Related papers: Orbit determination with the Keplerian integrals
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
In order to show the principle viability of a recently proposed relativistic positioning method based on the use of pulsed signals from sources at infinity, we present an application example reconstructing the world-line of an idealized…
We present two methods to algorithmically compute both least and greatest solutions of polynomial equation systems over absorptive semirings (with certain completeness and continuity assumptions), such as the tropical semiring. Both methods…
Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long…
In the new era of large-scale astronomical surveys, automated methods of analysis and classification of bulk data are a fundamental tool for fast and efficient production of deliverables. This becomes ever more imminent as we enter the Gaia…
The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and…
A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…
The period, mass ratio, eccentricity, and other orbital parameters are fundamental for investigating binary star evolution. However, the number of binaries with known orbital parameters remains limited. Utilizing the LAMOST-MRS survey, we…
Accurate measurements of osculating orbital elements are essential in order to understand and model the complex dynamic behavior of Near Earth Asteroids (NEAs). ESA's Gaia mission promises to have great potential in this respect. In this…
We examine the ability of the Transiting Exoplanet Survey Satellite (TESS) to detect and improve our understanding of planetary systems in the Kepler field. By modeling the expected transits of all confirmed and candidate planets detected…
In this paper the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUC's). There are four main results: the…
We define and analyze the photometric orbit (PhO) of an extrasolar planet observed in reflected light. In our definition, the PhO is a Keplerian entity with six parameters: semimajor axis, eccentricity, mean anomaly at some particular time,…
Detection of a planetary ring of exoplanets remains as one of the most attractive but challenging goals in the field. We present a methodology of a systematic search for exoplanetary rings via transit photometry of long-period planets. The…
The classical fuel-optimal two-impulse rendezvous problem between Keplerian orbits is revisited from a family-based perspective. Conventional approaches often yield isolated optimal solutions whose mutual relationships remain unclear; yet,…
Consider the action of a connected complex reductive group on a finite-dimensional vector space. A fundamental result in invariant theory states that the orbit closure of a vector v is separated from the origin if and only if some…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
In the study of long-time correlations extremely long orbits must be calculated. This may be accomplished much more reliably using fixed-point arithmetic. Use of this arithmetic on the Cray-1 computer is illustrated.
Stellar rotation periods can be determined by observing brightness variations caused by active magnetic regions transiting visible stellar disk as the star rotates. The successful stellar photometric surveys stemming from the Kepler and…
Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard…