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Conic Section

(orbit shapes, like the intersection of a plane and cone)

Conic Section is a term for a set of shapes or curves that happen to describe the shape of orbits and interactions between two objects interacting with an force proportional to their distance-of-separation squared (e.g., Gravity, or the attractive electric force), and can be described by equations consisting of second degree polynomials (up to square terms). These shapes or curves happen to match those created by the intersection of a plane with a cone.

  • Ellipse - the shape of a "bound" orbit, generated by a plane intersecting the cone such as to create a circuit.
  • Circle - special case of an ellipse, generated if the plane is perpendicular to the axis of the cone.
  • Hyperbola - a curve an object follows if passing another object fast enough to continue away from it, generated by a plane that intersects a cone forming an infinite, "open" curve.
  • Parabola - similar to a hyperbola: the shape of the curve if the passing object is moving exactly at the other object's escape velocity; the shape generated if the intersecting plane is parallel to a straight line along the cone from its point.

Points and lines are also special cases, which correspond to two objects attached by gravity, and to an object dropping straight into another.


Referenced by:
Keplerian Orbit