Why are the orbit of planets usually ellipses? [duplicate]

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?

• Possible duplicates: physics.stackexchange.com/q/112668/2451 , physics.stackexchange.com/q/56657/2451 and links therein. Commented Jul 31, 2022 at 8:06
• 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 Commented Jul 31, 2022 at 8:07
• 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. Commented Jul 31, 2022 at 8:09
• 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) Commented Jul 31, 2022 at 8:26
• What do you mean. usually?
– J.G.
Commented Jul 31, 2022 at 13:14