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NASA NTRS1979

Detecting a gravitational-radiation background using spacecraft Doppler tracking

The sensitivity of NASA's Deep Space Network spacecraft tracking system to an isotropic cosmological background of gravitational radiation is analyzed. It is found that by using the autocovariance function of the Doppler record in the so-called 'three-way' tracking mode to dig into the noise it is possible to put significant limits on this background with current and future planned deep-space missions.

Hellings, R. W.↗

NASA NTRS1979

Gravitational spectra from direct measurements

A simple rapid method is described for determining the spectrum of a surface field (in spherical harmonics) from harmonic analysis of direct (in situ) measurements along great circle arcs. The method is shown to give excellent overall trends (smoothed spectra) to very high degree from even a few short arcs of satellite data. Three examples are taken with perfect measurements of satellite tracking over a planet made up of hundreds of point masses using (1) altimetric heights from a low-orbiting spacecraft, (2) velocity (range rate) residuals between a low and a high satellite in circular orbits, and (3) range rate data between a station at infinity and a satellite in a highly eccentric orbit. In particular, the smoothed spectrum of the earth's gravitational field is determined to about degree 400(50-km half wavelength) from 1 x 1 deg gravimetry and the equivalent of 11 revolutions of GEOS 3 and Skylab altimetry. This measurement shows that there is about 46 cm of geoid height (rms worldwide) remaining in the field beyond degree 180.

Wagner, C. A.↗

NASA NTRS1979

Gravitational lens of the sun - Its potential for observations and communications over interstellar distances

The gravitational field of the sun acts as a spherical lens to magnify the intensity of radiation from a distant source along a semi-infinite focal line. A spacecraft anywhere on that line in principle could observe, eavesdrop, and communicate over interstellar distances, using equipment comparable in size and power with what is now used for interplanetary distances. If one neglects coronal effects, the maximum magnification factor for coherent radiation is inversely proportional to the wavelength, being 100 million at 1 millimeter. The principal difficulties are that the nearest point on the focal half-line is about 550 times the sun-earth distance, separate spacecraft would be needed to work with each stellar system of interest, and the solar corona would severely limit the intensity of coherent radiation while also restricting operations to relatively short wavelengths.

Eshleman, V. R.↗

NASA NTRS1979

Effect of gravitation stress and hypokinesia on blood vessels of the testicle

Rabbits were exposed to single maximum endurable stresses of cranio-caudal direction, hypokinesia for periods of one to eight weeks, and hypokinesia followed by gravitation stresses. The stresses caused dilatation of vessels, greater sinuosity, and occasional ruptures of the walls and extravasation. The greater part of the capillaries were dilated; the greatest part constricted. In hypokinesia there was an increasing atrophy of the testes. Significant results are reported.

Palazhchenko, E. F.↗

NASA NTRS1980

Effect of gravitational acceleration, hypokinesia and hypodynamia on the structure of the intestinal vascular bed

A series of experiments comparing single and combined effects of hypokinesia and gravitational acceleration on morphology of intestinal blood vessels are discussed. Results indicate that hypokinesia has a whole body nonspecific effect reflected even in an organ whose activity shows little or no change due to hypokinesia. In early hypokinetic stages blood redistribution caused anorexia, intestinal atonia, and secretory disruption. Destructive changes from further exposure include aneurisms, varicoses, extravascular movement of blood elements, and vascular wall muscle fiber degeneration. The effect of acceleration is greatest in the ventrodorsal direction. Changes due to acceleration then hypokinesia are like those due to hypokinesia alone; changes due to acceleration before and after hypokinesia are like those due to acceleration. Adaptation raises acceleration tolerance but the effects do not survive four-week hypokinesia.

Nikitin, M. V.↗

NASA NTRS1980

Effects of gravitational stress, hypokinesia and hypodynamia on the structure of the vascular bed of the spleen

The effects of two extreme factors, hypokinesia and hypodynamia, on spleen vascular beds were studied on 180 male and female albino rats. Vessels were studied by roentgenography, microroentgenography, clearing of sections and histology. Gravity stress yielded construction of all links of arterial bed and of order 5-7 veins. Large intraorganic vein diameters changed significantly but erratically. Hypokinesia in early phases produced pronounced spleen size reduction. Veins and arteries constricted along entire length. Later hypokinetic stages showed arteries still constricted; veins began to dilate from week 4 of hypokinesia. Sinuosity, uneven contours and varicose dilations of walls in large arteries and veins occurred. Abrupt changes in parenchyma, e.g., atrophy of folliculi, narrowing of lumen of central arteries from thickening of muscular wall. After exposure to hypokinesia followed by gravitational stress, pronounced lesions such as deformation of vascular wall, including rupture, in all vessels of the spleen vascular bed.

Nesterenko, N. T.↗

NASA NTRS1979

Gravitational potential energy of the earth - A spherical harmonic approach

A spherical harmonic equation for the gravitational potential energy of the earth is derived for an arbitrary density distribution by conceptually bringing in mass-elements from infinity and building up the earth shell upon spherical shell. The zeroth degree term in the spherical harmonic expansion agrees with the usual expression for the energy of a radial density distribution. The second degree terms give a maximum nonhydrostatic energy in the crust and mantle of -2.77 x 10 to the 29th ergs, an order of magnitude below McKenzie's (1966) estimate. McKenzie's result stems from mathematical error. Our figure is almost identical with Kaula's (1963) estimate of the minimum shear strain energy in the mantle, a not unexpected result on the basis of the virial theorem. If the earth is assumed to be a homogeneous viscous oblate spheroid relaxing to an equilibrium shape, then a lower limit to the mantle viscosity of 1.3 x 10 to the 20th P is found by assuming that the total geothermal flux is due to viscous dissipation of energy. This number is almost six orders of magnitude below MacDonald's (1966) estimate of the viscosity and removes his objection to convection. If the nonequilibrium figure is dynamically maintained by the earth acting as a heat engine at 1% efficiency, then the viscosity is 10 to the 22nd P, a number preferred by Cathles (1975) and Peltier and Andrew (1976) as the viscosity of the mantle.

Rubincam, D. P.↗

NASA NTRS1979

Influence of a weak gravitational wave on a bound system of two point-masses

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Turner, M. S.↗

NASA NTRS1979

The quantum limit for gravitational-wave detectors and methods of circumventing it

The Heisenberg uncertainty principle prevents the monitoring of the complex amplitude of a mechanical oscillator more accurately than a certain limit value. This 'quantum limit' is a serious obstacle to the achievement of a 10 to the -21st gravitational-wave detection sensitivity. This paper examines the principles of the back-action evasion technique and finds that this technique may be able to overcome the problem of the quantum limit. Back-action evasion does not solve, however, other problems of detection, such as weak coupling, large amplifier noise, and large Nyquist noise.

Thorne, K. S.↗

NASA NTRS1980

Solar gravitational redshift

Wavelengths of solar spectrum lines should be shifted toward the red by the sun's gravitational field as predicted by metric theories of gravity according to the principle of equivalence. Photographic wavelengths of 738 solar Fe I lines and their corresponding laboratory wavelengths have been studied. The measured solar wavelength minus the laboratory wavelength averaged for the strong lines agrees well with the theoretically predicted shift. Studies show that the departures depend on line strength. No dependence of the departures on wavelength was found within the existing data. By studying strong lines over a wide spectral range, velocity shifts caused by the complex motions in the solar atmosphere seem to affect the results in a minimal fashion.

Lopresto, J. C.↗

NASA NTRS1980

On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields

The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.

Lerche, I.↗

NASA NTRS1980

The heating of a thermally conducting stratified medium. I - Self-gravitating gas threaded by magnetic fields

Two theoretical problems are presented to illustrate the equilibrium structure of a gravitating gas threaded by magnetic fields. The gas is heated everywhere at a rate proportional to the local density and cooled by thermal conduction channeled along the magnetic field. Emphasis is placed on the influence of anisotropic thermal conduction on the distribution of the gas. In the first problem, the magnetic field has straight field lines that are nearly parallel. The simple field line geometry allows us to calculate, in closed form, the equilibria configurations of a gas slab which is cooled nonuniformly by thermal conduction along field lines which leave the gas slab at varying angles. The problem involves the gas having a free boundary, which is one of the unknowns to be determined. A discussion is given of the set of all possible equilibria so constructed. In the second problem there is no electric current flowing in the gas but there is a potential magnetic field having curved field lines. Exact solutions of equilibriums are presented to illustrate the heating of stellar and galactic coronas.

Lerche, I.↗

NASA NTRS1980

Combustion at reduced gravitational conditions

The theoretical structures needed for the predictive analyses and interpretations for flame propagation and extinction for clouds of porous particulates are presented. Related combustion theories of significance to reduced gravitational studies of combustible media are presented. Nonadiabatic boundaries are required for both autoignition theory and for extinction theory. Processes that were considered include, pyrolysis and vaporization of particulates, heterogeneous and homogeneous chemical kinetics, molecular transport of heat and mass, radiative coupling of the medium to its environment, and radiative coupling among particles and volume elements of the combustible medium.

Berlad, A. L.↗

NASA NTRS1980

The solar gravitational figure: J2 and J4

The theory of the solar gravitational figure is derived including the effects of differential rotation. It is shown that J sub 4 is smaller than J sub 2 by a factor of about 10 rather than being of order J sub 2 squared as would be expected for rigid rotation. The dependence of both J sub 2 and J sub 4 on envelope mass is given. High order p-mode oscillation frequencies provide a constraint on solar structure which limits the range in envelope mass to the range 0.01 M sub E/solar mass 0.04. For an assumed rotation law in which the surface pattern of differential rotation extends uniformly throughout the convective envelope, this structural constraint limits the ranges of J sub 2 and J sub 4 in units of 10 to the -8th power to 10 J sub 2 15 and 0.6 -J sub 4 1.5. Deviations from these ranges would imply that the rotation law is not constant with depth and would provide a measure of this rotation law.

Ulrich, R. K.↗

NASA NTRS1980

A gravitational kinetic theory for planetesimals

An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.

Stewart, G. R.↗

NASA NTRS1981

Gravitational focusing and the association of distant quasars with foreground galaxies

The surface density of quasars brighter than a given threshold is enhanced near a galaxy by the gravitational focusing of light from those quasars that are nearly co-aligned with individual stars in the galaxy halo. The focusing can intensify and make detectable quasars which would otherwise have been below the threshold. If galaxies have massive haloes of macroscopic objects then the resulting enhancement could explain the apparent association between quasars and galaxies with discrepant redshifts found in a statistical analysis. Therefore, such quasar-galaxy associations need not require the abandonment of the cosmological interpretation of the redshift.

Canizares, C. R.↗

NASA NTRS1982

The role of the deep space network's frequency and timing system in the detection of gravitational waves

A review of the Deep Space Network's (DSN) use of precision Doppler-tracking of deep space vehicles is presented. The review emphasizes operational and configurational aspects and considers: the projected configuration of the DSN's frequency and timing system; the environment within the DSN provided by the precision atomic standards within the frequency and timing system--both current and projected; and the general requirements placed on the DSN and the frequency and timing system for both the baseline and the nominal gravitational wave experiments. A comment is made concerning the current probability that such an experiment will be carried out in the foreseeable future.

Mankins, J. C.↗

NASA NTRS1981

On gravitational lenses and the cosmological evolution of quasars

A heuristic model for the effect of gravitational lenses on the apparent cosmological evolution of quasars is considered. The model satisfies the requirement of average flux conservation and has no net mean amplification. This requirement is shown to be numerically important in studying the effect. On the basis of the values of the evolution indicators calculated from the model, it is concluded that it is premature to assert that lensing plays an important role in affecting the apparent evolution. A qualitative, model independent observational test for the effect is suggested. The test estimates the distances where lensing is dominant. An application of this test to a complete sample of quasars indicates that lensing cannot completely account for the apparent evolution, except in an extreme situation.

Avni, Y.↗