Related papers: Orbit determination with the Keplerian integrals
The Kepler space telescope leaves a legacy of tens of thousands of stellar rotation period measurements. While many of these stars show strong periodicity, there exists an even bigger fraction of stars with irregular variability for which…
In transiting planetary systems, the angle between the orbital angular momentum and the stellar spin is usually constrained through the Rossiter-McLaughlin effect observed in radial velocity and can be subject to large uncertainties,…
We present the spectroscopic orbit solutions of three double-lines eclipsing binaries, BG Ind, IM Mon and RS Sgr. The first precise radial velocities (RVs) of the components were determined using high resolution echelle spectra obtained at…
Armed with an astrolabe and Kepler's laws one can arrive at accurate estimates of the orbits of planets.
The architectures of multiple planet systems can provide valuable constraints on models of planet formation, including orbital migration, and excitation of orbital eccentricities and inclinations. NASA's Kepler mission has identified 1235…
Observatories and satellites around the globe produce tremendous amounts of imaging data to study many different astrophysical phenomena. The serendipitous observations of Solar System objects are a fortunate by-product which have often…
The stellar obliquity of a transiting planetary system can be constrained by combining measurements of the star's rotation period, radius, and projected rotational velocity. Here we present a hierarchical Bayesian technique for recovering…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…
Orbit-determination programs find the orbit solution that best fits a set of observations by minimizing the RMS of the residuals of the fit. For near-Earth asteroids, the uncertainty of the orbit solution may be compatible with trajectories…
We present and discuss five candidate exoplanetary systems identified with the Kepler spacecraft. These five systems show transits from multiple exoplanet candidates. Should these objects prove to be planetary in nature, then these five…
This paper makes the first systematic attempt to determine using perturbation theory the positions of images by gravitational lensing due to arbitrary number of coplanar masses without any symmetry on a plane, as a function of lens and…
Following Ford et al. (2011, 2012) and Steffen et al. (2012) we derived the transit timing of 1960 Kepler KOIs using the pre-search data conditioning (PDC) light curves of the first twelve quarters of the Kepler data. For 721 KOIs with…
During its four years of photometric observations, the Kepler space telescope detected thousands of exoplanets and exoplanet candidates. One of Kepler's greatest heritages has been the confirmation and characterization of hundreds of…
Here we describe a story behind the discovery of Kepler-46, which was the first exoplanetary system detected and characterized from a method known as the transit timing variations (TTVs). The TTV method relies on the gravitational…
We present an analysis of 18 short-cadence (SC) transit lightcurves of TrES-2b using quarter 0 (Q0) and quarter 1 (Q1) from the Kepler Mission. The photometry is of unprecedented precision, 237ppm per minute, allowing for the most accurate…
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg…
Two-line elements are widely used for space operations to predict the orbit with a moderate accuracy for 2-3 days. Local optimization methods, such as the nonlinear least squares method with differential corrections, can estimate a TLE as…
We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time.…
The nearby high-mass star binary system Theta 1 Orionis C is the brightest and most massive of the Trapezium OB stars at the core of the Orion Nebula Cluster, and it represents a perfect laboratory to determine the fundamental parameters of…