A generalization of the Kepler problem, one that encompasses all previously known generalizations in the last six decades, is given here. Introduction. The Kepler problem, owing to its significant role in the major developments of physics in the last three centuries, is probably the most wellknown scientific problem in the western civilization. It has been known for quite a while that the Keple...

The Kepler Mission is uniquely suited to study the frequencies of extrasolar planets. This goal requires knowledge of the incidence of false positives such as eclipsing binaries in the background of the targets, or physically bound to them, which can mimic the photometric signal of a transiting planet. We perform numerical simulations of the Kepler targets and of physical companions or stars in...

We present a verified enumeration of tame graphs as defined in Hales’ proof of the Kepler Conjecture and confirm the completeness of Hales’ list of all tame graphs while reducing it from 5128 to 2771 graphs.

We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We have shown that for l̃ = 0, the system admits an 1-parameter family of self-adjoint extension and for l̃ 6= 0 but l̃ < 1 2 , it has also an 1parameter family of self-adjoint extension.

ABSTRACT Up to date planet ephemerides are becoming increasingly important as exoplanet science moves from detecting exoplanets characterizing their architectures and atmospheres in depth. In this work, updated for 22 Kepler planets 4 candidates, constituting all candidates with sufficient signal noise the TESS 2 min data set. A purely photometric method is utilized here allow ephemeris updates...

We present a consecutive derivation of mapping equations of motion for the one-dimensional classical hydrogenic atom in a monochromatic field of any frequency. We analyze this map in the case of high and low relative frequency of the field and transition from regular to chaotic behavior. We show that the map at aphelion is suitable for investigation of transition to chaotic behavior also in the...

We present the results of our Hubble Space Telescope program and describe how our analysis methods were used to re-evaluate the habitability of some of the most interesting Kepler planet candidates. Our program observed 22 Kepler Object of Interest (KOI) host stars, several of which were found to be multiple star systems unresolved by Kepler. We use our high-resolution imaging to spatially reso...

We present the results of our Hubble Space Telescope program and describe how our analysis methods were used to re-evaluate the habitability of some of the most interesting Kepler planet candidates. Our program observed 22 Kepler Object of Interest (KOI) host stars, several of which were found to be multiple star systems unresolved by Kepler. We use our high-resolution imaging to spatially reso...