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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Contribution of zonal harmonics to gravitational moment

A celestial body produces a gravitational moment about the mass center of a small orbiting body, which affects the orientation of the smaller body. Each zonal harmonic in the gravitational potential of a celestial body is shown to make a contribution to the gravitational moment which can be expressed in a recursive vector-dyadic form. A formal derivation is presented, followed by an example in which the result is employed in obtaining the contribution of the zonal harmonic of 2nd degree. The contribution of the zonal harmonic of 3rd degree is also reported.

Roithmayr, Carlos M.↗
NASA NTRS1989

Temporal variations in low degree zonal harmonics from Starlette orbit analysis

The dynamical effect of temporal variations in the zonal harmonics of the earth's gravitational potential due to tidal and meteorological mass redistribution has been observed using satellite laser ranging (SLR) measurements to Starlette. The secular variations in the Earth's zonal harmonics and the year-to-year fluctuation of the even degree annual and semi-annual tides, S(a) and S(sa) have been determined from a continuous Starlette orbit spanning from 1983 through 1985. The mean values for S(a) and S(sa) tides are in good agreement with other tide solutions. The year-to-year fluctuations of the even degree S(a), deduced from Starlette node variations, are about 25 percent of the mean value obtained during the three-year Starlette orbit span.

Cheng, M. K.↗
NASA NTRS1991

Contribution of zonal harmonics to gravitational moment

It is presently demonstrated that a recursive vector-dyadic expression for the contribution of a zonal harmonic of degree n to the gravitational moment about a small body's center-of-mass is obtainable with a procedure that involves twice differentiating a celestial body's gravitational potential with respect to a vector. The recursive property proceeds from taking advantage of a recursion relation for Legendre polynomials which appear in the gravitational potential. The contribution of the zonal harmonic of degree 2 is consistent with the gravitational moment exerted by an oblate spheroid.

Roithmayr, Carlos M.↗
NASA NTRS1972

Earth zonal harmonics from rapid numerical analysis of long satellite arcs

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites including 2 of low inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 200 to 800 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, was accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation of the earth's pole, atmospheric drag, radiation pressure and luni-solar gravity are added at from 1- to 8-day intervals in the integrated orbits. The results agree well with recent solutions from other authors using different methods and different satellite sets.

Wagner, C. A.↗
NASA NTRS1982

Zonal harmonic model of Saturn's magnetic field from Voyager 1 and 2 observations

An analysis of the magnetic field of Saturn is presented which takes into account both the Voyager 1 and 2 vector magnetic field observations. The analysis is based on the traditional spherical harmonic expansion of a scale potential to derive the magnetic field within 8 Saturn radii. A third-order zonal harmonic model fitted to Voyager 1 and 2 observations is found to be capable of predicting the magnetic field characteristics at one encounter based on those observed at another, unlike models including dipole and quadrupole terms only. The third-order model is noted to lead to significantly enhanced polar surface field intensities with respect to dipole models, and probably represents the axisymmetric part of a complex dynamo field.

Connerney, J. E. P.↗
NASA NTRS1978

Possible measurement of the coefficient of the second zonal harmonic of the sun's gravitational field with a solar probe

The use of radio tracking of a solar probe to estimate accurately the coefficient of the second zonal harmonic of the sun's gravitational field was examined. Preliminary results indicate that the coefficient can be estimated with a standard error of 10 to the minus 8th power or less, provided that the probe is equipped with a suitable drag-free system to compensate for the effects of non-gravitational accelerations. For signal paths that pass near the sun, dual-band ranging to the probe can provide the tracking accuracy needed to insure that the standard of error is equal to or less than 10 to minus 8th power. The possibility of achieving such accuracy with a single-band radio uplink and a dual-band downlink is discussed.

Reasenberg, R. D.↗