of Perihelion Passage is generally not given, but left to be inferred from the other.
π = Longitude of the Perihelion, or the longitude of the body when it reaches that point. In the case of a comet (or planet), this is measured along the ecliptic from the vernal equinox to the comet's ascending node, and thence along the comet's (or planet's) orbit to its Perihelion; in the case of the Earth, it is measured along the ecliptic from the vernal equinox to the Perihelion. [Crommelin has drawn attention to the fact that some founts of Greek type have the small Pi in this shape (ϖ) instead of the common (π). This anomalous Pi too nearly resembles the Omega (ω) employed in stating the elements of an orbit: hence the risk of confusion.]
Ω = Longitude of the Ascending Node of the body's orbit as seen from the Sun (or Primary); measured on the ecliptic from the vernal equinox to the ascending node of the orbit.
i = Inclination of the plane of the orbit to the plane of the ecliptic.
e = Eccentricity of the orbit, sometimes given as a decimal, and sometimes as an angle, φ. The decimal represents the ratio of the linear distance of the centre of the ellipse from the focus, to the semi-axis major, the latter being taken as 1⋅0. When φ is given, then e = the natural sine of φ. This is the angle formed by the minor axis at its extremity on the border of the ellipse with a line drawn from thence to the focus. The greater this angle the more eccentric the ellipse.
q = Perihelion distance of the body; expressed in terms of the mean radius of the Earth's orbit as unity.
For a parabolic orbit e is always 1⋅0 (or Unity) ; and in that case the elements are frequently given by stating T, ω, Ω, i, and log. q. Here π has been replaced by:—
ω = π — Ω, (1)
which is counted on the comet's orbit, backward, from the
