(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.
liquid mirror telescope
semi-major axis (a)