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According to wikipedia and other sources, a planet and a star always move in a circular orbit around the common center of mass of the both bodies, in case of Earth and sun, this center of mass lies inside the sun. Therefore, Earth should orbit the sun in a circular orbit. So, my question is, why does the Earth orbits the sun in an Elliptical orbit?

And, if it does, and one focus is the sun, then what is the other focus?

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    $\begingroup$ i would suggest you to go through kepler's first law. That would answer your question. $\endgroup$ – Strikers Dec 18 '14 at 10:03
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According to wikipedia and other sources, a planet and a star always move in a circular orbit around the common center of mass of the both bodies ...

This is not true. In the absence of other gravitational sources, a planet and a star move in elliptical orbits about the common center of mass. Ancient scientists assumed circular orbits, but only because circles were somehow most pure. There were problems with this: It didn't match what those ancient scientists saw. So they modified these circular orbits by tacking on other circles. It was a mess.

Kepler cleaned this mess up by noting that the orbits of the planets are very close to elliptical rather than circular. This empirical result was later strengthened by Newton, who derived that elliptical orbits (not circular orbits) are a natural consequence of a force that follows an inverse square law. Gravitation is such a force.

The orbits of the planets about the solar system are not quite elliptical because planets are attracted to one another as well as to the Sun. Nonetheless, the orbits are still very close to elliptical. The Sun is more than 1000 times more massive than Jupiter. Jupiter, Saturn, and the other planets represent tiny perturbations on the nearly elliptical orbits of the planets about the Sun.

What about other perturbing effects, such as nearby stars and the Milky Way as a whole? These are immeasurably small. A passing star will perturb planetary orbits over the course of the tens of millions of years or more. The Milky Way as a whole has essentially no effect whatsoever. Theoretically, the effect most certainly does exist, but it is so small that it can be ignored, even over the lifespan of the solar system.

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  • $\begingroup$ "a planet and a star move in elliptical orbits about the common center of mass", is the common center of mass center of that ellipse? $\endgroup$ – Dheeraj Kumar Dec 18 '14 at 15:39
  • $\begingroup$ @DheerajKumar no, or rather, it's the center only in the case where the ellipse is a circle (a special case) $\endgroup$ – Stan Liou Dec 18 '14 at 15:40
  • $\begingroup$ Anyway, if one focus is the sun then what is the second focus? $\endgroup$ – Dheeraj Kumar Dec 18 '14 at 15:40
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    $\begingroup$ @DheerajKumar There's nothing special at the second focus, but there's a derivation of how to find it at Why are orbits elliptical instead of circular?. $\endgroup$ – Stan Liou Dec 18 '14 at 15:46
  • $\begingroup$ so orbit is elliptical basically due to conservation of angular momentum. $\endgroup$ – Dheeraj Kumar Dec 18 '14 at 15:57
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The trajectory of Earth's orbit is shaped not only by Sun's gravity. Earth's orbit is being changed by different sources of gravity as well, for example center of our galaxy. This is why it's not perfectly round.

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  • $\begingroup$ So, that means that the second foci of the elliptical orbit (one being the sun) of which kepler wrote is towards the center of the Milky Way. $\endgroup$ – Dheeraj Kumar Dec 18 '14 at 13:03
  • $\begingroup$ Precisely, this is a good explanation of this phenomenon: astro.washington.edu/users/smith/Astro150/Tutorials/Kepler $\endgroup$ – duke Dec 18 '14 at 13:41
  • $\begingroup$ @duke How can the second foci be the center of the galaxy? $\endgroup$ – Yashbhatt Dec 18 '14 at 14:24
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    $\begingroup$ -1. This answer is incorrect. $\endgroup$ – David Hammen Dec 18 '14 at 15:25
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    $\begingroup$ Hmm. We're currently close to perihelion (which will be on Jan 4), and the Sun is in or near Sagittarius, which is in the direction of the galactic core. So the second focus of the Earth's orbit around the sun is in the direction of the galactic core. I believe this is purely coincidental. Can you demonstrate that it's not? (The same effect should apply to the other planets.) $\endgroup$ – Keith Thompson Dec 18 '14 at 21:30

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