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As we know in order the earth to make this elliptical movement around the sun it needs two foci as we know from the first law of Kepler. The first foci is the sun. So my question is what is the other foci?

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marked as duplicate by sammy gerbil, Jon Custer, stafusa, John Rennie newtonian-mechanics Sep 28 '17 at 14:56

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The second focus is... a point in space. An orbit (by Kepler's laws) is not symmetric between the two foci, but the planet travels faster when near the sun (equal area swept out in equal times) and slower when far from the sun. No similar relation holds with respect to the second focus.

An ellipse is a kind of generalized circle, generated by not one central point and a rule, but by two points and a rule. An orbit, while having the ellipse shape, also has a time-dependent planet position, and only the shape, not the orbit, respects that second focus.

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  • $\begingroup$ I think it's disingenuous to call an ellipse "a kind of generalized circle". Rather, a circle is a specialized ellipse, which itself is a closed form of a conic section. Can you explain that last sentence about the orbit not respecting the second focus? $\endgroup$ – Floris Sep 27 '17 at 12:52
  • $\begingroup$ The sun position is a vertex of a construction, in Kepler's second law of orbital dynamics, which states that the orbiting object sweeps out, in any time interval, the same area. That area is bounded by a sector of the orbital path, and the beginning and ending radial displacement line segments which connect the planet to the sun. That law only applies to the sun, not to the 'other' focus. $\endgroup$ – Whit3rd Sep 28 '17 at 11:16

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