Method For The Calculation Of Spacecraft Umbra And Penumbra Shadow Terminator Points

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.

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. Ortizlongo, Carlos R. and Rickman, Steven L. Johnson Space Center ...

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How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge–Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

This book de-emphasizes the formal mathematical description of spacecraft on-board attitude and orbit applications in favor of a more qualitative, concept-oriented presentation of these topics. The information presented in this book was originally given as a set of lectures in 1999 and 2000 instigated by a NASA Flight Software Branch Chief at Goddard Space Flight Center. The Branch Chief later suggested this book. It provides an approachable insight into the area and is not intended as an essential reference work. ACS Without an Attitude is intended for programmers and testers new to the field who are seeking a commonsense understanding of the subject matter they are coding and testing in the hope that they will reduce their risk of introducing or missing the key software bug that causes an abrupt termination in their spacecraft’s mission. In addition, the book will provide managers and others working with spacecraft with a basic understanding of this subject.