1. Fundamentals

a Mean distance, or semi-major axis e Eccentricity T Time at perihelion

q Perihelion distance = a * (1 - e)

i Inclination, i.e. the "tilt" of the orbit relative to the ecliptic. The inclination varies from 0 to 180 degrees. If the inclination is larger than 90 degrees, the planet is in a retrogade orbit, i.e. it moves "backwards". The most well-known celestial body with retrogade motion is Comet Halley. N (usually written as "Capital Omega") Longitude of Ascending Node. This is the angle, along the ecliptic, from the Vernal Point to the Ascending Node, which is the intersection between the orbit and the ecliptic, where the planet moves from south of to north of the ecliptic, i.e. from negative to positive latitudes. w (usually written as "small Omega") The angle from the Ascending node to the Perihelion, along the orbit.

q Perihelion distance = a * (1 - e) Q Aphelion distance = a * (1 + e) P Orbital period = 365.256898326 * a**1.5/sqrt(1+m) days, where m = the mass of the planet in solar masses (0 for comets and asteroids). sqrt() is the square root function. n Daily motion = 360_deg / P degrees/day t Some epoch as a day count, e.g. Julian Day Number. The Time at Perihelion, T, should then be expressed as the same day count. t - T Time since Perihelion, usually in days M Mean Anomaly = n * (t - T) = (t - T) * 360_deg / P Mean Anomaly is 0 at perihelion and 180 degrees at aphelion L Mean Longitude = M + w + N E Eccentric anomaly, defined by Kepler's equation: M = E - e * sin(E) An auxiliary angle to compute the position in an elliptic orbit v True anomaly: the angle from perihelion to the planet, as seen from the Sun r Heliocentric distance: the planet's distance from the Sun. x,y,z Rectangular coordinates. Used e.g. when a heliocentric position (seen from the Sun) should be converted to a corresponding geocentric position (seen from the Earth).

r * cos(v) = a * (cos(E) - e) r * sin(v) = a * sqrt(1 - e*e) * sin(E)