Related papers: Simplified derivation of the collision probability…
A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly…
We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multi-electron atomic case or mutually…
We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable…
The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian…
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…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
In a Keplerian system, a large number of bodies orbit a central mass. Accretion disks, protoplanetary disks, asteroid belts, and planetary rings are examples. Simulations of these systems require algorithms that are computationally…
We give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on the two-dimensional lattice. By `collision' we mean collision between the random walks as well as…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an…
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…
The behaviour of resonances in the spin-orbit coupling in Celestial Mechanics is investigated. We introduce a Hamiltonian nearly-integrable model describing an approximation of the spin-orbit interaction. A parametric representation of…
We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation, measured along their inter-center vector. This directional distance is derived from the Elliptic Contact…
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…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for…
Estimating the marginal likelihoods is an essential feature of model selection in the Bayesian context. It is especially crucial to have good estimates when assessing the number of planets orbiting stars when the models explain the noisy…