Related papers: Orbit determination with the Keplerian integrals
Solar system, exoplanet and stellar science rely on transits, eclipses and occultations for dynamical and physical insight. Often, the geometry of these configurations are modelled by assuming a particular viewpoint. Here, instead, I derive…
Several asteroids are known to be shaped like toy tops. This paper models Top-Shaped Asteroids (TSAs) as Homogeneous Symmetric Lenses (HSLs), and derives their rotational, self-gravitational, and total energies as functions of their mass,…
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…
Transit timing variations (TTVs) can provide useful information for systems observed by transit, as they allow us to put constraints on the masses and eccentricities of the observed planets, or even to constrain the existence of…
Using speckle-interferometry we have carried out repeated measurements of relative positions for the components of 34 T Tauri binary systems. The projected separation of these components is low enough that orbital motion is expected to be…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
Orbits of 44 close and fast visual binaries are computed using the latest speckle observations; 23 orbits are determined for the first time, the rest are revisions, some quite substantial. Six combined orbits use radial velocities. The…
The pulsar timing technique, which compares the observed arrival times of electromagnetic radiation from a pulsar with the predicted arrival times derived from a theoretical model of the pulsar system, is used in pulsar astronomy to infer a…
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…
For a solar-like star, the surface rotation evolves with time, allowing in principle to estimate the age of a star from its surface rotation period. Here we are interested in measuring surface rotation periods of solar-like stars observed…
Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of \"Opik (1951) and Wetherill (1967), the collision probability was derived by…
The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the…
We present an exact solution of the equations for orbit determination of a two body system in a hyperbolic or parabolic motion. In solving this problem, we extend the method employed by Asada, Akasaka and Kasai (AAK) for a binary system in…
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…
NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable…
The Hipparcos catalog and its Double and Multiple System Annex (DMSA) lists 4099 components with individual proper motions and coordinates on the epoch 1991.25. Many of these long-period binary stars are also present in the Gaia Data…
The validity of Kepler Laws for the {\it spherical Kepler problem} -- namely, the problem of the motion of a particle on the unit sphere {in $\mathbb R^3$} undergoing an attraction by another particle in the sphere, tangent to the geodesic…
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 outline a proposal to use the Kepler spacecraft in two-wheel mode to monitor a handful of young associations and open clusters, for a few weeks each. Judging from the experience of similar projects using ground-based telescopes and the…
Anomalous orbits are found when minimum-chi^{2} estimation is applied to synthetic Gaia data for orbits with astrometric signatures comparable to the single-scan measurement error (Pourbaix 2002). These orbits are nearly parabolic, edge-on,…