Changing the Elements -- Help File

Changing the Elements Help File

This program allows you to convert between orbital elements and position and velocity vectors in cartesian coordinates.

The one-body problem, whereby a small body (such as the Earth) moves subject to the gravitational pull of a massive body (such as the Sun) can be uniquely solved. That is, if one knows the initial position and velocity of the small body, one can solve for its position and velocity at any time in the future (or past).

There are many ways to represent the initial conditions for the small body. One is simply to state its position (x,y,z) and velocity (vx,vy,vz) in cartesian coordinates. Another way is by using the so called orbital elements, the definitions which can be found below.

Note: This program uses dimensionless units. That is, we arbitrarily set GM = 1. This greatly simplifies the representation of the orbital elements.

a: SEMIMAJOR AXIS. This parameter is defined as half the length of the maximum dimension of an ellipse.

e: ECCENTRICITY. This parameter is a dimensionless number that ranges from 0 to 1. It is a measure of how much an ellipse deviates from a circle, whose eccentricity is 0. An ellipse with an eccentricity of 1 would essentially be a straight line with a length equal to twice the semimajor axis of the ellipse.

i: INCLINATION. This parameter is only used in 3-D space and it specifies by how many degrees the 3-D orbit is tilted with respect to some plane (called the reference plane). In 2-D, the orbit lies in the reference plane and, therefore, the inclination is 0 degrees. Inclination can have a value from 0 to 180 degrees.

Ω: LONGITUDE OF NODES. This parameter is only used in 3-D space. A node is a position in the orbit where the plane of the orbit crosses the reference plane. An orbit generally has two nodes, the Ascending Node, where the orbit pierces up through the reference plane, and the Descending Node, where the orbit plunges back down through reference plane. The Longitude of Nodes is measured from a reference direction to the Ascending Node, and can have a value between 0 and 360 degrees.

ω: ARGUMENT OF PERICENTER. This parameter determines the orientation of the ellipse in the orbital plane. It is an angle measured from the ascending note (see Longitude of Nodes above) to the pericenter (the point along the orbit where the planet-sun distance is smallest). This angle can have values between 0 and 360 degrees.

ν: TRUE ANOMALY. This parameter specifies the angle between pericenter (see Argument of Pericenter above) and the position of the planet along its orbit. This angle can have values between 0 and 360 degrees.

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