相关论文: Keplerian integrals, elimination theory and identi…
We review two initial orbit determination methods for too short arcs (TSAs) of optical observations of a solar system body. These methods employ the conservation laws of Kepler's problem, and allow to attempt the linkage of TSAs referring…
In this paper we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector and a very short arc (VSA) of optical observations. Using the conservation laws of the two-body dynamics, we…
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…
We investigate the behaviour of two recent methods for the computation of preliminary orbits. These methods are based on the conservation laws of Kepler's problem, and enable the linkage of very short arcs of optical observations even when…
We consider different choices of Keplerian conservation laws for the computation of preliminary orbits with two very short arcs (VSAs) of astrometric observations. In total we have 7 equations in 4 unknowns. Adding two auxiliary variables…
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…
If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…
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…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
Modeling of microlensing events poses computational challenges for the resolution of the lens equation and the high dimensionality of the parameter space. In particular, numerical noise represents a severe limitation to fast and efficient…
The Asteroid Terrestrial-impact Last Alert System (ATLAS) observes the visible sky every night in search of dangerous asteroids. With four soon five) sites ATLAS is facing new challenges for scheduling observations and linking detections to…
The Euclidean algorithm in algebra is applied to a class of gravitational lenses for which the lens equation consists of any set of coupled polynomial equations in the image position. In general, this algorithm allows us to reduce an…
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…
The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves, which relies crucially on maintaining three-spacecraft constellation as close to an equilateral triangle with a designed…
We present a proof of concept for a new algorithm which can be used to detect exoplanets in high contrast images. The algorithm properly combines mutliple observations acquired during different nights, taking into account the orbital motion…
We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular…
Keplerian-Stacker is an algorithm able to combine multiple observations acquired at different epochs taking into account the orbital motion of a potential planet present in the images to boost the ultimate detection limit. In 2019, a total…
Upcoming telescopes like the Vera Rubin Observatory (VRO) and the Argus Array will image large fractions of the sky multiple times per night yielding numerous Near Earth Object (NEO) discoveries. When asteroids are measured with short…
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm,…