Related papers: A Simple Procedure to Extend the Gauss Method of D…
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…
A geometric interpretation of the equinoctial elements is given with a connection to orthogonal rotations and attitude dynamics in Euclidean 3-space. An identification is made between the equinoctial elements and classic Rodrigues…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
(abridged)Multiple systems for which the astrometric and spectroscopic orbit are known offer the unique possibility of determining the distance to these systems directly without any assumptions. They are therefore ideal objects for a…
We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…
We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi static evolutions, we adopt a Lagrangian formulation of our own…
To the first post-Newtonian order, the gravitational action of mass-energy currents is encoded by the off-diagonal gravitomagnetic components of the spacetime metric tensor. If they are time-dependent, a further acceleration enters the…
Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position…
The orbital dynamics of a spacecraft orbiting around irregular small celestial bodies is a challenging problem. Difficulties to model the gravity field of these bodies arise from the poor knowledge of the exact shape as observed from the…
We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the…
Periodic orbits (POs) play a central role in the circular restricted three-body problem (CRTBP). This paper introduces a method to search for POs by identifying single- and multiple-revolution fixed points in chosen Poincare maps that…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
We describe a new iteration method to estimate asteroid coordinates, which is based on the subpixel Gaussian model of a discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
It is difficult to discover pulsars via their gamma-ray emission because current instruments typically detect fewer than one photon per million rotations. This creates a significant computing challenge for isolated pulsars, where the…
In this paper, we study fixed points of N-point gravitational lenses. We use complex form of lens mapping to study fixed points. Complex form has an advantage over coordinate one because we can describe N-point gravitational lens by system…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body…
In this work, we study the periodic orbits in the spatial isosceles three-body problem. These periodic orbits form a one-parameter set with a rotation angle $\theta$ as the parameter. Some new phenomenons are discovered by applying our…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…