The most common way of defining the orbit of a satellite is by what is known as a "two-line element set" or TLE. This data consists of two lines of text, each 70 characters in length. The TLE contains mathematical parameters describing the position and orbital path at a defined moment in time called the "epoch". These parameters can be plugged into an "orbital model", which is able to predict the exact position of the satellite at any point in time. The two most commonly used orbital models are SGP4 (used to describe near-earth orbiting bodies) and SDP4 (used to describe deep-space bodies). These orbital models are described using a computer language called "FORTRAN" which was widely used for programming mainframe computers during the 1960's and 1970's. This code has subsequently been converted to "C", and was converted to "Javascript" for the purpose of this project.
An example of a TLE for the international space station is shown below:

The numbers "03338" on the first line indicate that the epoch was on the 338'th day in 2003 (December 4th).

TLE's of man-made orbiting bodies are maintained by the North American Aerospace Defense Command (NORAD). This agency owns powerful radar and tracking installations which are able to accurately track these bodies.

In theory a TLE is able to predict the exact motion of a satellite for any point in the future. In practise, several factors cause the accuracy to degrade over time. These are (a) small errors in the initial measurement, (b) corrective manouvers performed by the satellite itself, (c) drag caused by the small amount of atmosphere still present at orbital altitudes, (d) effect of solar wind, (e) relativistic effects. Because of this, TLE's are updated by NORAD on a regular basis (the TLE for the international space station is updated several times a day.) Recently aquired TLE's are only needed for tracking a satellite to extreme accuracy - the TLE used for this project was grabbed on November 15th, and is expected to yield results accurate to within one degree of latitude and longitude for the next six months.

Thanks to Mark Leather for satellite orbit javascript conversion.