First you have to make three observations of the sky location of the comet so that the comet has moved an appreciable distance in the sky. Then, these sky coordinates are translated into ecliptic heliocentric coordinates, and an ellipse is 'fit' through the three data points. As more observations are available, a better fit can be achieved. The dimensions of the ellipse give its inclination, size and period.
It generally requires a few days after discovery to have enough data for the preliminary orbit to be calculated. This preliminary orbit typically assumes that the comet is traveling in a parabolic orbit. That is, the comet has an infinite period (ie, it will never come back). We know this isn't true. All comets orbit the Sun and travel in ellipses around the Sun. For long period comets, such as Comet Lee, these ellipses are stretched so that they look long and narrow. The orbital period of such a comet is generally a thousand years or more. Because of this, a parabolic orbit (eccentricity or e = 1.0) is usually a good approximation to the real orbit.
A preliminary orbit is based on relative few observations and covers a tiny portion of the actual orbit. While the first orbital parameters are in the correct ballpark, they will change as new observations are made and included in the orbital solution. However, the changes become smaller as more and more observations are made and a larger arc of orbit is covered.
Copyright 1997 Dr. Sten Odenwald
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