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A comet that's bound to the sun and appears periodically is in an elliptical orbit.

A comet that whizzes through the solar system only once and then leaves

for good is in a hyperbolic orbit.

If the comet is periodic but with an exceptionally long period ... thousands

of years e.g. ... then we can't tell, from the small part of its orbit that we can

see, whether it's elliptical or hyperbolic.

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