Application of Hansen's theory to the motion of an artificial satellite in the gravitational field of the Earth

In order to draw geophysical and geodetic conclusions from the motion of the artificial satellite, we need an accurate theory that will permit the easy inclusion of any gravitational term. This articles contains a theory of Hansen's type adaptable to the use of large computing machines. The form of the disturbing function suggests the use of the process of iteration. The computations can be carried out to any desired order compatible with the accuracy of the geodetic parameters. The theory as written is valid for zonal harmonics of all orders in the earth's gravitational field. A program based on this theory was developed by Dr. Herget and his collaborators and was used by the Vanguard Computing Center to produce the numerical theories of several satellites.