Planetary orbits for a moving Sun

1969 ◽  
Vol 47 (20) ◽  
pp. 2161-2164 ◽  
Author(s):  
Peter Rastall

The scalar theory of gravitation is known to be in agreement with observed planetary motions if the Sun is assumed to be stationary with respect to the preferred coordinate systems of the theory. We now assume that the Sun is moving, and we find that, unless its speed is improbably small, there are observable effects on the planetary orbits. The difficulty can be overcome if one assumes that the Newtonian charts are determined by the distribution of matter.

1960 ◽  
Vol 38 (8) ◽  
pp. 975-982 ◽  
Author(s):  
Peter Rastall

The form of the space–time metric in a scalar theory of gravitation follows from the assumption that the potential is arbitrary to the extent of an additive constant. No field equations are needed. Expressions are found for the gravitational red shift, the perihelion motion of a planet, and the bending of light by the sun. From the observed values of these quantities one can determine the metric and the potential due to a gravitating mass.


2020 ◽  
Vol 3 (1) ◽  
pp. 266-282
Author(s):  
Niccolò Guicciardini

AbstractRobert Hooke’s theory of gravitation is a promising case study for probing the fruitfulness of Menachem Fisch’s insistence on the centrality of trading zone mediators for rational change in the history of science and mathematics. In 1679, Hooke proposed an innovative explanation of planetary motions to Newton’s attention. Until the correspondence with Hooke, Newton had embraced planetary models, whereby planets move around the Sun because of the action of an ether filling the interplanetary space. Hooke’s model, instead, consisted in the idea that planets move in the void space under the influence of a gravitational attraction directed toward the sun. There is no doubt that the correspondence with Hooke allowed Newton to conceive a new explanation for planetary motions. This explanation was proposed by Hooke as a hypothesis that needed mathematical development and experimental confirmation. Hooke formulated his new model in a mathematical language which overlapped but not coincided with Newton’s who developed Hooke’s hypothetical model into the theory of universal gravitation as published in the Mathematical Principles of Natural Philosophy (1687). The nature of Hooke’s contributions to mathematized natural philosophy, however, was contested during his own lifetime and gave rise to negative evaluations until the last century. Hooke has been often contrasted to Newton as a practitioner rather than as a “scientist” and unfavorably compared to the eminent Lucasian Professor. Hooke’s correspondence with Newton seems to me an example of the phenomenon, discussed by Fisch in his philosophical works, of the invisibility in official historiography of “trading zone mediators,” namely, of those actors that play a role, crucial but not easily recognized, in promoting rational scientific framework change.


2015 ◽  
Vol 11 (A29A) ◽  
pp. 360-364
Author(s):  
Rim Fares

AbstractIn Sun-like stars, magnetic fields are generated in the outer convective layers. They shape the stellar environment, from the photosphere to planetary orbits. Studying the large-scale magnetic field of those stars enlightens our understanding of the field properties and gives us observational constraints for field generation dynamo models. It also sheds light on how “normal” the Sun is among Sun-like stars. In this contribution, I will review the field properties of Sun-like stars, focusing on solar twins and planet hosting stars. I will discuss the observed large-scale magnetic cycles, compare them to stellar activity cycles, and link that to what we know about the Sun. I will also discuss the effect of large-scale stellar fields on exoplanets, exoplanetary emissions (e.g. radio), and habitability.


1831 ◽  
Vol 121 ◽  
pp. 199-207

In the annexed Table are given the results of a series of observations on the vibrations of the magnetic needle, which I undertook last summer, for the purpose of ascertaining whether its intensity is or is not affected by the changes in the earth’s distance from the sun, or by its declination with respect to the plane of his equator; for, if we refer the nodes of the planetary orbits to this plane, there appears to be so considerable a degree of coincidence in most of them, as would seem to imply the existence of a more definite law than we are ac­customed to attach to the abstract principle of gravitation. I am not at present prepared to say much respecting this part of my investigation; but I have obtained results, which appear to be interesting, relative to the variable force of the magnetic attraction, and the action of the aurora borealis on the direction and intensity of the needle.


2019 ◽  
Vol 34 (20) ◽  
pp. 1950159
Author(s):  
Q. H. Liu ◽  
Q. Li ◽  
T. G. Liu ◽  
X. Wang

The local curvature of the space produced by the Sun causes not only the perihelion precession of Mercury’s elliptical orbit, but also the variations of the whole orbit, in comparison with those predicted by the Newtonian theory of gravitation. Calculations show that the gravitational major-axis contraction of Mercury’s elliptical orbit is 1.3 km which can in principle be confirmed by the present astronomical distance measurement technology.


1965 ◽  
Vol 33 (2) ◽  
pp. 162-163
Author(s):  
A. L. Harvey

The Whitehead gravitation tensor for the exterior field due to a finite, uniform rotating sphere is evaluated in closed form. The advance of perihelion of an equatorial orbit is then calculated, making no assumption as to the smallness of the angular velocity of the central sphere. Finally, the perturbing forces on the Newtonian elliptical orbit due to rotation of the central sphere are determined with neglect of the square of this angular velocity. It is remarkable that the results of the present paper based on Whitehead’s theory agree very closely with those obtained by Lense & Thirring (1918) using Einstein’s linearized law of gravitation. In fact, for a homogeneous sphere, it is impossible to distinguish between the results in the two theories, to the order of approximation considered.


1981 ◽  
Vol 59 (2) ◽  
pp. 283-288 ◽  
Author(s):  
J. W. Moffat

The predictions for the perihelion shift, the deflection of light, and the delay time of a light ray are calculated in the nonsymmetric theory of gravitation. An upper bound for the parameter l (that occurs as a constant of integration in the static, spherically symmetric solution of the field equations) is obtained for the sun for the experimental value of the perihelion shift of Mercury, yielding [Formula: see text]. The upper bound on [Formula: see text] obtained from the Viking spacecraft time-delay experiment is [Formula: see text]. For [Formula: see text], we find that the theory is consistent with the standard relativistic experiments for the solar system. The theory predicts that the perihelion of a satellite could reverse its direction of precession if it orbits close enough to the sun. The results for a highly eccentric satellite orbit are calculated in terms of the value [Formula: see text].


2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Tanmay Kumar Poddar ◽  
Subhendra Mohanty ◽  
Soumya Jana

AbstractThe standard model leptons can be gauged in an anomaly free way by three possible gauge symmetries namely $${L_e-L_\mu }$$ L e - L μ , $${L_e-L_\tau }$$ L e - L τ , and $${L_\mu -L_\tau }$$ L μ - L τ . Of these, $${L_e-L_\mu }$$ L e - L μ and $${L_e-L_\tau }$$ L e - L τ forces can mediate between the Sun and the planets and change the perihelion precession of planetary orbits. It is well known that a deviation from the $$1/r^2$$ 1 / r 2 Newtonian force can give rise to a perihelion advancement in the planetary orbit, for instance, as in the well known case of Einstein’s gravity (GR) which was tested from the observation of the perihelion advancement of the Mercury. We consider the long range Yukawa potential which arises between the Sun and the planets if the mass of the gauge boson is $$M_{Z^{\prime }}\le \mathcal {O}(10^{-19})\mathrm {eV}$$ M Z ′ ≤ O ( 10 - 19 ) eV . We derive the formula of perihelion advancement for Yukawa type fifth force due to the mediation of such $$U(1)_{L_e-L_{\mu ,\tau }}$$ U ( 1 ) L e - L μ , τ gauge bosons. The perihelion advancement for Yukawa potential is proportional to the square of the semi major axis of the orbit for small $$M_{Z^{\prime }}$$ M Z ′ , unlike GR where it is largest for the nearest planet. For higher values of $$M_{Z^{\prime }}$$ M Z ′ , an exponential suppression of the perihelion advancement occurs. We take the observational limits for all planets for which the perihelion advancement is measured and we obtain the upper bound on the gauge boson coupling g for all the planets. The Mars gives the stronger bound on g for the mass range $$\le 10^{-19}\mathrm {eV}$$ ≤ 10 - 19 eV and we obtain the exclusion plot. This mass range of gauge boson can be a possible candidate of fuzzy dark matter whose effect can therefore be observed in the precession measurement of the planetary orbits.


Sign in / Sign up

Export Citation Format

Share Document