Related papers: Orbital precession due to central-force perturbati…
This study focuses on the long-term evolution of two bodies in nearby initially coplanar orbits around a central dominant body perturbed by a fourth body on a distant Keplerian orbit. Our previous works that considered this setup enforced…
We consider the Casimir force including all important corrections to it for the configuration used in a recent experiment employing an atomic force microscope. We calculate the long-range hypothetical forces due to the exchange of light and…
This work focuses on providing closed form analytical expressions to define frozen orbits under the effects of the zonal harmonics of an Earth-like planet. Particularly, the perturbation effects from the terms J2, J3, J4, J5, J6, and J7 are…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…
We revisit the connection between relativistic orbital precession, the Laplace-Runge-Lenz symmetry, and the $t$-channel discontinuity of scattering amplitudes. Applying this to scalar-tensor theories of gravity, we compute the conservative…
The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the…
In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around…
Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are…
We consider the observational effects of a deficit angle, w, in the topology of the solar system and in the 'double pulsar' system PSR J0737-3039A/B. Using observations of the perihelion precession of Mercury, and the gravitational…
Orbital motion of a body can be found from Newtonian equation of motion. However, it is useful to express the motion through time derivatives of Keplerian orbital elements, mainly if the motion is perturbed by small perturbing force. The…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial…
Binary systems subject to generic perturbations evolve on quasiperiodic orbits. We derive the most generic class of perturbations, which allow to evaluate secular effects via generalized complex true and eccentric anomaly parameters, by use…
In the weak field limit general relativity reduces, as is well known, to the Newtonian gravitation. Alternative theories of gravity, however, do not necessarily reduce to Newtonian gravitation; some of them, for example, reduce to…
Let $r(\varphi)$ denote the orbit of Mercury. We compare the formulae obtained via general relativity for $r(\varphi)$ and for the corresponding perihelion precession angle $\Delta \varphi$, with the formulae obtained via the relativistic…
We construct time-evolving gravitational potential models for a Milky Way-mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical…
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…
Accurate inclusion of both spin precession and orbital eccentricity effects in gravitational waveform models represents a key hurdle in our ability to fully characterize the properties of compact binaries. Virtually all efforts to model…
Spin precession for an EPR pair of spin-1/2 particles in equatorial orbits around a Kerr-Newman black hole is studied. Hovering observers are introduced to ensure fixed reference frames in order to perform the Wigner rotation. These…
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.