Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.Comment: 13 pages, 2 figures, accepted for publication in General Relativity and Gravitatio

Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit

We will investigate the influence of the inhomogeneity of the universe, especially that of the Lema{\^i}tre-Tolman-Bondi (LTB) model, on a gravitationally bound local system such as the solar system. We concentrate on the dynamical perturbation to the planetary motion and derive the leading order effect generated from the LTB model. It will be shown that there appear not only a well-known cosmological effect arisen from the homogeneous and isotropic model, such as the Robertson-Walker (RW) model, but also the additional terms due to the radial inhomogeneity of the LTB model. We will also apply the obtained results to the problem of secular increase in the astronomical unit, reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of the universe cannot have a significant effect for explaining the observed $d{\rm AU}/dt = 15 \pm 4 ~{\rm [m/century]}$.Comment: 12 pages, no figure, accepted for publication in Journal of Astrophysics and Astronom

Apollo asteroids (1566) Icarus and 2007 MK6: Icarus family members?

Although it is more complicated to search for near-Earth object (NEO) families than main belt asteroid (MBA) families, since differential orbital evolution within a NEO family can cause current orbital elements to drastically differ from each other, we have found that Apollo asteroids (1566) Icarus and the newly discovered 2007 MK6 are almost certainly related. Specifically, their orbital evolutions show a similar profile, time shifted by only ~1000 yr, based on our time-lag theory. The dynamical relationship between Icarus and 2007 MK6 along with a possible dust band, the Taurid-Perseid meteor swarm, implies the first detection of an asteroidal NEO family, namely the "Icarus asteroid family".Comment: 11 pages, 1 figure, to appear on Astrophysical Journal Letters (journal info added

A new set of integrals of motion to propagate the perturbed two-body problem

A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131?150,2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez?s method for near-circular motion under the J2 perturbation is transformed into linear.Moreover, themethod reveals to be competitive with two very popular elementmethods derived from theKustaanheimo-Stiefel and Sperling-Burdet regularizations

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. The present paper gives the physical interpretation of the observed light-ray deflections and discusses the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by the Jupiter and the Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.

Quasi-Hilda comet 147P/Kushida-Muramatsu

Context. The quasi-Hilda comets (QHCs), being in unstable 3:2 Jovian mean motion resonance, are considered a major cause of temporary satellite capture (TSC) by Jupiter. Although the QHCs may be escaped Hilda asteroids, their origin and nature have not yet been studied in sufficient detail. Of particular interest are long TSCs/orbiters. Orbiters – in which at least one full revolution about the planet is completed – are rare astronomical events, because only four have been known to occur in the last several decades. Every case has been associated with a QHC: 82P/Gehrels 3, 111P/Helin-Roman-Crockett, P/1996 R2 (Lagerkvist), and the possibly QHC-derived D/1993 F2 (Shoemaker-Levy 9, SL9). Aims. We focus on long TSC/orbiter events involving QHCs and Jupiter. Thus we survey the known QHCs, searching for other long TSCs/orbiters over the past century. Methods. First, we confirmed the long TSC/orbiter events of 82P, 111P, and 1996 R2 in order to test our method against previous work, applying a general N-body Newtonian code. We then used the same procedure to survey the remaining known QHCs and search for long TSC/orbiter events. Results. We newly identified another long TSC/orbiter: 147P/Kushida-Muramatsu from 1949 May 14$^{+97 {\rm days}}_{-106 {\rm days}}$-1961 July 15. Our result is verified by integrations of 243 cloned orbits that take account of the present orbital uncertainty of this comet. The event involves an L2 $\to$ L1 transition as with 82P and 1996 R2. This may represent a distinct subtype of TSCs from QHC-derived (L1 $\to$) longer captures exemplified by 111P and (probably) SL9, though this classification is still only based on a small database of TSCs. Conclusions. This is the third long TSC and the fifth orbiter to be found, thus long TSC/orbiter events involving Jupiter have occurred once per decade. Two full revolutions about Jupiter were completed and the capture duration was 12.17$^{\rm +0.29}_{-0.27}$ years. Both these numbers rank 147P as third among long TSC/orbiter events, behind SL9 and 111P. This study also confirms the importance of the QHC region as a dynamical route into and out of Jovian TSC, via the Hill's sphere

Apollo asteroid 2005 UD: split nucleus of (3200) Phaethon?

Context.The recently discovered Apollo asteroid 2005 UD is the most likely candidate for being a large member of the Phaethon-Geminid stream Complex (PGC). Aims.Detecting more complex members like this should clarify the formation and evolution of the PGC. Methods.Our backward and forward (±$10\,000$-yr) integration of the Kustaanheimo-Stiefel regularized equation of motion revealed that the orbital evolutions of Apollo asteroids (3200) Phaethon and 2005 UD show a similar profile, time-shifting by ~4600 yr. Results. Within the PGC, this time shift is rather large against the time-lag of 220 yr for Phaethon-Geminids and ~3900 yr between Phaethon-Sextantids, although much smaller than that of ~$19\,000$ yr between Phaethon-Canis Minorids. Conclusions.This is a km-order object, hence may be a split nucleus of Phaethon. Besides, the orbital parameters of 2005 UD and the Sextantids are in good agreement along with the time-lag of 100 yr. Therefore, the Sextantid meteor shower seems to be associated more closely with 2005 UD than Phaethon