Evolution of gravitational orbits in the expanding universe

Abstract

The gravitational action of the smooth energy-matter components filling in the universe can affect the orbit of a planetary system. Changes are related to the acceleration of the cosmological scale size R. In a universe with significant dark matter, a gravitational system expands or contracts according to the amount and equation of state of the dark energy. At present time, the Solar system, according to the ΛCDM scenario emerging from observational cosmology, should be expanding if we consider only the effect of the cosmological background. Its fate is determined by the equation of state of the dark energy alone. The mean motion and periastron precession of a planet are directly sensitive toR/R, whereas variations with time in the semi-major axis and eccentricity are related to its time variation. Actual bounds on the cosmological deceleration parameters q0 from accurate astrometric data of perihelion precession and changes in the third Kepler's law in the Solar system fall short of ten orders of magnitude with respect to estimates from observational cosmology. Future radio-ranging measurements of outer planets could improve actual bounds by five order of magnitude.PACS numbers: 04.80. Cc,95.10.Ce,95.30.Sf,95.36.+x,

On gravitational waves in spacetimes with a nonvanishing cosmological constant

“…In principle the cosmological constant should take part in phenomena on every physical scale. For instance, it has been studied which limits on Λ can be put from solar system measurements, such as the effect on the perihelion precession of the solar systemplanets [2,3,4,5,6,7,8]. The cosmological constant could also influence gravitationallensing [9,10] and play a role in the gravitational equilibrium of large astrophysical structures [11].…”

The kinematic origin of the cosmological redshift

“…Again, explicit calculation shows this belief not to be correct. 18,19 The tendency to expand due to the stretching of space is nonexistent, not merely negligible.…”

The Lingering Anomalous Secular Increase of the Eccentricity of the Orbit of the Moon: Further Attempts of Explanations of Cosmological Origin

“…At the Newtonian level, the cosmological expansion induces a Hooke-type two-body acceleration proportional to the binary's separation r through an "elastic" constant K given by the relative acceleration rateSS −1 of the cosmic scale factor S; see, e.g., [11] and references therein. Such an acceleration, proportional to the square of the Hubble parameter H, affects neither the shape nor the size of the orbit of a localized binary system, as it was calculated by several authors with a variety of different approaches [12][13][14][15][16].…”