• This paper presents the image processing algorithms (and associated mathematics) of Moon or Earth pictures taken by a visible camera to accurately measure the vector to an observed illuminated body (Moon or Earth). Using a sequence of these vectors it is then possible to perform initial trajectory estimation in cislunar trajectories. Even though Moon can be considered a sphere and Earth an axial-symmetric ellipsoid, the theory presented is developed for the general case of three-axis ellipsoid. It is proved that, using a pin-hole camera model, the observed image is a projected ellipse that is obtained by the intersection of an elliptical cone with a unit-radius sphere. This paper proves that the observed ellipse center and the body center are displaced by an offset. The paper show how to quantify this offset and how to take it into account in the image processing. The equation of the terminator of a three-axis ellipsoid is also derived. High accuracy estimation of body center and radius is obtained by least-squares using circular and elliptical sigmoid functions. A numerical example and a flowchart is provided to clarify the image processing steps.

author list (cited authors)

  • Mortari, D., de Dilectis, F., & D'Souza, C.

publication date

  • January 2014