Statistics – Computation
Scientific paper
Jan 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977aiaa.meetq....l&link_type=abstract
American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 15th, Los Angeles, Calif., Jan. 24-26, 1977, 9 p
Statistics
Computation
Celestial Geodesy, Geoids, Geopotential, Numerical Integration, Rotating Bodies, Satellite Observation, Axisymmetric Bodies, Convection Currents, Density Distribution, Ellipticity, Finite Difference Theory, Mathematical Models, Moments Of Inertia, Secular Variations, Shear Stress
Scientific paper
The Clairaut equation for rotating bodies in hydrostatic equilibrium was numerically integrated up to its third order approximation using the 1969 Haddon-Bullen Earth's density model. The computations, based on finite difference methods, were executed in double precision on the Texas Instruments ASC-7 computer. The results are: (1) the coefficients of the second, fourth and sixth harmonic of the geopotential, and (2) the geoid to the same approximation inclusive of its moments of inertia and ellipticity. It is suggested that the newly determined geoid be used as the reference surface in gravimetric work. The results are compared with Kopal's 1963 work based on the 1940 Bullen density model and second order approximation. Discrepancies with satellite geodesy are attributed to shear stresses in the Earth's interior due to convection currents. To better compare our density-based results with satellite geodesy, we analytically obtained expressions for the secular variations of the elements of a Keplerian orbit and advocate that the formulae be used to evaluate the harmonics from satellite data. The Clairaut equation can also be applied to Jupiter by assuming the planet to be a rotating polytrope and solving a nonhomogeneous Lane-Emden equation to determine its density.
Daley J. C.
Lanzano Paolo
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