What is the other focus in an elliptical orbit?

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Elliptical orbits of planets in the Solar System have the Sun at one focus, while the second focus does not contain any mass or object. The discussion clarifies that gravity acts as a central force, allowing the velocity vector of a planet to be decomposed into components relative to its displacement from the Sun. It is noted that orbits are not perfectly elliptical but are approximately so, with slow wobbles in their planes due to gravitational perturbations, especially from larger planets like Jupiter. The necessity of considering a three-dimensional generalization of these orbits is questioned, with the conclusion that it is not essential for understanding basic orbital mechanics. Overall, the focus remains on the nature of gravitational forces and the dynamics of planetary motion.
ShadowDatsas
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Hello.
I've read in many books that the orbits of the planets of our Solar system are ellipses.
With the one Focus as the Sun.
Well, what is the other one? I mean every ellipse has two focuses...
 
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Yay! It's good enough to understand the half!
Thanks, now I see that there isn't something at the second focus. (like a mass or a something)
Thanks.
 
Hippasos said:
I guess there is generalization to 3D as well somewhere...

Or is that really necessary?

It isn't. Gravity is a central force. The velocity vector can always be represented as a sum of two vectors, one parallel to and the other normal to this displacement between the two bodies. The force between the two bodies is directed against the displacement vector between the two bodies. The bodies will always on the plane defined by the initial displacement and velocity vectors.

Planets do not really follow elliptical orbits. The orbits are instead approximately elliptical and the planes slowly (very slowly) wobble. The planets (particularly Jupiter) perturb the orbits of the other planets.
 

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