Engineering Papers⌕ Search

Engineering topics

Musen, P.

Publications and source records attributed to Musen, P..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

On the tidal oscillations of the liquid core of the earth

An important goal of a tidal theory is the improvement of nutational amplitude and of the parameters of the earth's elastic response. A theory of tidal oscillations inside a rotating elliptical earth was developed, with special emphasis on tides in the liquid core. The Molodensky and Kramer theory of the resonance effect, as caused by the proximity of the frequency of the free diurnal wobble of the liquid core to the frequency of K sub 1 astronomical tide, was amended to include the effect of the possible deviation of the liquid core from the state of neutral stability. Coupling effects between the toroidal and spheroidal oscillations, as caused by the Coriolis force, were taken into consideration.

Musen, P.↗
NASA NTRS1975

The exterior tidal potential acting on a satellite

A theory is presented that points out the existence of several long period and 'cross effects' in the coefficients in the expansion of the geopotential and in the motion of satellites. The tidal potential, defined as small periodic variations in the geopotential, was calculated. The influence of these geopotential variations on satellite perturbation is examined. Spherical harmonics were employed.

Musen, P.↗
NASA NTRS1975

The exterior tidal potential acting on a satellite

The tidal potential is related to small periodic variations in the geopotential which are caused by the formation of the tidal bulge and by the redistribution of masses in the earth's interior under the influence of lunisolar tidal attraction. The tidal effects in the motion of a satellite can be interpreted as the result of tidal periodic oscillations. An investigation of the tidal disturbing potential is conducted and the differential equations for the variations of the elements are considered. It is suggested that a future planning should include the tidal observations on the earth surface.

Musen, P.↗
NASA NTRS1975

On the oscillation of the laterally heterogeneous earth, 1

The perturbative effects, as cause by lateral inhomogeneities in the earth structure and by Coriolis force, contaminate the originally toroidal and spheroidal earth's oscillations, making them of mixed type. For this reason, in order to make the computation of the perturbations more uniform and homogeneous, it was suggested that the earth's free oscillations be expanded into a series in terms of generalized harmonics familiar from the theory of angular momentum in quantum mechanics. Making use of Gibbsian symbolism and of some operators from the theory of angular momentum, explicit expressions were deduced for the perturbative terms in the differential equation of the earth's free oscillations. Decomposition of the strain tensor in terms of canonical vectors was also obtained.

Musen, P.↗
NASA NTRS1974

Contribution to the theory of tidal oscillations of an elastic earth. External tidal potential

The differential equations of the tidal oscillations of the earth were established under the assumption that the interior of the earth is laterally inhomogeneous. The theory was developed using vectorial and dyadic symbolism to shorten the exposition and to reduce the differential equations to a symmetric form convenient for programming and for numerical integration. The formation of tidal buldges on the surfaces of discontinuity and the changes in the internal density produce small periodic variations in the exterior geopotential which are reflected in the motion of artificial satellites. The analoques of Love elastic parameters in the expansion of exterior tidal potential reflect the asymmetric and inhomogeneous structure of the interior of the earth.

Musen, P.↗
NASA NTRS1973

A semi-analytical method of computation of oceanic tidal perturbations in the motion of artificial satellites

The method of expansion of the satellite's perturbations, as caused by the oceanic tides, into Fourier series is discussed. The coefficients of the expansion are purely numerical and peculiar to each particular satellite. Such a method is termed as semi-analytical in celestial mechanics. Gaussian form of the differential equations for variation of elements, with the right hand sides averaged over the orbit of the satellite, is convenient to use with the semi-analytical expansion.

Musen, P.↗
NASA NTRS1972

On the tidal effects in the motion of earth satellites and the love parameters of the earth

The tidal effects in the motion of artificial satellites are studied to determine the elastic properties of the earth as they are observed from extraterrestrial space. Considering Love numbers, the disturbing potential is obtained as the analytical continuation of the tidal potential from the surface of the earth into-outer space, with parameters which characterize the earth's elastic response to tidal attraction by the moon and the sun. It is concluded that the tidal effects represent a superposition of a large number of periodic terms, and the rotation of the lunar orbital plane produces a term of 18 years period in tidal perturbations of the ascending node of the satellite's orbit.

Musen, P.↗
NASA NTRS1972

On the tidal effects in the motion of artificial satellites.

The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorial elements of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal 'waves' over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the 'global' Love numbers for the Earth.

Musen, P.↗
NASA NTRS1972

On the determination of the long period tidal perturbations in the elements of artificial earth satellites

The magnitude of the tidal effects depends upon the elastic properties of the earth as described by Love numbers. The Love numbers appear as the coefficients in the expansion of the exterior tidal potential in terms of spherical harmonics (in Maxwellian form). A single averaging process was performed only along the parallels of latitude. This process preserves additional long period tidal effects (with periods of a few days or more). It also eliminates the short period effects with periods of one day or less.

Musen, P.↗
NASA NTRS1971

The influence of the great inequality on the secular disturbing function of the planetary system.

This paper derives the contribution by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations. The Krylov-Bogoliubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing function derived in this paper can be included in existing theories of the secular effects of principal planets.

Musen, P.↗