Related papers: A Study on Effective Initial Guess Finding Method …
Numerical solutions of Kepler's Equation are critical components of celestial mechanics software, and are often computation hot spots. This work uses symbolic regression and a genetic learning algorithm to find new initial guesses for…
Initial orbit determination (IOD) from line-of-sight (i.e., bearing) measurements is a classical problem in astrodynamics. Indeed, there are many well-established methods for performing the IOD task when given three line-of-sight…
This work introduces the problem of initial orbit determination (IOD) from only heading measurements. Such a problem occurs in practice when estimating the orbit of a spacecraft using visual odometry measurements from an optical camera.…
The commercial interest in producing low-cost space missions by exploiting the superior propellant management of low-thrust propulsion technology has become increasingly popular. Typical to such missions is the design of transfer…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
B\'ezier splines are widely available in various systems with the curves and surface designs. In general, the B\'ezier spline can be specified with the B\'ezier curve segments and a B\'ezier curve segment can be fitted to any number of…
Initial Orbit Determination (IOD) is the classical problem of estimating the orbit of a body in space without any presumed information about the orbit. The geometric formulation of the ''angles-only'' IOD in three-dimensional space: find a…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
We present the results of our investigation on the use of the two-body integrals to compute preliminary orbits by linking too short arcs of observations of celestial bodies. This work introduces a significant improvement with respect to the…
In orbital mechanics, Gauss's method for orbit determination (OD) is a popular, minimal assumption solution for obtaining the initial state estimate of a passing resident space object (RSO). Since much of the cislunar domain relies on…
Here we revisit an initial orbit determination method introduced by O. F. Mossotti employing four geocentric sky-plane observations and a linear equation to compute the angular momentum of the observed body. We then extend the method to…
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…
The growing interest in cislunar space exploration in recent years has driven an increasing demand for efficient low-thrust missions to key cislunar orbits. These missions, typically possessing long thrust arcs, are particularly susceptible…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
Given a set of astrometric observations of the same object, the problem of orbit determination is to compute the orbit and to assess its uncertainty and reliability. For the next generation surveys, with much larger number density of…
B\'ezier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of B\'ezier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a…
This paper examines the influence of initial guesses on trajectory planning for Unmanned Aerial Vehicles (UAVs) formulated in terms of Optimal Control Problem (OCP). The OCP is solved numerically using the Pseudospectral collocation method.…
Electronic structure calculations, such as in the Hartree-Fock or Kohn-Sham density functional approach, require an initial guess for the molecular orbitals. The quality of the initial guess has a significant impact on the speed of…
Short-arc orbit determination is crucial when an asteroid is first discovered. In these cases usually the observations are so few that the differential correction procedure may not converge. We have developed an initial orbit computation…