Optimal selenodetic control
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Date
1971-08
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
This study was undertaken to solve the problem of determination of an optimal selenodetic control network on the Moon. Selenodetic control is defined by the coordinates of a network of well identifiable features on the lunar surface with respect to a selenodetic Cartesian coordinate system, which is fixed to the lunar crust, is centered at its mass center and is oriented along the three principal axes of inertia of the Moon. The method developed for solving the problem is fully consistent with the theoretical and numerical models for the motion of the Moon in space. For this purpose, the parameters of orientation of the selenodetic system with respect to the mean ecliptic system, identified in this study with the physical librations of the Moon, are made an integral part of the solution for selenodetic control. The solution is based on optical data obtained by photography or by direct angular observations of the Moon taken from the Earth or on board a spacecraft and on range and range-rate data obtained from tracking stations on Earth to a spacecraft orbiting the Moon. In order to achieve orientation of the control network at least part of the optical data is considered oriented with respect to a certain celestial coordinate system. Scale is introduced to the control solution through the assumption that the lunar ephemeris describes the motion of the center of mass of the Moon, or in this case, the translatory motion of the origin of the selenodetic coordinate system with respect to the geocenter. The lunar ephemeris introduced by JPL under the code-name LE-16 is used for the above purpose. The total observational material modeled in terms of the parameters of the solution is processed by a weighted least squares adjustment procedure and results in estimates for the following parameter groups and their covariances: a. selenodetic coordinates of a selected number of fundamental control points on the lunar surface, b. parameters of orientation of the Moon (physical libration angles and time rates at a standard epoch), c. parameters featuring the low degree terms in the lunar gravitational field. In case the optical data was taken on board a spacecraft, an orbit determination procedure is appled to the range and range-rate data which results in estimates for the selenocentric state vector of the spacecraft and also in estimates for the higher degree terms in the lunar gravitational field. In order to test numerically the mathematical procedure developed in this study, a simulated environment was created which reflects very closely the true world. The Earth, the Moon and a variety of satellites move and rotate in this simulated environment strictly according to the laws of Newton and Kepler. The observational material generated is free of unaccounted phenomena and simulates very closely real observations. [Full text of abstract available in document.]
Description
Prepared for National Aeronautics and Space Administration, Manned Spacecraft Center, Houston, Texas: Contract No. NAS 9-9695, OSURF Project No. 2841