We investigated the impact of three different modifications of Newtonian gravity on motions of Keplerian objects within the Solar System. These objects are located at distances of the order of the distance to the Oort cloud. With these three modifications we took into account a heliocentric Dark-Matter halo as was indicated by Diemand et al, Modified Newtonian Dynamics (MOND) and a vacuum-induced force due to a locally negative cosmological constant $Λ_-$ derived by Fahr & Siewert. In gravitationally bound systems it turns out that all three modifications deliver the same qualitative results: Initially circular orbits for the pure Newtonian case are forced to convert into ellipses with perihelion migrations. The quantitative consideration, however, of the orbital parameters showed strong differences between MOND on the one side, and Dark-Matter and $Λ_-$ effects on the other side.
Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between bodies in the disk drive exponential growth of their orbital inclinations and clustering in their angles of pericenter, expanding an initially thin disk into a conical shape by giving each orbit an identical 'tilt' with respect to the disk plane. This new instability dynamically produces the unusual distribution of orbits observed for minor planets beyond N…
We propose a mechanism for the observed non-keplerian motion (Tiscareno et al. 2010, ApJL) of "propeller" moons embedded in Saturn's rings. Our mechanism, in which radial variations in surface density -- external to, and unaffected by, the embedded moon -- result in an equilibrium semimajor axis for the moon due to "Type I" angular momentum exchange (Crida et al. 2010, AJ), provides a good fit to the observations. Future observations should distinguish between our model and others recently proposed.
The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in celestial mechanics and astrodynamics, e.g. to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits over many revolutions. For this, the method uses the high-order Taylor expansion of a Poincaré or stroboscopic map, which is accurate close to the expansion point. In this paper, we investigate the performance of the HOTM method using different element sets for building the high-order map. The elem…
Post-Keplerian perturbations of the hyperbolic motion in the field of a rotating massive object. Analysis in terms of osculating and nonosculating (contact) elements
Axisymmetric disks of eccentric orbits in near-Keplerian potentials are unstable to an out-of-plane buckling. Recently, Zderic et al. (2020) showed that an idealized disk saturates to a lopsided mode. Here we show that this apsidal clustering also occurs in a primordial scattered disk in the outer solar system which includes the orbit-averaged gravitational influence of the giant planets. We explain the dynamics using Lynden-Bell (1979)'s mechanism for bar formation in galaxies. We also show surface density and line of sight velocity plots at different times during the instability, highlightin…
In the past few decades, various versions of modified gravity theories were proposed to mimic the effect of dark matter. Compared with the conventional Newtonian or relativistic dynamics, these theories contain some extra apparent force terms in the dynamical equations to replace the role of dark matter. Generally speaking, the extra apparent force terms usually scale with radius so that the effect would be significant only on large scale to explain the missing mass in galaxies or galaxy clusters. Nevertheless, the apparent effect may still be observable in small structures like the solar syst…
In this paper, we study different Solar System tests in a modified Teleparallel gravity theory based on an arbitrary function $f(T,B)$ which depends on the scalar torsion $T$ and the boundary term $B$. To do this, we first find new perturbed spherically symmetric solutions around Schwarzschild for different power-law forms of the arbitrary Lagrangian. Then, for each model we calculated the photon sphere, perihelion shift, deflection of light, Cassini experiment, Shapiro delay and the gravitational redshift. Finally, we confront these computations with different known experiments from these Sol…
Many long-range modifications of the Newtonian/Einsteinian standard laws of gravity have been proposed in the recent past to explain various celestial phenomena occurring at different scales ranging from solar system to the entire universe. The most famous ones are the so-called Pioneer anomaly, {i.e.} a still unexplained acceleration detected in the telemetry of the Pioneer 10/11 spacecraft after they passed the 20 AU threshold in the solar system, the non-Keplerian profiles of the velocity rotation curves of several galaxies and the cosmic acceleration. We use the latest observational determ…
A unique signature of the modified Newtonian dynamics (MOND) paradigm is its peculiar behavior in the vicinity of the points where the total Newtonian acceleration exactly cancels. In the Solar System, these are the saddle points of the gravitational potential near the planets. Typically, such points are embedded into low-acceleration bubbles where modified gravity theories a` la MOND predict significant deviations from Newton's laws. As has been pointed out recently, the Earth-Sun bubble may be visited by the LISA Pathfinder spacecraft in the near future, providing a unique occasion to put th…
We present EnckeHH, a new, highly accurate code for orbital dynamics of perturbed Keplerian systems such as planetary systems or galactic centre systems. It solves Encke's equations of motion, which assume perturbed Keplerian orbits. By incorporating numerical techniques, we have made the code follow optimal roundoff error growth. In a $10^ {12}$ day integration of the outer Solar System, EnckeHH was $3.5$ orders of magnitude more accurate than IAS15 in a fixed time step test. Adaptive steps are recommended for IAS15. Through study of efficiency plots, we show that EnckeHH reaches significantl…
`Oumuamua (1I/2017 U1) is the first object of interstellar origin observed in the Solar System. Recently, \citet{Micheli2018} reported that `Oumuamua showed deviations from a Keplerian orbit at a high statistical significance. The observed trajectory is best explained by an excess radial acceleration $Δa \propto r^{-2}$, where $r$ is the distance of `Oumuamua from the Sun. Such an acceleration is naturally expected for comets, driven by the evaporating material. However, recent observational and theoretical studies imply that `Oumuamua is not an active comet. We explore the possibility that th…
The error in the Solar system ephemeris will lead to dipolar correlations in the residuals of pulsar timing array for widely separated pulsars. In this paper, we utilize such correlated signals, and construct a Bayesian data-analysis framework to detect the unknown mass in the Solar system and to measure the orbital parameters. The algorithm is designed to calculate the waveform of the induced pulsar-timing residuals due to the unmodelled objects following the Keplerian orbits in the Solar system. The algorithm incorporates a Bayesian-analysis suit used to simultaneously analyse the pulsar-tim…
We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier (${\bf k}$-)space, we identified three types of active modes that define turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled the vital area and are: (i) the channel mode - uniform in the disk plane with the smallest vertical wavenumber,(ii) the zonal flow mode - azimuthally and vertically uniform with the smallest radia…
We analytically work out the orbital effects caused by a Rindlertype extra-acceleration ARin which naturally arises in some recent models of modified gravity at large distances. In particular, we focus on the perturbations induced by it on the two-body range ρ and range-rate ρ\cdot which are commonly used in satellite and planetary investigations as primary observable quantities. The constraints obtained for ARin by comparing our calculations with the currently available range and range-rate residuals for some of the major bodies of the solar system, obtained without explicitly modeling ARin, …
We looked at the orbital motions of test particles according to the External Field Effect (EFE) predicted by the MOdified Newtonian Dynamics (MOND) in the Oort cloud which falls in the deep MONDian regime (r\approx 50-150 kAU). Concerning the interpolating function μ(x), we extensively used the forms μ_1=1/(1+x),μ_2=x/(1+x^2)^1/2,μ_3/2=x/(1+x^3/2)^2/3. We integrated both the MOND and the Newtonian equations of motion in Cartesian coordinates sharing the same initial conditions. We considered both ecliptic and nearly polar trajectories, all with high eccentricities (e>0.1). In order to evaluate…
We study the dynamics of large dust grains >1 micron with orbits outside of the heliosphere (beyond 250 AU). Motion of the Solar System through the interstellar medium (ISM) at a velocity of 26 km/s subjects these particles to gas and Coulomb drag (grains are expected to be photoelectrically charged) as well as the Lorentz force and the electric force caused by the induction electric field. We show that to zeroth order the combined effect of these forces can be well described in the framework of the classical Stark problem: particle motion in a Keplerian potential subject to an additional cons…
The Galaxy is conventionally thought to be surrounded by a massive dark matter (DM) halo. As the Sun goes through this halo, it excites a DM wake behind it. This local asymmetry in the DM distribution would gravitationally affect the motions of Solar System planets, potentially allowing the DM wake to be detected or ruled out. Hernandez (2019) recently calculated that the DM-induced perturbation to Saturn's position is 252 metres net of the effect on the Sun. No such anomaly is seen in Saturn's motion despite very accurate tracking of the Cassini spacecraft, which orbited Saturn for >13 years.…
In the framework of the Parameterized Post-Newtonian (PPN) formalism, we calculate the long-term Preferred Location (PL) effects, proportional to the Whitehead parameter $ξ$, affecting all the Keplerian orbital elements of a localized two-body system, apart from the semimajor axis $a$. They violate the gravitational Local Position Invariance (LPI), fulfilled by General Relativity (GR). We obtain preliminary bounds on $ξ$ by using the latest results in the field of the Solar System planetary ephemerides. The non-detection of any anomalous perihelion precession for Mars allows us to indirectly i…
