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.

If two stars are gravitationally bound, then their orbits are always either elliptical or circular, and in direct proportion to each other. This is Kepler’s first law of planetary motion.

The majority of comets are in hyperbolic or parabolic orbits.
Credit: Robert Jones (SAO student)

If a comet falls from a great distance, with no initial velocity the path is parabolic, whereas if a fly-by occurs where the initial velocity is significant, the path is hyperbolic.