Lunar gravitational field - A thirteenth degree and order spherical harmonic estimate
Lunar Orbiter tracking data analyzed to yield thirteenth degree and order spherical harmonic approximation to lunar gravitational potential function
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Lunar Orbiter tracking data analyzed to yield thirteenth degree and order spherical harmonic approximation to lunar gravitational potential function
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Experimental tests of gravitation theories - conferences
A hydrogen maser clock is proposed for enclosure in an orbiting satellite to measure the gravitational effect on time scales with high accuracy. This experiment is used to test the principle of equivalence for clocks in space. Extremely narrow linewidth of Fe-57 radiation and absorption due to Mossbauer effect over 75 ft vertical distance was used to confirm the prediction of the equivalence principle to 1 part in 100. The fractional frequency shift of a satellite-borne oscillator observed from earth is also given.
Two perturbations, the earth's quadrupole moment and the earth's revolution around the sun, are discussed. Schiff's proposed gyroscope test of gravitation is analyzed, along with the capability of deciphering each separate contribution to the angular velocity of spin precession.
Direct measurements of the effects of gravitation on time are discussed. Using the earth's gravity these measurements can now be made to 20 parts per million. At present, there is a 1% verification of the equivalence principle for clocks made over a 75-ft vertical distance by use of Mossbauer gamma ray emission and absorption. Measurements made to greater accuracy and spanning distances where appreciable curvature of the metric of spacetime will help verify the equivalence principle, a postulate upon which Einstein developed his General Theory of Relativity.
Two models of the earth's gravitational field have been computed at Goddard Space Flight Center. The first, Goddard Earth Model 1 (GEM 1), has been derived from satellite tracking data. The second, Goddard Earth Model 2 (GEM 2), has been derived from a combination of satellite tracking and surface gravimetric data. The geopotential models are represented in spherical harmonics complete to degree and order 16 for the combined solution and complete to degree and order 12 for the satellite solution. Both solutions include zonal terms to degree 21 and related satellite resonant coefficients to degree 22. The satellite data consisted primarily of optical data processed on 300 weekly orbital arcs for 25 close earth satellites. Surface gravity data were employed in the form of 5 deg x 5 deg mean free-air gravity anomalies providing about 70% world coverage. Station locations were obtained for 46 tracking sites by combining electronic, laser, and additional optical tracking data with the above satellite data. Analysis of the radial positions of these stations and a value of mean gravity on the geoid indicated a mean equatorial radius for the earth of about 6378145 meters. Results of geopotential tests on satellite data not used in the solution show that better agreement was obtained with the GEM 1 and GEM 2 models than with the 1969 Smithsonian Standard Earth 2 model.
This article describes a Lorentz-like transformation between a fixed frame and an inertial frame that is free falling due to the presence of a uniform gravitation field. The application to the clock paradox problem and some connections with similar works are also discussed.
The paper represents the earth's gravitational potential V, outside a sphere bounding the earth, by means of its difference from the author's spheroidal potential. The difference is in turn represented as arising from a surface density on the sphere bounding the earth. Because of the slow decrease with order n of the normalized coefficients in the spherical harmonic expansion of V, the density anomalies from which the higher coefficients arise must occur in regions close to the earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thickness. Values of surface density are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of surface density and for its contour map. The numerical values obtained for surface density are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cu cm, and occur in the crust alone.