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The value of the geocentric gravitational constant was determined from the analysis of Doppler and range data during the near-earth phases of the trajectories of Mariners 9 and 10. Geocentric gravitational constant values (in units of cu km/sq s) for the two spacecraft were found to be: 398,600.7 plus or minus 0.2 for Mariner 9 and 398,600.6 plus or minus 0.2 for Mariner 10.
An investigation is conducted concerning the possibility that neutrino radiation rather than gravitational radiation may be the dominant way by which nonradial pulsations are damped out in a collapsing star. The effects of neutrino radiation on the nonradial oscillations of such objects are examined and damping times corresponding to a particular neutrino production mechanism are evaluated. The obtained results imply that neutrino radiation, by more rapid damping of the nonradial oscillations of a newly formed neutron star in a supernova explosion, would hinder gravitational radiation, thus reducing the possibility of its detection.
The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitational and rotational terms in the equations are of first order in the space variables, the pressure-gradient terms are of second order, and the turbulent-viscosity term is of third order. The presence of turbulent viscosity ensures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial flow is always inward and allows collapse to occur (axially) even when the rotation is large. An approximate solution of the governing partial differential equations is also given in order to study the spatial distributions of the density and velocity.
The anisotropic generalization of the parameterized post-Newtonian (PPN) gravitational metric field is made for the case of theories with energy and momentum conservation laws. Such an anisotropic metric field will generally result in two-tensor or bimetric theories of gravity in an anisotropic universe. New anisotropic 3 x 3 spatial PPN matrices are introduced into the general metric expansion. Earth gravimeter measurements strongly restrict some anisotropies, while anisotropic inertial and gravitational mass for celestial bodies result from other combinations of the PPN matrices.
The possibility of a Brans-Dicke scalar-tensor gravitation theory with a negative coupling constant is considered. The admissibility of a negative-coupling theory is investigated, and a simplified cosmological solution is obtained which allows a negative derivative of the gravitation constant. It is concluded that a Brans-Dicke theory with a negative coupling constant can be a viable alternative to general relativity and that a large negative value for the coupling constant seems to bring the original scalar-tensor theory into close agreement with perihelion-precession results in view of recent observations of small solar oblateness.
General formulas are derived which describe the gravitational radiation at large distances from a system of bodies whose sizes are small compared with their separations. The calculation is carried out through post-Newtonian order within general relativity. More explicit formulas are derived for two-body systems, and detailed results are presented for circular orbits, gravitational bremsstrahlung, and head-on collisions.
Malin's (1975) gravitational theory, which was recently shown by Lindblom and Nester (1975) to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the post-Newtonian approximation framework.
A gravitational-contraction history is calculated for a homogeneous quasi-equilibrium Saturn model of solar composition without a rock-ice core and without allowance for the possible separation of hydrogen and helium. The calculations begin at the time when Saturn's radius was ten times its current value, and the subsequent gravitational contraction is followed for 4.5 billion years. The results obtained are given in terms of the path of the evolving model on the H-R diagram, the variation of central temperature with central density, the time variation of radius and internal luminosity, and the energy changes that take place during the evolution. These results are compared with those of similar calculations for Jupiter, and the internal structure of the evolutionary models is examined in detail. The Saturn calculations yield a radius at the current epoch that is 9% larger than the observed value and an excess luminosity comparable to that observed. It is noted that an inhomogeneous model containing a solar-mix envelope and a central rocky core has a radius equal to the observed value.
The salient feature of a gravitationally-stabilized satellite solar power system (SSPS) for a photovoltaic system is that the large solar array is separated into smaller segments or subunits, joined together in a linear array oriented along the local vertical. Applicability of gravitational stabilization to the design of photovoltaic SSPS is demonstrated. Both actively controlled systems using multiple solar panels oriented to the sun and passively controlled systems requiring no sun orientation are considered and determined to be feasible. Expressions for gravity-gradient induced tension and restoring torques about the local vertical are assessed. Particular attention is directed to the applicability of solid-state approaches to the design of SSPS. It is shown that an all solid-state SSPS utilizing the LITOMIC (light-to-microwave conversion) concept is feasible but that a hybrid system employing a combination of both solid-state and cryogenic cooled low-voltage techniques to the design of the power management and distribution subsystem may also provide a solution.
Two different versions of the Green's function for the scalar wave equation in weakly curved spacetime (one due to DeWitt and DeWitt, the other to Thorne and Kovacs) are compared and contrasted; and their mathematical equivalence is demonstrated. Then the DeWitt-DeWitt Green's function is used to construct several alternative versions of the Thorne-Kovacs postlinear formalism for gravitational-wave generation. Finally it is shown that, in calculations of gravitational bremsstrahlung radiation, some of our versions of the postlinear formalism allow one to treat the interacting bodies as point masses, while others do not.
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
Formulas are derived describing the gravitational waves produced by a stellar encounter of the following type. The two stars have stationary (i.e., nonpulsating) nearly Newtonian structures with arbitrary relative masses; they fly past each other with an arbitrary relative velocity; and their impact parameter is sufficiently large that they gravitationally deflect each other through an angle that is small as compared with 90 deg.
Formulae and numerical results are presented for the gravitational radiation emitted during a low-deflection encounter between two massive bodies. Results are valid through post-Newtonian order within general relativity. The gravitational waveform, the total luminosity and total emitted energy, the angular distribution of emitted energy, and the frequency spectrum are discussed in detail. A method boosting the accuracy of these quantities to post Newtonian order is also presented. A numerical comparison of results with those of Peters, and of Kovacs and Thorne shows that the post Newtonian method is reliable to better than 0.1 percent at v = 0.1 c, to a few percent at v = 0.35 c, and to 10 to 20 percent at v = 0.5 c.
Investigations of several problems of gravitation are discussed. The question of the existence of black holes is considered. While black holes like those in Einstein's theory may not exist in other gravity theories, trapped surfaces implying such black holes certainly do. The theories include those of Brans-Dicke, Lightman-Lee, Rosen, and Yang. A similar two-tensor theory of Yilmaz is investigated and found inconsistent and nonviable. The Newman-Penrose formalism for Riemannian geometries is adapted to general gravity theories and used to implement a search for twisting solutions of the gravity theories for empty and nonempty spaces. The method can be used to find the gravitational fields for all viable gravity theories. The rotating solutions are of particular importance for strong field interpretation of the Stanford/Marshall gyroscope experiment. Inhomogeneous cosmologies are examined in Einstein's theory as generalizations of homogeneous ones by raising the dimension of the invariance groups by one more parameter. The nine Bianchi classifications are extended to Rosen's theory of gravity for homogeneous cosmological models.
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.
A very high sensitivity rotating gravity gradiometer onboard the spacecraft is described for measuring the gravitational oblateness of the Sun during a solar probe mission. The proposed instrument would be a self-contained structure in a thermal-vacuum-magnetic shield in the shape of a cross, with a mass of 20 kg and arm length of 1.0 m and thickness of 0.1 m. The sensor inside would have a resonant frequency of 1/30 Hz, a mechanical Q of one million and would use gravitational radiation antenna technology to achieve a sensitivity of 6 x 10 to the minus 8th power Eotvos, which would provide a measurement of the solar oblateness to an accuracy of 1.5 to 6 x 10 to the minus 8th power. The gravity gradiometer will require a spinning spacecraft, so that it will not sense the spacecraft gravity fields, but the gradiometer does not need to be at the spacecraft center of mass, or even on the spacecraft spin axis. Major problem areas to be addressed are demonstration of the instrument sensitivity prior to flight and the measurement and compensation for any residual spacecraft angular rates.
The magnitude of Doppler signals produced by gravitational wave burst, continuous gravitational waves, and oscillations of the sun interacting with a spacecraft are considered. Expressions are worked out for the appropriate noise entering each measurement. The noise sources considered are the Doppler extractor, fluctuations in the solar wind and the troposphere, and fluctuations in the reference oscillator.
D. R. Long (1976) and others have speculated that the gravitational force between point masses in the Newtonian regime might not be exactly proportional to 1/r squared. Distance-dependent deviations from the 1/r squared law can be represented by a distance-dependent gravitational 'constant', G(r). Long has summarized the experimental evidence which constrains G(r) to be very nearly constant for 5 cm less than r less than 1 m. This paper presents observational evidence for constancy in the range 1000 km less than r less than 10 to the eighth km, and points out that the value of G(r) identical to Gc in this range has not been experimentally determined. Constraints on G(r) in the intermediate distance range 10 m less than r less than 1 km are so poor that one cannot rule out the possibility that Gc differs greatly from the laboratory value Go. Models of the earth and sun are used to argue that Gc differs from Go by not more than approximately 40%. Methods of improving the determination of Gc are suggested.