Gravitational Field Of Sun Research Articles

The first attempts to measure light deflection by the Sun

Soon after Einstein's calculation of the effect of the Sun's gravitational field on the propagation of light in 1911, astronomers around the world tried to measure and verify the value. If the first attempts in Brazil in 1912 or Imperial Russia in 1914 had been successful, they would have proven Einstein wrong.

Modeling of Earth rotation in the gravitational field of Sun and Moon

A celestial mechanics model of the deformable Earth is studied within the limits of the spatial variant of the problem “deformable Earth - Moon in the gravitational field of the Sun”. An amplitude-frequency analysis of the perturbed Chandler wobble of the Earth pole due to the precessional motion of the lunar orbit is provided. Using a numerical-analytical approach, we consider the possibilities for identifying the Chandler wobble parameters and fitting the developed refined theoretical model to the real trajectory measurements of the Earth pole.

Concerning the Paper by A. Einstein “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”

It is shown that in A. Einstein’s 1915 paper “Explanation of the perihelion motion of Mercury from the general theory of relativity” an error was actually incurred in the integration of the equation $$ \phi =\left[1+\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ , and in the result instead of $$ \phi \approx \uppi \left[1+\frac{5}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ (if we limit ourselves to first-order terms in the small quantity (α1 + α2)) the value $$ \phi \approx \uppi \left[1+\frac{3}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ was obtained, where α1 and α2 are the inverse values of the maximum and minimum distances of Mercury from the Sun, $$ \upalpha =\frac{2G{m}_0}{c^2} $$ is the gravitational radius, G is the gravitational constant, m0 is the mass of the Sun, c is the velocity of light (i.e., the Chinese mathematician Hua Di was actually right). And, as a result, for the precession of the orbit of Mercury in the gravitational field of a spherical Sun in the general theory of relativity (after 100 years) one obtains not ~43”, as A. Einstein obtained, but ~71.63”. Exactly this latter result is obtained by direct numerical modeling of the precession of the perihelion of Mercury’s orbit in the gravitational field of the Sun within the framework of the general theory of relativity if the fitting coefficient α in the equation of motion of Mercury (not to be confused with α in the above equations) is set equal to zero. The result $$ \phi \approx \uppi \left[1+\frac{3}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ , obtained by A. Einstein if it is obtained, happens only upon integration of either the equation $$ \phi =\left[1+\frac{\upalpha}{2}\left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ (if we also limit ourselves to first-order terms in the small quantity (α1 + α2)), i.e., in front of the integral in brackets the coefficient 1/2 should stand in front of the quantity α, or the equation $$ \phi =\left[1+\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ (if we also limit ourselves to first-order terms in the small quantity (α1 + α2)), i.e., in the denominator under the differential in the integral, inside the square root\ a plus sign should stand in front of the quantity αx.

Bending space-time: a commentary on Dyson, Eddington and Davidson (1920) 'A determination of the deflection of light by the Sun's gravitational field'.

The famous eclipse expedition of 1919 to Sobral, Brazil, and the island of Principe, in the Gulf of Guinea, led by Dyson, Eddington and Davidson was a turning point in the history of relativity, not only because of its importance as a test of Einstein's General Theory of Relativity, but also because of the intense public interest which was aroused by the success of the expedition. The dramatic sequence of events which occurred is reviewed, as well as the long-term impact of its success. The gravitational bending of electromagnetic waves by massive bodies is a subject of the greatest importance for contemporary and future astronomy, astrophysics and cosmology. Examples of the potential impact of this key tool of modern observational astronomy are presented. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

F (T) gravity: effects on astronomical observations and Solar system experiments and upper bounds

The effects of the f (T) gravity have previously been investigated and constrained by using perihelion advances. As an extension of previous work and as an attempt to find more stringent constraints on its parameters, we investigate here its effects on astronomical observations and on experiments conducted in the Solar system. The expression for f (T) contains a quadratic correction of α*T2 (where α is a model parameter) and the cosmological constant Λ. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, in addition to the light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. From these results, we find qualitatively that the light deflection provides a unique bound on α, without dependence on Λ, and that the time delay experiments during inferior conjunction impose a clean constraint on Λ, regardless of α. Based on observations and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper bounds quantitatively: |α| ≤ 1.2 × 102 m2 and |Λ| ≤ 1.8 × 10−43 m−2, which are at least 10 times tighter than the previous results.

Solar system constraints onf(T) gravity

We use recent observations from solar system orbital motions in order to constrain f(T) gravity. In particular, imposing a quadratic f(T) correction to the linear-in-T form, which is a good approximation for every realistic case, we extract the spherical solutions of the theory. Using these spherical solutions to describe the Sun's gravitational field, we use recently determined supplementary advances of planetary perihelia, to infer upper bounds on the allowed f(T) corrections. We find that the maximal allowed divergence of the gravitational potential in f(T) gravity from that in the teleparallel equivalent of General Relativity is of the order of 6.2 \times 10^{-10}, in the applicability region of our analysis. This is much smaller than the corresponding (significantly small too) divergence that is predicted from cosmological observations, as expected. Such a tiny allowed divergence from the linear form should be taken into account in f(T) model building.

"IMPRINTING" IN GENERAL RELATIVITY TESTS?

We investigate possible a priori "imprinting" of general relativity itself on spaceraft-based tests of it. We deal with some performed or proposed time-delay ranging experiments in the Sun's gravitational field. The "imprint" of general relativity on the Astronomical Unit and the solar gravitational constant GM⊙, not solved for in the spacecraft-based time-delay test performed so far, may induce an a priori bias of the order of 10-6 in typical solar system ranging experiments aimed to measuring the space curvature PPN parameter γ. It is too small by one order of magnitude to be of concern for the performed Cassini experiment, but it would affect future planned or proposed tests aiming to reach a 10-7–10-9 accuracy in determining γ.

Should we assess climate model predictions in light of severe tests?

According to Austro‐British philosopher Karl Popper, a system of theoretical claims is scientific only if it is methodologically falsifiable, i.e., only if systematic attempts to falsify or severely test the system are being carried out [Popper, 2005, pp. 20, 62]. He holds that a test of a theoretical system is severe if and only if it is a test of the applicability of the system to a case in which the system's failure is likely in light of background knowledge, i.e., in light of scientific assumptions other than those of the system being tested [Popper, 2002, p. 150]. Popper counts the 1919 tests of general relativity's then unlikely predictions of the deflection of light in the Sun's gravitational field as severe. An implication of Popper's above condition for being a scientific theoretical system is the injunction to assess theoretical systems in light of how well they have withstood severe testing. Applying this injunction to assessing the quality of climate model predictions (CMPs), including climate model projections, would involve assigning a quality to each CMP as a function of how well it has withstood severe tests allowed by its implications for past, present, and nearfuture climate or, alternatively, as a function of how well the models that generated the CMP have withstood severe tests of their suitability for generating the CMP.

The Logical Structure of Scientific Explanation and Prediction: Planetary Orbits in a Sun’s Gravitational Field

We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet's elliptical orbit in the Sun's gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in accordance with the hypotheticodeductive model.

A Priori “Imprinting” of General Relativity Itself on Some Tests of It?

We investigate the effect of possible a priori “imprinting” effects of general relativity itself on satellite/spacecraft‐based tests of it. We deal with some performed or proposed time‐delay ranging experiments in the sun′s gravitational field. It turns out that the “imprint” of general relativity on the Astronomical Unit and the solar gravitational constant GM⊙, not solved for in the so far performed spacecraft‐based time‐delay tests, induces an a priori bias of the order of 10−6 in typical solar system ranging experiments aimed to measure the space curvature PPN parameter γ. It is too small by one order of magnitude to be of concern for the performed Cassini experiment, but it would affect future planned or proposed tests aiming to reach a 10−7–10−9 accuracy in determining γ.

Varying alpha: New constraints from seasonal variations

We analyze the constraints obtained from new atomic clock data on the possible time variation of the fine structure ``constant'' and the electron-proton mass ratio, and show how they are strengthened when the seasonal variation of the Sun's gravitational field at the Earth's surface is taken into account. We compare these bounds with those obtainable from tests of the weak equivalence principle and high redshift observations of quasar absorption spectra.

Phase-space distribution of unbound dark matter near the Sun

We resolve discrepancies in previous analyses of the flow of collisionless dark matter particles in the Sun's gravitational field. We determine the phase-space distribution of the flow both numerically, tracing particle trajectories back in time, and analytically, providing a simple correct relation between the velocity of particles at infinity and at the Earth. We use our results to produce sky maps of the distribution of arrival directions of dark matter particles on Earth at various times of the year. We assume various Maxwellian velocity distributions at infinity describing the standard dark halo and streams of dark matter. We illustrate the formation of a ring, analogous to the Einstein ring, when the Earth is directly downstream of the Sun.

Expansion of solar corona in the Sun's gravitational field and formation of the heliospheric current sheet

Expansion of solar corona in the Sun's gravitational field and formation of the heliospheric current sheet

Solar wakes of dark matter flows

We analyze the effect of the Sun's gravitational field on a flow of cold dark matter (CDM) through the solar system in the limit where the velocity dispersion of the flow vanishes. The exact density and velocity distributions are derived in the case where the Sun is a point mass. The results are extended to the more realistic case where the Sun has a finite size spherically symmetric mass distribution. We find that regions of infinite density, called caustics, appear. One such region is a line caustic on the axis of symmetry, downstream from the Sun, where the flow trajectories cross. Another is a cone-shaped caustic surface near the trajectories of maximum scattering angle. The trajectories forming the conical caustic pass through the Sun's interior and probe the solar mass distribution, raising the possibility that the solar mass distribution may some day be measured by a dark matter detector on Earth. We generalize our results to the case of flows with continuous velocity distributions, such as that predicted by the isothermal model of the Milky Way halo.

Continuous tracking of coronal outflows: Two kinds of coronal mass ejections

We have developed a new technique for tracking white‐light coronal intensity features and have used this technique to construct continuous height/time maps of coronal ejecta as they move outward through the 2–30 Rs field of view of the Large‐Angle Spectrometric Coronagraph (LASCO) on the Solar and Heliospheric Observatory (SOHO) spacecraft. Displayed as gray‐scale images, these height/time maps provide continuous histories of the motions along selected radial paths in the corona and reveal a variety of accelerating and decelerating features, including two principal types of coronal mass ejections (CMEs): (1) Gradual CMEs, apparently formed when prominences and their cavities rise up from below coronal streamers: When seen broadside, these events acquire balloon‐like shapes containing central cores, and their leading edges accelerate gradually to speeds in the range 400–600 km/s before leaving the 2–30 Rs field of view. The cores fall behind with speeds in the range 300–400 km/s. Seen along the line of sight, these events appear as smooth halos around the occulting disk, consistent with head‐on views of optically thin bubbles stretched out from the Sun. At the relatively larger radial distances seen from this “head‐on” perspective, gradually accelerating CMEs fade out sooner and seem to reach a constant speed more quickly than when seen broadside. Some suitably directed gradual CMEs are associated with interplanetary shocks and geomagnetic storms. (2) Impulsive CMEs, often associated with flares and Moreton waves on the visible disk: When seen broadside, these CMEs move uniformly across the 2–30 Rs field of view with speeds typically in excess of 750 km/s. At the relatively larger radial distances seen from a head‐on perspective, impulsive events tend to have a more ragged structure than the gradual CMEs and show clear evidence of deceleration, sometimes reducing their speeds from 1000 to 500 km/s in 1 hour. Such decelerations are too large to represent ballistic motions in the Sun's gravitational field but might be caused by shock waves, sweeping up material far from the Sun.

Solar Activity and Interplanetary Disturbances

The Sun is not only a source of energy but also a tremendous source of interplanetary disturbances. The continuous stream of plasma (solar wind) is propelled by a pressure gradient near the photosphere. The pressure gradient and the Sun's gravitational field drive the plasma to supersonic velocities at the Earth's orbit. Solar activity is discussed in terms of the characteristics of the origin, x-ray flare class, optical classification, radio emission, energy particle emission and geophysical effects. Solar activities during March–June 1991 and February 20–21, 1994 are but two activities in recent times which resulted in large scale Interplanetary Waves (IPW), medium-scale gravity waves and geomagnetic disturbances. The disturbances of these activities are also discussed.

Microarcsecond astrometry in space - Relativistic effects and reduction of observations

view Abstract Citations (86) References (36) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Microarcsecond Astrometry in Space: Relativistic Effects and Reduction of Observations Klioner, S. A. ; Kopeikin, S. M. Abstract The paper applies the framework of general relativity to the problem of reduction of high-precision astrometric observations of the order of 1 microarcsec. Theoretical methods making it possible to construct astrometric reference systems involving the barycentric, geocentric, and satellite (observer) systems are described. Relativistic transformations between the reference systems employed are derived. Equations of geometric optics for the nonstationary gravitational field of the solar system are deduced. The effects of relativistic deflection of the light due to monopole and quadrupole components of the sun's gravitational field and the planets are calculated, with their motions and rotations taken into account. Transformations between the reference systems are used to calculate the light aberration occurring when passing from the satellite system to the geocentric system and from the geocentric system to the barycentric systems. Aberrational corrections are applied to transform the observed position of a celestial object to the barycentric system, taking the relativistic light deflection into account. Publication: The Astronomical Journal Pub Date: August 1992 DOI: 10.1086/116284 Bibcode: 1992AJ....104..897K Keywords: Astrometry; Celestial Reference Systems; Relativistic Effects; Relativity; Computational Astrophysics; Gravitational Fields; Perturbation Theory; Solar System; Stellar Parallax; Astronomy; ASTROMETRY; RELATIVITY; TECHNIQUES: INTERFEROMETRIC full text sources ADS |

Can the Sun shed light on neutrino gravitational interactions?

We have examined the effects of a large gravitational field on the phenomenon of neutrino oscillations as contemplated in the Mikheyev-Smirnov-Wolfenstein mechanism. We find that the Sun's gravitational field would amplify any small breakdown in the universality of the gravitational coupling by many orders of magnitude. A breakdown of only 1 part in ${10}^{14}$ would still make the gravitational effect comparable to the conventional weak interaction. The differing energy dependences of the two level-crossing mechanisms can therefore be used as a very sensitive tool to test the conventional universality hypothesis.

New measurement of solar gravitational deflection of radio signals using VLBI

RADIO observations using very-long-baseline interferometry (VLBI) can measure the deflection of electromagnetic radiation by the Sun's gravitational field with an accuracy of better than 1 milliarcsecond, and can thus be used to test General Relativity. For an object at an angle a from the centre of the Sun, the expected deflection is1 (1 + γ) (Ms/re)((l + cos α)/(l-cos α))1/2, where Ms is the mass of the Sun in geometrized units2 (1.477 × 105 cm), re is the distance from the Earth to the Sun in cm, and y is a parameter whose value is 1 if General Relativity is correct but which takes on different values in other theories of gravity. For γ = 1, the deflection is 1,750 mas at the Sun's limb, 4 mas at α =90° and 0 at α = 180°. Our analysis of ten years of VLBI data, including observations of objects in the range 2.5° < a< 178°, yields an estimate γ = 1.0002 with a formal standard error of 0.00096 and an estimated standard error of 0.002. This determination is comparable in accuracy and in good agreement with the determination from Mars–Viking time-delay measurements3.

Classical model for angular momentum mixing of Rydberg states.

A classical model for l mixing of Rydberg states in atomic collisions is described. The primary assumption of the model is that l changing occurs in a single hard-sphere collision between the Rydberg electron and the perturbing atom which is represented by the zero-energy scattering length L. Predictions of the model, which are in the form of cross sections as functions of principal quantum number n, are compared with data for l mixing of Na(nd) and Rb(nf) by rare-gas atoms. Agreement is, in most cases, quite good, comparable with that of other, more sophisticated, models. It is shown that, because the calculation must be carried out in the reference frame of the ion core, the energy deficit between low angular momentum states and the nearest hydrogenic manifold can be made up in a single collision between the Rydberg electron and the perturbing atom, an effect that is analogous to the gravitational slingshot effect used to alter the orbits of a spacecraft under the influence of the Sun's gravitational field. Comparison of data for l mixing by ground-state Rb atoms with model calculations in which L is treated as a free parameter leads to an estimate of 10 a.u. for the zero-energy scattering length of Rb.