The planetary motions do not all take place in the same plane and consequently the plane of the orbit of a particular planet must be specified with reference to some fundamental plane: the plane chosen is that of the earth's orbit and is called the plane of the ecliptic. Imagine a sphere drawn with the sun at the centre. The plane of the earth's orbit will cut the sphere in a circle (the ecliptic) and the orbital plane of any other planet will cut the sphere in another circle inclined at some definite angle to the plane of the ecliptic. The two circles intersect at two points N and M—called the Nodes. Let V denote a definite ref erence point on the ecliptic—the direction S V may be thought of as the direction of a particular star as seen from the sun. The point V is known as the "vernal equinox" or "First point of Aries"; it is not necessary here to specify it more particularly. The plane of the planet's orbit is completely specified—with ref erence to the ecliptic and the point V--by (i) the inclination of the planet's plane to the plane of the ecliptic and (ii) the posi tion of the node N with respect to the point V. The latter is evidently given by the angle subtended at the sun by the radii S V and S N, and this angle is known as the longitude of the node. One thing more requires to be done and that is to specify the orientation of the orbital ellipse in its plane; this is accom plished by specifying the direc tion of perihelion—in the figure this is indicated by the direc tion S A. The sum of the angles subtended at S by the arcs V N and N A is called the longitude of perihelion. It
should be noticed that there is an ambiguity as to the mean ing of the expression "longitude of the node" for there are two nodes N and M. If the upper hemisphere in the figure contains the north pole of the heavens, the radius vector of the earth's orbit moves in the direction S V towards S N as indicated by the arrow ; and if the radius vector of the planet moves in the direc tion S N towards S A, as indicated by the arrow, then N is called the ascending node and M the descending node and (ii) above more precisely should be "the longitude of the ascending node." The ambiguity consequently disappears.
To summarize ; a planet's orbit in space is completely speci fied by the six elements: (i) the semi-major axis, (ii) the eccen tricity, (iii) the time of perihelion passage, (iv) the longitude of the ascending node, (v) the longitude of perihelion, (vi) the inclination of the orbital plane to the plane of the ecliptic.
When the six elements of a planet's orbit are known the posi tion of the planet (the effects of the attractions of the other planets not being taken into account) with reference to the sun and the fundamental plane (the ecliptic) can be calculated for any future date by principles essentially contained in Kepler's laws. The earth's orbit also being known, the position of the planet in the heavens, as seen from the earth, can then be deduced.