In space a comet's orbit is completely specified by six quantities called its orbital elements. Identifying comets and determining their orbits Up to the beginning of the 19th century, comets were discovered exclusively by visual means. Many discoveries are still made visually with moderate-size telescopes by amateur astronomers. Although comets can be present in any region of the sky, they are often discovered near the western horizon after sunset or near the eastern horizon before sunrise, since they are brightest when closest to the Sun. Because of the Earth's rotation and direction of motion in its orbit, discoveries before sunrise are more likely, as confirmed by discovery statistics.
Most comets are and remain extremely faint.
Today, a larger and larger proportion of comet discoveries are thus made fortuitously from high-resolution photographs, as, for instance, those taken during sky surveys by professional astronomers engaged in other projects. Several successive photographic observations of these faint moving objects are necessary to ensure identification and simultaneous calculation of a preliminary orbit. The best conic section representing the path of the comet at a given instant is known as the osculating orbit. It is tangent to the true path of the chosen instant, and the velocity at that point is the same as the true instantaneous velocity of the comet. Formulas representing the smooth variation of the nongravitational force with heliocentric distance are now included for many orbits.