Applications of laser ranging and VLBI observations for selenodetic control
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Date
1971-11
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
This study was undertaken so as to develop the observation equations necessary to utilize lunar laser ranging and Very Long Baseline Interferometry (VLBI) measurements for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The determination of coordinates of points on the moon using earth-based observations requires the knowledge of the following dynamic behavior of the earth and the moon: the orbital motion of the moon about the barycenter, the rotation of the moon on its axis and the motion of the earth about its center of mass. In addition, the knowledge of the geocentric positions of the terrestrial stations is essential. Since our knowledge of the parameters related to the above phenomena can be improved simultaneously with the determination of coordinates of lunar points, the observation equations derived in this study are based on a general model in which the unknown parameters included the following: (a) The selenodetic Cartesian coordinates. (b) The geocentric coordinates of earth stations. (c) Parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system. (d) The parameters of the orientation of the ''average" terrestrial coordinate system with respect to a fixed celestial coordinate system. (e) The geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris. The orientation parameters of both the earth-fixed and the moon-fixed coordinate system were represented in this study by three Eulerian angles which, along with their time rates, could be obtained by numerically integrating the differential equations of motion of the respective bodies. This resulted in the reduction of the number of parameters (in the adjustment model), which are related to the orientation of the two bodies. The general adjustment model developed for the analyses of laser and VLBI observations is based on the theory of adjustment computations with matrix algebra. The numerical tests performed in this study with simulated as well as real data demonstrated that the numerical integration of the earth's orientation angles yields values which are very close to the classically computed angles, and that the initial conditions for the integration are capable of being solved in an adjustment process. Also, the results of the numerical experiments performed with simulated laser data confirmed the feasibility of the method developed in this study.
Description
Prepared for National Aeronautics and Space Administration, Manned Spacecraft Center, Houston, Texas: Contract No. NAS 9-9695, OSURF Project No. 2841