A comet is first seen at a distance of(adsbygoogle = window.adsbygoogle || []).push({}); dAUs from the Sun and is travelling with a speed ofqtimes the Earth's speed.

Apparently it can be shown that ifq^{2}·dis 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, ε (eccentricity) is less than, equal to, or greater than 1 for an ellipse, parabola, and hyperbola respectively.

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# Hyperbolic, Parabolic or Elliptical Orbit?

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