Gravitational Moments Research Articles

Sources, transmitters, Hertz potentials, and radiation fields

The essay is concerned with that class of dynamical systems sufficiently isolated that the gravitational fields that they produce are asymptotically flat. It is argued that as far as the definitions of multipole moments and radiation fields are concerned, whether electromagnetic or gravitational, the original curved manifold is an unsuitable arena for their description. Instead, physical laws are to be formulated in space-times of image points. An example is the equality between the time rate of change of the gravitational quadrupole moment and the spin-2 Hertz potential.

The abundance of water and rock in Jupiter as derived from interior models

Models of Jupiter's interior were computed using a new molecular hydrogen equation of state, and a more precise algorithm for computing gravitational moments. Models with H/H e ratios of 13.5, 11.25, and 10 were computed, and it was found that the models had rocky cores of 16 to 18 Earth masses and envelopes with 20 to 50 Earth masses of water. Models with temperatures of less than 180°K at 1 bar had water-to-rock ratios which were less than the solar value, thus removing a difficulty of previous computations. Models were also constructed in which rock was put into the envelope in place of water. It was found that, to a good approximation, a given mass of rock will replace an equal mass of water. At present the two cases are indistinguishable.

Electromechanical System for Attitude Control and Stabilization of Autonomous Modules and Light-weight Orbital Stations

Interconnection between the orbital station arrangement and attitude control modes and the mass and power consumption for the electromechanical system-controlled stations is considered. Advisability of the observation equipment Earth-and-stars guidance due to the station revolution around longitudinal axis, oriented in the orbit plane is shown. Moment pulses are evaluated. The electromechanical system is able to transfer from orbital to inertial orientation without using jet engines, and thus compensate gravitational moments without fuel consumption. The wheel system merits, and particularly combination of the stabilization ball wheel with the revolution ring wheel, are being discussed. Problems of optimization of the ring wheel structural and electromechanical parameters are considered. Main characteristics of the orientation system for light-weight orbital stations with the -ring and ball motor-wheels are given in the article.

The geology and geophysics of Mars

The current state of knowledge concerning the regional geology and geophysics of Mars is summarized. Telescopic observations of the planet are reviewed, pre-Mariner models of its interior are discussed, and progress achieved with the Mariner flybys, especially that of Mariner 9, is noted. A map of the Martian geological provinces is presented to provide a summary of the surface geology and morphology. The contrast between the northern and southern hemispheres is pointed out, and the characteristic features of the surface are described in detail. The global topography of the planet is examined along with its gravitational field, gravity anomalies, and moment of inertia. The general sequence of events in Martian geological history is briefly outlined.

Further investigations of Jupiter models

In our previous investigation of Jupiter models, subject to the constraint that the hydrogen-to-helium ratio is solar, we found a need to include considerable additional mass in the form of volatilized condensates in the atmosphere and excess mass in a central core. The stricter constraints imposed by the measurement of the gravitational moments of the planet as a result of the Pioneer 10 flyby indicate that the mass of the excess volatilized condensates, assumed to be water, relative to the core mass, assumed to be rock, exceeds the ratio of the relevant elements in the solar composition. In this paper we have tested the sensitivity of this conclusion to varying assumptions about the constraints and the equation of state: in particular, to variations in the hydrogen-to-helium ratio, in the softness of the equation of state for water, in the treatment of the internal adiabat, in departures from an internal adiabat, and to variations in the temperature at the 1 bar level. The above conclusion is not changed if any of these alterations are made within reasonable limits.

Measurement of the angular momentum of Jupiter and the Sun by use of the Lense-Thirring effect

We investigate the feasibility of using the Lense-Thirring effect to measure the rotational angular momentum of Jupiter and the Sun. This experiment uses gyroscopes in close Jovian and solar orbits. It is important because it provides direct, unique information. The angular momentum is not derivable from the gravitational moments when non-uniform rotation is present. Analysis shows that this experiment could be done around Jupiter with current technology, but could not be done around the Sun for some years.

Significance of gravitational moments for interior structure of Jupiter and Saturn

We present the case for liquid models of Jupiter and Saturn. We then discuss the information which can be obtained about their interior structure from a knowledge of their gravitational moments, and we discuss the nature of presently available data and data which will be necessary to fully exploit future results.

Determination of the equation of state of the molecular envelopes of Jupiter and Saturn from their gravitational moments

We develop a method for the determination of the density and equation of state of the matter in the outer layers of the planets Jupiter and Saturn using data for their external gravitational field.

Mercury's Perihelion Advance: Determination by Radar

Measurements of echo delays of radar signals transmitted from Earth to Mercury have yielded an accurate value for the advance of the latter's perihelion position. Given that the Sun's gravitational quadrupole moment is negligible, the result in terms of the Eddington-Robertson parameters is $\frac{(2+2\ensuremath{\gamma}\ensuremath{-}\ensuremath{\beta})}{3}\ensuremath{\simeq}1.005\ifmmode\pm\else\textpm\fi{}0.007$, where $\ensuremath{\gamma}=\ensuremath{\beta}=1$ in general relativity, and where 0.007 represents the statistical standard error. Inclusion of the probable contribution of systematic errors raises the uncertainty to about 0.02.

Testing general relativity: Progress, problems, and prospects

Recent results from radar and radio gravity experiments are: (1) Retardation of radar signals: 1.02 +−0.05 (planetary radar), 1.00 +− 0.04 (spacecraft); (2) Deflection of radio waves: 0.99 +− 0.12 (short baseline interferometry), +0.15 1.04 (short baseline interferometry), −0.10. 0.90 +− 0.05 (short baseline interferometry); (3) Relativistic perihelion advance of Mercury: 0.99 +− 0.03 (planetary radar), 1.00 +− 0.01 (radar plus optical); (4) Time variation of the gravitational constant: (G/G) < 4 ×10−10/yr (planetary radar). The first three results are expressed as fractions of the corresponding effects predicted by general relativity. In terms of the Eddington-Robertson parameters, the first two are approximately equal to (1+γ)/2 and the third to (2 + 2γ-β)/3. The third result depends on the assumption that the solar gravitational quadrupole moment vanishes; its effects cannot be separated usefully from those of general relativity with the present data set. The uncertainties are as given by the individual experimenters; in some cases they represent formal standard errors, in others an allowance for possible systematic errors is included.

Consequences of the transversality of the graviton emission amplitude

The divergence condition is used to reconstruct the amplitude for the soft graviton emission in n-particle collisions up to terms linear in graviton momentum q, taking into account terms depending on the spins of the colliding particles. It is shown that the vertex parts for graviton emission are determined uniquely up to the same order in q. In particular, it is proved that no gravitational dipole moments can appear, and it is shown that the existence of dipole moments would contradict the general covariance of the gravitational interaction and the equivalence principle. The cases of colliding particles with spins 0 and 1 2 and of arbitrary integer spin are considered.

Use of the principle of equivalence to search for gravitational and inertial dipole moments

Use of the principle of equivalence to search for gravitational and inertial dipole moments

The Rotation of the Sun (Review Paper)

AbstractThe author’s 1964 article inNatureon the sun’s rotation is rediscussed in the light of new data. This article suggested that the sun might be oblate because of a gravitational quadrupole moment induced by a core rotating with a period &lt; 2 days. Angular momentum lost from the core by molecular diffusion was assumed to be transferred to the solar wind which kept the sun’s surface rotating slowly. The estimated solar wind torque was found to be in good agreement with the torque calculated from a solution of the diffusion equation.

Thermal Models of Jupiter and Saturn

view Abstract Citations (62) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Thermal Models of Jupiter and Saturn Hubbard, W. B. Abstract Models corresponding to completely convective structure are calculated for Jupiter and Saturn. The equations of state used in the calculation are those given by DeMarcus, as well as more recent results of Salpeter and Zapoisky. The models are chemically homogeneous and without a dense core. In the case of Jupiter, chemical abundances are chosen to be X = 0 54, V = 046, in accordance with a recent observational determination of Beckman. The central temperature as estimated from the surface condi- tion is about 150000 K. The model of Jupiter is in full accord with the observed gravitational moments. The temperature in the Jovian interior is estimated to be everywhere above the melting temperature of metallic hydrogen, so that the planet is probably entirely fluid. Convective models of Saturn indicate that it has a central temperature of about 100000 K and is richer in helium than Jupiter. Thermal effects apparently play a much larger role in Saturn than in Jupiter. The Saturnian models do not provide good agreement with the observed gravitational moments, possibly owing to inadequacies in the assumed equation of state Publication: The Astrophysical Journal Pub Date: January 1969 DOI: 10.1086/149868 Bibcode: 1969ApJ...155..333H full text sources ADS |

Solar Oblateness and Magnetic Field

It has been suggested that the observed Solar oblateness may be caused by a gravitational quadrupole moment. The answer may not be so simple, however, because of magnetic stress and differential rotation between the radiation layer and the core.

Separation of the Relativistic Perihelion Precession from the Precession due to the Gravitational Quadrupole Moment

The gravitational quadrupole moment is considered insofar as its effect on the perihelion precession of Mercury and pericenter precession of satellites is concerned. It is found possible to separate the quadrupole precession from the precession due to the general theory of relativity. As a corollary, it is found that an exchange of angular momentum between planet and sun takes place due to the quadrupole moment. This exchange may help to explain the phenomenon of sunspots and solar flares.

On the motion of a satellite about its center of mass under the action of gravitational moments

We investigate analytically and numerically the variation of the obliquity (the axial tilt) of a hypothetical exo-Earth. A large number of exoplanets was discovered recently; since not much information is available about the masses and orbits of the stars and planets comprising a planetary exo-system, unlike for the planets of the Solar system, the problem is considered in a general setup. The exo-Earth is assumed to be rigid, axially symmetric and almost spherical, the difference between the largest and the smallest principal moments of inertia being a small parameter of the problem. Assuming the orbits of the celestial bodies to be quasiperiodic, we apply time averaging to study rotation of the exo-Earth at times large compared to the respective periods. In the present paper, we consider the case of non-resonant frequencies; we intend to study resonances in the future. In addition, we investigate numerically how the range of obliquity of the exo-Earth in a particular system comprised of a star and two planets varies on modifying the geometry of the orbits, the mass of the second planet and the initial obliquity.