Earth orientation from lunar laser range-differencing
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Date
1978-06
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Ohio State University. Division of Geodetic Science
Abstract
For the optimal use of high precision Lunar Laser Ranging (LLR), an investigation regarding a clear definition of the underlying coordinate systems, identification of estimable quantities, favorable station geometry and optimal observation schedule is given. In Section 2, the least squares adjustment formulation for range-differencing is presented. Taking advantage of the earth-moon geometry, this procedure determines the coordinate differences of the stations particularly well. The body-fixed motions of the celestial pole (polar motion) and the earth rotation parameter are derived from an orthogonal transformation relative to a standard epoch. This is accomplished by a second least squares solution which utilizes the estimable parameters of the first adjustment as new "observations." A separation between earth rotation variations and ephemeris errors in lunar right ascension is not possible. Various station distributions are analyzed. A station geometry consisting of two north-south lines, being separated in longitude by 90°, and one east-west line determine the three orientation parameters virtually independent of ephemeris errors in declination. However, they include the common motions of the stations due to crustal motions. The third section presents various analyses of variance models and numerical results. The simplifications consist of neglecting the earth rotation during the travel time of the pulse. In some models, the terms of the characteristic order of 1/60, i.e., those terms depending on the ratio of geocentric station distance to geocentric reflector distance, are neglected and the declination is taken constant during one interval. The analysis shows that for the given station distribution and an adequate observation schedule, the orientation parameters can be given daily with at least the measurement accuracy.
Description
Prepared for National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland: Grant No. NSG 5265, OSURF Project 711055