Related papers: A Kepler's note on secular inequalities
While Kepler was still working in Graz during 1598, some letters to his mentor Michael Maestlin demonstrate his interest in astronomical clocks and machines. The first letter, dated January 6, 1598 contains a detailed description of a…
We examine the equant model for the motion of planets, which has been the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for…
In this note we collect some known facts concerning central projection correspondances and time parametrizations of Kepler problems in Euclidean spaces and on Spheres.
The Kepler mission, launched in March 2009, has revolutionized asteroseismology, providing detailed observations of thousands of stars. This has allowed in-depth analysis of stars ranging from compact hot subdwarfs to red giants, and…
We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular…
Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
Before the launch of the Kepler Space Telescope, models of low-mass planet formation predicted that convergent Type I migration would often produce systems of low-mass planets in low-order mean-motion resonances. Instead, Kepler discovered…
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…
The principle that celestial bodies must move on circular orbits or on paths resulting from the composition of circular orbits has been assumed as a constant guide in the astronomical thougth of the peoples facing the Mediterranean sea as…
I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it; the present analysis is also valid for a variation of the Newtonian constant of gravitation. I perturbatively…
The manuscripts provides a novel starting guess for the solution of Kepler's equation for unknown eccentric anomaly E given the eccentricity e and mean anomaly M of an elliptical orbit.
Kepler will monitor a sufficient number of stars that it is likely to detect single transits of planets with periods longer than the mission lifetime. We show that by combining the exquisite Kepler photometry of such transits with precise…
The eccentricity distribution of exoplanets is known from radial velocity surveys to be divergent from circular orbits beyond 0.1 AU. This is particularly the case for large planets where the radial velocity technique is most sensitive. The…
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions…
We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
Kepler Mission results are rapidly contributing to fundamentally new discoveries in both the exoplanet and asteroseismology fields. The data returned from Kepler are unique in terms of the number of stars observed, precision of photometry…
Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and…
Many have have taken in hand to write a treatise on the Star of Bethlehem, particularly on Kepler's explanation as a stellar birth, triggered by Mars joining a great conjunction (a meeting of Jupiter and Saturn), as he observed it in…