Related papers: A Kepler's note on secular inequalities
Ptolemy-s planetary model is an ancient geocentric astronomical model, describing the observed motion of the Sun and the planets. Ptolemy accounted for the deviations of planetary orbits from perfect circles by introducing two small and…
Asteroseismology of solar-type stars has an important part to play in the exoplanet program of the NASA Kepler Mission. Precise and accurate inferences on the stellar properties that are made possible by the seismic data allow very tight…
Consider the spatial three-body problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The…
In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital…
The Kepler Observatory offers unprecedented photometric precision (<1 mmag) and cadence for monitoring the central stars of planetary nebulae, allowing the detection of tiny periodic light curve variations, a possible signature of binarity.…
The North-South asymmetry of solar activity has been recognized for different solar phenomena. Following Waldmeier, it is now assumed that solar activity dominates in the Northern solar hemisphere during the ascending part of the secular…
Relativistic Keplerian orbital frequency and related epicyclic frequencies play an important role in physics of accretion discs orbiting Kerr black holes and can by resonant or trapping effects explain quasiperiodic oscillations observed in…
If one wants to translate the heliocentric picture of planets moving uniformly on circular orbits about the sun to the perspective of a terrestrial observer, using classical (ancient) geometric means only, one is naturally led to the…
The non-resonant secular dynamics of compact planetary systems are modeled by a perturbing function which is usually expanded in eccentricity and absolute inclination with respect to the invariant plane. Here, the expressions are given in a…
The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses…
In this paper we analyze the impact on the orbital motions of the outer planets of the solar system from Jupiter to Pluto of some velocity-dependent forces recently proposed to phenomenologically explain the Pioneer anomaly, and compare…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
Second-order mean-motion resonances lead to an interesting phenomenon in the sculpting of the period ratio distribution due to their shape and width in period-ratio/eccentricity space. As the osculating periods librate in resonance, the…
We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincar\'e canonical variables, we determine the fundamental…
This paper presents an interdisciplinary analysis of the "Star of Bethlehem" narrative described in the Gospel of Matthew (Mt 2:1-12), examining the hypothesis, originally proposed by Johannes Kepler, that the reported phenomenon may be…
Using Gauss' averaged equations, we compute the secular relativistic effects generated by the Sun on the argument of the perihelion and the mean anomaly of an orbit. Then we test different alternative simpler models that have been proposed…
We investigate the distributions of the orbital period ratios of adjacent planets in high multiplicity \kepler\ systems (four or more planets) and low multiplicity systems (two planets). Modeling the low multiplicity sample as essentially…
Kepler is a space telescope that searches Sun-like stars for planets. Its major goal is to determine {\eta}_Earth, the fraction of Sunlike stars that have planets like Earth. When a planet 'transits' or moves in front of a star, Kepler can…
In a recent article by Scafetta, 2010, the author investigates whether or not the decadal and multi-decadal climate oscillations have an astronomical origin. In particular, the author note that several global surface temperature records,…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…