相关论文: A lower bound of the distance between two elliptic…
We present an algorithm to compute the minimum orbital intersection distance (MOID), or global minimum of the distance between the points lying on two Keplerian ellipses. This is achieved by finding all stationary points of the distance…
We consider the Keplerian distance $d$ in the case of two elliptic orbits, i.e. the distance between one point on the first ellipse and one point on the second one, assuming they have a common focus. The absolute minimum $d_{\rm min}$ of…
The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The…
We study the possible values of the nodal distance $\delta_{\rm nod}$ between two non-coplanar Keplerian trajectories ${\cal A}, {\cal A}'$ with a common focus. In particular, given ${\cal A}'$ and assuming it is bounded, we compute optimal…
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.…
The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of…
In this paper, the minimum orbit intersection distances (MOIDs) of near-Earth asteroids (NEAs) over the next 200 years were computed and analyzed in detail. It was shown that the MOID of a NEA relative to the Earth-Moon barycenter (EMB) is…
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 propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations).…
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…
Given a set of endomorphisms on $\mathbb{P}^N$, we establish an upper bound on the number of points of bounded height in the associated monoid orbits. Moreover, we give a more refined estimate with an associated lower bound when the monoid…
The catalog of km-sized near-Earth objects (NEOs) is nearly complete. Typical impact monitoring analyses search for possible impacts over the next 100 years and none of the km-sized objects represent an impact threat over that time…
We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortest physical axis and is perpendicular to the orbital plane.…
We study the orbits in the MOND theory within a dwarf galaxy of mass Md at a distance of ~100kpc from a neighboring galaxy of mass Mg, such as ours. It is assumed that a second mass m<<Md is gravitationally bound to Md by a previously…
We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…
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…
We have made an extensive search for grouping amongst the near Earth asteroids (NEAs). We used two D- functions and rigorous cluster analysis approach. We have found sev- eral new groups (associations) among the NEAs: the objects moving on…
We numerically investigate the features of typical orbits occurring in the Oort cloud (r\approx 50-150 kAU) in the low-acceleration regime of the MOdified Newtonian Dynamics (MOND). We take into account the so-called External Field Effect…
It is shown that the MOdified Newtonian Dynamics (MOND) explains the tilt of the fundamental plane of elliptical galaxies without the need of non-baryonic dark matter. Results found for elliptical galaxies extends to globular clusters and…
It is shown that the lowest order general relativistic correction produces elliptic orbits with a non-Newtonian eccentricity.