second sight:
i read that comet lulin is on a parabolic orbit and that this may be the first time it has entered the inner portion of the solar system. is it orbitng the sun or is it passing through our solar system just once?
A perfectly parabolic orbit is statistically impossible. Its eccentricity would have to be precisely 1. A nearly parabolic orbit would actually have an eccentricity a little less than 1 (elliptical and closed, thus orbiting the Sun) or a little more than 1 (hyperbolic and open, thus a temporary visitor). Although that just considers the simplified two-body problem of Sun and comet. Perturbations due to planets complicate the situation and cause comets’ orbits to differ slightly from perfect conic sections. Those perturbations can also cause a comet’s orbit to switch either way between an ellipse and a hyperbola.
If Comet Lulin originated from beyond the solar system, I suspect it would have been detected that its orbit is slightly hyperbolic. Since that is not the case, it probably has orbited the Sun in the very deep reaches of the solar system for eons before being gravitationally disturbed by a star or other object. That could have it sent it hurtling toward the Sun in a new orbit. If that new orbit is still elliptical, the comet will remain in the solar system. If it has become hyperbolic, then bye bye.