290. _Recognition of a Telescopic Comet._--It is impossible to distinguish telescopic comets by their appearance from another class of heavenly bodies known as _nebulæ_. Such comets can be recognized only by their motion. Thus, in Fig. 322, the upper and lower bodies look exactly alike; but the upper one is found to remain stationary, while the lower one moves across the field of view. The upper one is thus shown to be a nebula, and the lower one a comet. [Illustration: Fig. 322.] 291. _Orbits of Comets._--All comets are found to move in _very eccentric ellipses_, in _parabolas_, or in _hyperbolas_. Since an ellipse is a _closed_ curve (48), all comets that move in ellipses, no matter how eccentric, are permanent members of the solar system, and will return to the sun at intervals of greater or less length, according to the size of the ellipses and the rate of the comet's motion. Parabolas and hyperbolas being _open_ curves (48), comets that move in either of these orbits are only temporary members of our solar system. After passing the sun, they move off into space, never to return, unless deflected hither by the action of some heavenly body which they pass in their journey. [Illustration: Fig. 323.] Since a comet is visible only while it is near the sun, it is impossible to tell, by the form of the portion of the orbit which it describes during the period of its visibility, whether it is a part of a very elongated ellipse, a parabola, or a hyperbola. Thus in Fig. 323 are shown two orbits, one of which is a very elongated ellipse, and the other a parabola. The part _ab_, in each case, is the portion of the orbit described by the comet during its visibility. While describing the dotted portions of the orbit, the comet is invisible. Now it is impossible to distinguish the form of the visible portion in the two orbits. The same would be true were one of the orbits a hyperbola. Whether a comet will describe an ellipse, a parabola, or a hyperbola, can be determined only by its _velocity_, taken in connection with its _distance from the sun_. Were a comet ninety-two and a half million miles from the sun, moving away from the sun at the rate of twenty-six miles a second, it would have just the velocity necessary to describe a _parabola_. Were it moving with a greater velocity, it would necessarily describe a _hyperbola_, and, with a less velocity, an _ellipse_. So, at any distance from the sun, there is a certain velocity which would cause a comet to describe a parabola; while a greater velocity would cause it to describe a hyperbola, and a less velocity to describe an ellipse. If the comet is moving in an ellipse, the less its velocity, the less the eccentricity of its orbit: hence, in order to determine the form of the orbit of any comet, it is only necessary to ascertain its distance from the sun, and its velocity at any given time.