# Celestial Mechanics - Elements of Orbits

There are five elements of a Keplerian elliptical orbit.

Two parameters determine the position of the plane of the object’s orbit relative to the plane of the Earth’s orbit. (Remember that the plane of the Earth’s orbit is called the “ecliptic.”) Since the sun is the common focal point of both orbits, the two orbital planes intersect in a line, called the line of nodes. The two parameters describing the object’s plane are:

1. i—the angle of inclination (the angle between the planes)
2. Θ—the angle made by the line of nodes with some fixed axis in the plane of the Earth’s orbit. The usual point chosen is the First Point of Aries , one of the two points on the celestial sphere where the Ecliptic and the celestial equator cross one another. The First Point of Aries, which is actually in Pisces, defines the zero-point for right ascension. One parameter specifies the angle which the main axis of the object’s orbit within its own orbital plane makes with the line of intersection with the Earth’s orbit:
3. phi—for this parameter, we take the angle between the
major axis of the object’s orbit and the line of nodes.  Two parameters specify the shape and overall scale of the object’s Keplerian orbit:

1. Relative scale of the orbit, specified by its width when cut perpendicular to its major axis in through the focus (center of the sun)
2. e—eccentricity, a measure of the shape of the ellipse. Eccentricity can take on values 0<e<1. An eccentricity of e=1 occurs for parabolic orbits, and e>1 for hyperbolic orbits. Eccentricity is calculated as f/A (distance between one foci and the center/semi-major axis). A few more terms that might help with understanding are found here.

Now let’s cover some other effects that make this problem even more difficult.

*  Astronomers have an exasperating habit of defining the same concept in several different ways. (They blame this on the rich history of the science, which they are loathe to forget.) As a consequence, you can read some other definitions of terms for the parameters defined in slightly different ways here.