Hyperbolic, Parabolic or Elliptical Orbit?

[cj-redux]

A comet is first seen at a distance of <i>d</i> AUs from the Sun and is travelling with a speed of <i>q</i> times the Earth\'s speed.

Apparently it can be shown that if <i>q</i>²·<i>d</i> is greater than, equal to, or less than 2, then the comet\'s orbit will be hyperbolic, parabolic or elliptical respectively.

Any idea how this can be shown??

I know that, in general, &#949; (eccentricity) is less than, equal to, or greater than 1 for an ellipse, parabola, and hyperbola respectively.

[Fidelis Adhika]

The orbit\'s eccentricity is given by: sqrt (1 + 2 E L^2/(m C^2))
L = angular momentum E = total energy
m = reduced mass of the system
C = G M m

Try it.