Related papers: Approximating Orbits in a Rotating Gravity Field w…
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to…
Corrections to the relativistic orbits are studied considering higher order approximations induced by gravitomagnetic effects. We discuss in details how such corrections come out taking into account magnetic components in the weak field…
This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations…
First-order perturbative calculation of the frequency-shifts caused by special relativity is performed for a charged particle confined in a Penning trap. The perturbed motion is approximated by the Jacobian elliptic functions which describe…
Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured…
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 present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a…
The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the…
This note shows how to compute, to high relative accuracy under mild assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and…
In this paper, we consider a spherically curved symmetric spacetime to exact solving the orbit equation of a massive particle by using Jacobi's elliptic functions. Generally, the solution of the orbit equation provides the relativistic…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are…
In spherical symmetry with radial coordinate $r$, classical Newtonian gravitation supports circular orbits and, for $-1/r$ and $r^2$ potentials only, closed elliptical orbits [1]. Various families of elliptical orbits can be thought of as…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…
We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in (Gronchi et al 2015), which uses a…
In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity…