In Orbit Determination, you have the observations (also known as "Tracking Data"), but you have no idea what orbit the satellite had at the time of observation. In many ways, Orbit Determination is the reverse of Orbit Propagation.

The example presented here uses the Gaussian method of initial orbit determination. This method was initially derived by Karl Friedrich Gauss himself to determine the orbit of the newly discovered Ceres after it had been first observed by Giuseppe Piazzi in 1801.

The example uses three observations of a satellite whose name will not be revealed until the final step. Each step carefully guides you through the equations of Gauss' Method. This method heavily relies on vector and matrix algebra.

The equations for this method are mainly taken from pages 443-445 and page 456 of the excellent text "Fundamentals of Astrodynamics and Applications - 3rd ed." by David A. Vallado (ISBN 978-1-881883-14-2). Many thanks to the author for his permission to use these equations in this example.

Although the basis for this example is taken from this text, many equations and variables have been changed to simplify this process as much as possible. In most of this example, the language presented is for the advanced amateur astronomer who is mathematically inclined. You have been warned.