elliptical orbits?

if the sun caught in its gravity field objects that became the planet the planets' orbit should have been in on random plane and different direction

Sorry people, but I'm of reasonable intelligence and I don't understand a fraction of what has been written above.I've really like to get a clear explanation for this phenomenon here, because I come across a lot of substandard answers to this question across the web, so it would be good to set the record straight.Can we work together to do this?

If the solar system was created from rotating gas that became the sun and planets then the orbits should be round.if the sun caught in its gravity field objects that became the planet the palnets' orbit should have been in on random plane and different direction rather then on the same plane (almost) and rotating in the same direction.

If the total energy E pf the planet orbiting a star is related to the shape of the orbit then E < 0 then the orbit is an ellipseE = 0 then the orbit is a circleE > 0 then the orbit is a hyperbolaSo you see the total energy has to be exactly equal to E for the orbit to be exactly a circle.If the orbit is a hyperbola then the planet, or what have you, will have escaped from the solar system a very long time ago.

All true, but nobody yet has shown that the orbit has to be a conic section (which the conservation of angular momentum demands).

The above list omits the trivial cases of zero angular momentum, that the orbit is a straight line (into the sun - crash) and an even more obscure one, the point at the centre of the sun.

Quote from: MolonLabeAll true, but nobody yet has shown that the orbit has to be a conic section (which the conservation of angular momentum demands).Circles, ellipses and hyperbolas are all conic sections

You mention the hyperbola. That is no more of an orbit than a straight line is.

And you still have not answered the question Why do planets have elliptical orbits?. You have explained why it is the preferred conic section, but not why it is a conic section.

A straight line into the Sun is not an orbit.

Quote from: MolonLabeYou mention the hyperbola. That is no more of an orbit than a straight line is.It's considered an orbit in physics parlance. Please learn the terminology at:https://en.wikipedia.org/wiki/Orbit [nofollow]It's referred to as an open trajectory and is a conic section. A straight line isn't.Quote from: MolonLabe And you still have not answered the question Why do planets have elliptical orbits?. You have explained why it is the preferred conic section, but not why it is a conic section.I already told you why. And your comment about "preferred conic section" is meaningless. I've correctly explained everything that the OP wanted to know. I have no desire to talk about irrelevant, and in this case erroneous, semantics. I really don't see why you're making a big deal out of this. In any case the problem is your ignorance in the language of the physics of gravitation and Keppler's laws and the orbits of planets/asteroids/comets etc.

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?

Conic sections were considered by Thomas Harriot who corresponded with Kepler via one of Keplers associates. In the Harriot papers there is evidence that Kepler passed on work he had done on the orbits since Harriot showed the parabolic nature of the orbits of comets. Harriot also observed the moon and sunspots through a telescope and produce illustrations of both. I didn't read this on wikipedia. I researched it personally. I have a microfilm of the Harriot papers which I transferred to CD and passed to other researchers. 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? We're here to help each other. It isn't a competition. You don't get a prize.

Quote from: jeffreyH on 09/10/2015 05:39:26I 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 ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN. (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.