There has been a similar question about planets' orbits being ellipses but the answer circulates around how the circle is a special type of orbit which doesn't really answer my question.

Elaborate Question: What are the factors or any mathematical idea or any law that suggests the elliptical orbits of a binary system? How does it explain the elliptical orbit concept? Or is it based simply on observations?

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/112668/2451 , physics.stackexchange.com/q/56657/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Jul 31, 2022 at 8:06
  • $\begingroup$ Hi, @Qmechanic, If this is a duplicate could you state why and how this relates to this because i know it involves Kepler's law but how is the question $\endgroup$ Commented Jul 31, 2022 at 8:07
  • 1
    $\begingroup$ Elliptical orbits were stated in Kepler's first law as the result of observations. Newton showed that Kepler's laws can be derived from his theory of gravity. $\endgroup$
    – Peter
    Commented Jul 31, 2022 at 8:09
  • 2
    $\begingroup$ astronomy.swin.edu.au/cosmos/c/Conic+sections "The four classic conic sections can be produced by the intersection of a plane through a cone. The four conic sections are the circle, ellipse, parabola and hyperbola." "Curiously, in astronomy, the Newtonian solutions to the two-body problem forces binary stars, planets and comets to trace a path that always corresponds to one of the four conic sections." For the existing planets, the probability they would be trapped in the symmetric in axis orbit of a circle is much smaller than the asymmetric of an elipse (answering title) $\endgroup$
    – anna v
    Commented Jul 31, 2022 at 8:26
  • $\begingroup$ What do you mean. usually? $\endgroup$
    – J.G.
    Commented Jul 31, 2022 at 13:14