Related papers: A Kepler's note on secular inequalities

Among all the theories proposed to explain the 'anomalous' perihelion precession of Mercury's orbit announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915, alone could calculate Mercury's…

The non-spherical shape of the Sun has been invoked to explain the anomalous precession of Mercury. A brief history of some methods for measuring solar diameter is presented. Archimedes was the first to give upper and lower values for solar…

We investigate the long time stability of the Sun-Jupiter-Saturn-Uranus system by considering the planar, secular model. Our method may be considered as an extension of Lagrange's theory for the secular motions. Indeed, concerning the…

Kepler will monitor enough stars that it is likely to detect single transits of planets with periods longer than the mission lifetime. We show that by combining the Kepler photometry of such transits with precise radial velocity (RV)…

In this paper we first calculate the post-Newtonian gravitoelectric secular rate of the mean anomaly of a test particle freely orbiting a spherically symmetric central mass. Then, we propose a novel approach to suitably combine the…

The similarity of Mercury to the Moon raises the question on mercurian analogues of lunar transient phenomena. However, since the mid-1960s, this topic has remained out of attention. Nevertheless, the discoveries of the 21st century and the…

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…

The Kepler mission has provided high quality light curves for more than 2000 eclipsing binaries. Tertiary companions to these binaries can be detected if they transit one or both stars in the binary or if they perturb the binary enough to…

We propose that the presence of additional planets in extrasolar planetary systems can be detected by long-term transit timing studies. If a transiting planet is on an eccentric orbit then the presence of another planet causes a secular…

Having started science operations in May 2009, the Kepler photometer has been able to provide exquisite data of solar-like stars. Five out of the 42 stars observed continuously during the survey phase show evidence of oscillations, even…

Although not designed as an astrometric instrument, Kepler is expected to produce astrometric results of a quality appropriate to support many of the astrophysical investigations enabled by its photometric results. On the basis of data…

It was believed until very recently that a near-equatorial satellite would always keep up with the planet's equator (with oscillations in inclination, but without a secular drift). As explained in Efroimsky and Goldreich (2004), this…

We show that the Kepler spacecraft in two-reaction wheel mode of operation is very well suited for the study of eclipsing binary star systems. Continued observations of the Kepler field will provide the most enduring and long-term valuable…

In 1680 Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadow by the Kepler's first law (1609), namely the planets move around the sun describing conic…

In addition to its great potential for characterizing extra-solar planetary systems the Kepler mission is providing unique data on stellar oscillations. A key aspect of Kepler asteroseismology is the application to solar-like oscillations…

A statistical analysis is performed over more than 1001 different integrations of the secular equations of the Solar system over 5 Gyr. With this secular system, the probability of the eccentricity of Mercury to reach 0.6 in 5 Gyr is about…

We explore the effects of an undetected outer giant planet on the dynamics, observability, and stability of Systems with Tightly-packed Inner Planets (STIPs). We use direct numerical simulations along with secular theory and synthetic…

Axisymmetric disks of eccentric Kepler orbits are vulnerable to an instability which causes orbits to exponentially grow in inclination, decrease in eccentricity, and cluster in their angle of pericenter. Geometrically, the disk expands to…

We calculate and analyze the distribution of period ratios observed in systems of Kepler exoplanet candidates including studies of both adjacent planet pairs and all planet pairs. These distributions account for both the geometrical bias…

Hot Jupiters may have formed in situ, or been delivered to their observed short periods through one of two categories of migration mechanisms: disk migration or high-eccentricity migration. If hot Jupiters were delivered by…