ascending node of the comet, and thence along the comet's orbit, in the direction of the comet's motion, to the comet's perihelion.
These definitions may perhaps be elucidated by the following statement. Imagine a perpendicular to the plane of the ecliptic, erected from the Sun. Then to an observer situated North of the ecliptic in that perpendicular, the motion of the Earth will be contrary to the hands of a clock, and longitudes in the Earth's orbit will increase in that direction. Now consider a comet's orbit; imagine a perpendicular affixed to it in such a way that when the inclination of the orbit to the plane of the ecliptic is i, the inclination of the perpendicular shall be (i + 90°); and suppose an observer so situated in the perpendicular that when i = 0° he shall be North of the ecliptic. Then, according to the old system of elements, for all possible values of i the observer will remain North of the ecliptic, and the motion of the comet will appear to him as contrary to the hands of a clock when Direct, and with the hands of a clock when Retrograde; but according to Gauss's system he will be North of the ecliptic when i is less than 90°, South of it when i is greater than 90°, and to him the apparent direction of the comet's motion will always be contrary to the hands of a clock.
Whichever system is adopted, from this point of view π will always increase contrary to the clock, and to find the intersection of the plane of the comet's orbit with the plane of the ecliptic, or, in other words, the line of the nodes, the observer must set off ω in the direction of the hands of a clock, from the perihelion of the orbit.
Cometary orbits cross the ecliptic at all sorts of angles between 0° and 90°. A small inclination (say, under 15°) may often be interpreted as a sign of periodicity,[1] because all the short-period cornets have small inclinations. By moving so near the ecliptic their chances of being "captured" by planets is great. On the other hand, a comet with a large inclination (say 70° to 90°) runs small risk of being "captured", because
- ↑ Because all the planets which have are periodical bodies (so to speak) small inclinations; except a few minor planets.
