Perihelion Of Mercury Research Articles

Experimental testing of relativistic effects, variability of the gravitational constant and topography of Mercury surface from radar observations 1964?1989

The new analysis of radar observations of inner planets for the time span 1964–1989 is described. The residuals show that Mercury topography is an important source of systematic errors which have not been taken into account up to now. The longitudinal and latitudinal variations of heights of Mercury surface were found and an approximate map of equatorial zone |ϕ|≤120° was constructed. Including three values characterizing global nonsphericity of Mercury surface into the set of parameters under determination allowed to improve essentially all estimates. In particular, the variability of the gravitational constantG was evaluated: $$\dot G/G = (0.47 \pm 0.47) \times 10^{ - 11} yr^{ - 1} $$ . The correction to Mercury perihelion motion: $$\Delta \dot \pi = - 0''.017 \pm 0''.052 cy^{ - 1} $$ and linear combination of the parameters of PPN formalism: $$\upsilon = (2 + 2\gamma - \beta )/3 = 0.9995 \pm 0.0013$$ were determined; they are in a good agreement with General Relativity predictions. The obtained values Δ.π and ν correspond to the negligible solar oblateness, the estimate of solar quadrupole moment being: $$J_2 = ( - 0.13 \pm 0.41) \times 10^{ - 6} $$ .

Some Aspects of Minimally Relativistic Newtonian Gravity

Abstract This paper aims to examine if the classical tests of General Relativity (GR) can be predicted by a simpler approach based on minimal changes in the Newtonian gravity. The approach yields a precession of the perihelion of Mercury by an amount 39.4"/century which is very close to the observed Dicke-Goldenberg value (39.6"/century), but less than the popularly accepted value (43"/ century). The other tests exactly coincide with those of GR. Our analysis also displays the genesis as well as the role of geometry in the description of gravitational processes. The time dependent spherically symmetric equations, which are mathematically interesting, call for a further study. The model also allows unambiguous formulation of conservation laws. On the whole, the paper illustrates the limited extent to which a second rank tensor analogy (nonlinear) with flat background Faraday-Maxwell electrodynamics can be pushed in describing gravitation

Relativistic Newtonian gravity: an improved version

In view of a serious error found in a recent article by Biswas (1988) an improved version of the author's flat spacetime theory of gravitation has been presented. Twofold modifications to Biswas' theory (BT) have been suggested. Firstly, to obtain particle trajectories, instead of using Biswas' noncovariant Hamiltonian formulation, a covariant Lagrangian formulation has been developed to obtain the equation of motion of test objects. Secondly, the nongeneral-relativistic field equations of BT have also been modified. It has been shown that with these changes the present theory when applied to a matter-free spherically symmetric situation, produces correct values for the advance of the perihelion of Mercury's orbit and bending of light near the Sun. The energy integral for a particle trajectory has been calculated. This has been used to obtain the general red shift formula. A brief survey of some other flat spacetime theories of gravitation is also presented, to demonstrate how in spite of its error, BT stands out in sharp contrast in its ability to provide a direction along which a viable relativistic theory of gravitation can be obtained.

Comment on ‘‘Precession of the perihelion of Mercury,’’ by Daniel R. Stump [Am. J. Phys. 5 6, 1097–1098 (1988)

Comment on ‘‘Precession of the perihelion of Mercury,’’ by Daniel R. Stump [Am. J. Phys. <b>5</b> <b>6</b>, 1097–1098 (1988)

Prediction and Theory Evaluation: The Case of Light Bending

Is a theory that makes successful predictions of new facts better than one that does not? Does a fact provide better evidence for a theory if it was not known before being deduced from the theory? These questions can be answered by analyzing historical cases. Einstein's successful prediction of gravitational light bending from his general theory of relativity has been presented as an important example of how "real" science works (in contrast to alleged pseudosciences like psychoanalysis). But, while this success gained favorable publicity for the theory, most scientists did not give it any more weight than the deduction of the advance of Mercury's perihelion (a phenomenon known for several decades). The fact that scientists often use the word "prediction" to describe the deduction of such previously known facts suggests that novelty may be of little importance in evaluating theories. It may even detract from the evidential value of a fact, until it is clear that competing theories cannot account for the new fact.

Possible test at Jupiter of the nonsymmetric gravitational theory.

Radiometric data generated during spacecraft flybys of Jupiter have the capability to provide an interesting constraint on the coupling of cosmions in the nonsymmetric gravitational theory (NGT) of Moffat. It is shown that the close flyby of Jupiter by Pioneer 11 could imply a possible limit on the NGT $l$ parameter of the Sun of ${l}_{\ensuremath{\bigodot}}&lt;2800$ km, a limit which could affect the ability of the NGT to account for the precession of the perihelion of Mercury with a large solar quadrupole moment.

Precession of the perihelion of Mercury

The equation of motion for a test mass in the gravitational field of a spherical mass is written in a form that can be used in an undergraduate mechanics course. A simple calculation of the general relativistic precession of the perihelion of Mercury is presented.

The modified Newtonian force law of Rood and the perihelion shift of Mercury

A modification of the Newtonian force law proposed by Rood is shown not to yield the correct value for the relativistic precession of the perihelion of Mercury, contrary to the claim by Rood. Instead, the theory is shown to yield 3/2 times the prediction of general relativity, in gross disagreement with solar system observations.

The real value of Mercury's perihelion advance

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones of general relativity. After the effects of the gravitational perturbations of the other planets have been accounted for, the remaining advance fits accurately to predictions according to the theory of general relativity, that is, 43 arc s per 100 yr. In fact, radar determinations of Mercury's motion since the mid-1960s have produced agreement with general relativity at the level of 0.5%, or to ±0.2arcs per 100 yr. We have recently been puzzled by an apparent uncertainty in the value of the theoretical prediction for the advance within general relativity, as cited in various sources. The origin of this discrepancy is a 1947 article by Clemence1, who used unconventional values for the astronomical unit (A) and the speed of light (c) in his calculation of the predicted advance. Since that time, virtually everyone has followed suit. Although the current value of the prediction, using the best accepted values for the astronomical constants and for the orbital elements of Mercury, is 42.98 arc s per 100 yr, there is a preponderance of citations over the past 25 years of Clemence's value 43.03 arc s per 100 yr. Here we derive the accurate value and uncover the source of Clemence's value.

Relativistic effects from planetary and lunar observations of the XVIII–XX centuries

Lunar and planetary observations of different types are discussed for the time span 1717–1982. The modern ranging observations and the historical ones (mainly transits of Mercury and Venus, solar eclipses and occultations of the inner planets by the Moon) are treated separately and some attempts to detect relativistic effects are carried out. From time delay observations linear combination ν = (2 + 2 γ-β) /3 of the parameters of the PPN formalism is evaluated: ν =0.997±0.003. Statistically significant estimate for the rate Ġ of changing of the gravitational constant G is found: Ġ/G=(4±0.8) · 10−11 /yr. (An alternative interpretation of this result due to Canuto et al. (1979) gives negative sign for Ġ). From transits of Mercury and Venus corrections to the adopted system of differences between the ephemeris (dynamic) and the atomic time scales and a correction to the Mercury's perihelion advance are deduced. With new ephemeris time scale it became possible to determine unambigiously lunar tidal deceleration ṅM making use of the historical lunar observations. The derived value ṅM = (−22.2 ± 0.8)′′/cy2 is in good agreement with reported lunar laser results. By comparing the estimates ṅM obtained by the two methods the rate Ġ has also been evaluated: Ġ/G=(0.5+0.5)·10−11/yr. The origin of the disagreement with the radar based result for Ġ is not yet clear. All the conclusions were checked by making use of different planetary and lunar theories and appear to be practically theory-independent.

Mercury's Perihelion from Le Verrier to Einstein. N. T. Roseveare

<i>Mercury's Perihelion from Le Verrier to Einstein</i>. N. T. Roseveare

Newtonian N-body calculations of the advance of Mercury's perihelion

The rate of advance of the perihelion of planet Mercury is calculated by a numerical integration of the Newtonian equations of motion and gravitation. It is found that the rate fluctuates but has a steady trend of ∼528.95 arcsec cy−1 over a long-term period of about five centuries. Taking into account the observed precession we therefore find that the general relativistic correction explains all but about 2.3 arcsec cy−1 of the discrepancy. It may be necessary to invoke another cause like solar oblateness to account for the residual effect.

Book Review: Mercury's Anomalous Motion: Mercury's Perihelion from Le Verrier to Einstein

Book Review: Mercury's Anomalous Motion: Mercury's Perihelion from Le Verrier to Einstein

Electrodynamical origins of Einstein's theory of general relativity

The failure of the Newtonian theory of gravitation to satisfactorily account for the motion of Mercury's perihelion cannot be held to have justified the development of general relativity. This paper shows how the origins of general relativity were firmly embedded in contemporary attempts to introduce the new mechanics of special relativity into gravitational theory. These new theories of gravitation took as their basis the electrodynamical equations as formulated by Minkowski and attempted to represent the gravitational potential first by a vector and then by a scalar (in the four-dimensional sense). That Einstein chose the symmetric fundamental tensorg ij as his gravitational potential is seen to have been both a natural and necessary development. With this viewpoint the full theory of general relativity can be seen to be remarkably similar to those theories of gravitation that preceded it. The paper also contains a previously unpublished letter written by Einstein to H. A. Lorentz.

Foundations for a theory of gravitation

In this paper we shall discuss some foundations for a theory of gravitation through which we shall explain the «four crucial effects» of general relativity (the red-shift, the precession of the perihelion of Mercury, the bending of light and the time delay of radar echoes). We shall show that, with the theory developed, it is possible to establish the proportionality between the energy content and the frequency, for a packet of waves of arbitrary nature.

Mercury's Perihelion, from Le Verrier to Einstein

<i>Mercury's Perihelion, from Le Verrier to Einstein</i>

Consequences of a New Experimental Determination of the Quadrupole Moment of the Sun for Gravitation Theory

A preliminary experimental determination by Hill, Bos, and Goode of the interior rotation of the sun leads to a nonzero value for the quadrupole moment coefficient ${J}_{2}$. This produces a deviation of 1.6% from Einstein's prediction of the precession of the perihelion of Mercury. A nonsymmetric gravitational theory can fit the measured precession with this ${J}_{2}$ and all other solar-system relativity experiments for one value of a post-Newtonian parameter in the theory. A prediction is made for the perihelion precession of Icarus.

On a nonlinear and Lorentz-invariant verson of Newtonian gravitation

This paper gives a full nonlinear version of Newtonian gravity in which the gravitational energy acts as a source of the gravitational field. The generalized field equation for the scalar gravitational potential is solved for a spherically symmetric localized distribution of matter. It is shown that the perihelia of orbits of test particles in such a field precess steadily. The effect is, however, too small to account for the observed shift in the perihelion of planet Mercury. Further, the bending of light in this theory is zero. It is suggested that these inadequacies of the quasi-Newtonian framework call for more sophisticated approaches to gravity.

Small oscillations of test bodies in circular orbits in the Schwarzschild and Kerr metrics (Shirokov's effect)

Shirokov's effect is reexamined and analyzed with the help of a monadic method for defining reference systems. It is shown that the difference in the periods of oscillations is of the same nature as the phenomenon of the displacement of Mercury's perihelion. This effect is calculated in an analogous manner in Kerr's metric.

Nonrelativistic contribution to Mercury’s perihelion precession

We present here a calculation of the precession of the perihelion of Mercury due to the perturbations from the outer planets. The time-average effect of each planet is calculated by replacing that planet with a ring of linear mass density equal to the mass of the planet divided by the circumference of its orbit. The calculation is easier than examples found in many undergraduate theoretical mechanics books and yields results which are in excellent agreement with more advanced treatments. The perihelion precession is seen to result from the fact that the outer planets slightly change the radial period of oscillation from the simple harmonic period usually calculated for small displacements from equilibrium. This new radial period therefore no longer matches the orbital period and the orbit consequently does not exactly retrace itself. The general question of whether a given perturbation will cause the perihelion to advance or regress is shown to have the following answer: if a perturbing force is central and repulsive and also becomes stronger as the distance from the force center increases, the perihelion will advance. If the central perturbing force is attractive and also becomes stronger as the distance from the force center increases, the perihelion will regress.