Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGravitational major-axis contraction of Mercurys elliptical orbit
264
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The local curvature of the space produced by the Sun causes not only the perihelion precession of Mercurys 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 the Mercurys elliptical orbit is 1.3 kilometers which can be confirmed by the present astronomical distance measurement technology.
rate research
Read More
The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed investigation on this problem, and reach the results: (I). The comoving coordinate system for the stellar system is only compatible with the zero-pressure free falling particles. (II). For the free falling dust, there are three kind of solutions respectively corresponding to the oscillating, the critical and the open trajectories. The solution of Oppenheimer and Snyder is the critical case. (III). All solutions are exactly derived. There is a new kind singularity in the solution, but its origin is unclear.
We analyze the trajectories of three geostationary satellites forming the GEOstationary GRAvitational Wave Interferometer (GEOGRAWI)~cite{tinto}, a space-based laser interferometer mission aiming to detect and study gravitational radiation in the ($10^{-4} - 10$) Hz band. The combined effects of the gravity fields of the Earth, the Sun and the Moon make the three satellites deviate from their nominally stationary, equatorial and equilateral configuration. Since changes in the satellites relative distances and orientations could negatively affect the precision of the laser heterodyne measurements, we have derived the time-dependence of the inter-satellite distances and velocities, the variations of the polar angles made by the constellations three arms with respect to a chosen reference frame, and the time changes of the triangles enclosed angles. We find that, during the time between two consecutive station-keeping maneuvers (about two weeks), the relative variations of the inter-satellite distances do not exceed a value of $0.05$ percent, while the relative velocities between pairs of satellites remain smaller than about $0.7 {rm m/s}$. In addition, we find the angles made by the arms of the triangle with the equatorial plane to be periodic functions of time whose amplitudes grow linearly with time; the maximum variations experienced by these angles as well as by those within the triangle remain smaller than $3$ arc-minutes, while the East-West angular variations of the three arms remain smaller than about $15$ arc-minutes during the two-weeks period. The relatively small variations of these orbit parameters result into a set of system functional and performance requirements that are less stringent than those characterizing an interplanetary mission.
The (1, 0)+(0, 1) representation of the group SL(2, C) provides a six-component spinor equivalent to the electromagnetic field tensor. By means of the (1, 0)+(0, 1) description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin-orbit coupling of photons. Once the gravitational spin-orbit coupling is taken into account, the traditional radius of the circular photon orbit in the Schwarzschild geometry should be replaced with two different radiuses corresponding to the photons with the helicities of +1 and -1, respectively. Owing to the splitting of energy levels induced by the spin-orbit coupling, photons (from Hawking radiations, say) escaping from a Schwarzschild black hole are partially polarized, provided that their initial velocities possess nonzero tangential components.
Performing a fully non-perturbative analysis using the tools of numerical general relativity, we demonstrate that a period of slow contraction is a `supersmoothing cosmological phase that homogenizes, isotropizes and flattens the universe both classically and quantum mechanically and can do so far more robustly and rapidly than had been realized in earlier studies.
We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, we find that the geometry first rapidly converges to an inhomogeneous, spatially-curved and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
