Method for the Calculation of Spacecraft Umbra and Penumbra Shadow Terminator Points

Book excerpt: A method for calculating orbital shadow terminator points is presented. The current method employs the use of an iterative process which is used for an accurate determination of shadow points. This calculation methodology is required, since orbital perturbation effects can introduce large errors when a spacecraft orbits a planet in a high altitude and/or highly elliptical orbit. To compensate for the required iteration methodology, all reference frame change definitions and calculations are performed with quaternions. Quaternion algebra significantly reduces the computational time required for the accurate determination of shadow terminator points.