Related papers: The Planetary Machine by Johannes Kepler
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 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 herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are…
We revisit the discovery and implications of the first candidate systems to contain multiple transiting exoplanets. These systems were discovered using data from the Kepler space telescope. The initial paper, presenting five systems…
We present a translation and analysis of a cosmic model published by Einstein in 1931. The paper, which is not widely known, features a model of a universe that undergoes an expansion followed by a contraction, quite different to his static…
This white paper discusses a repurposed mission for the Kepler spacecraft that focusses on solving outstanding problems in planet formation and evolution by targeting the study of the hot Jupiter population of young stars. This mission can…
The Kepler spacecraft, whose single instrument was a 0.95 m diameter wide-field telescope, operated in a heliocentric orbit for nearly a decade, returning a wealth of data that have revolutionized exoplanet science. Kepler data have been…
The Kepler Mission, launched on Mar 6, 2009 was designed with the explicit capability to detect Earth-size planets in the habitable zone of solar-like stars using the transit photometry method. Results from just forty-three days of data…
Armed with an astrolabe and Kepler's laws one can arrive at accurate estimates of the orbits of planets.
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…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
In March 2009, NASA will launch the Kepler satellite -- a mission designed to discover habitable Earth-like planets around distant Sun-like stars. The method that Kepler will use to detect distant worlds will only reveal the size of the…
This paper describes a series of activities in which students investigate and use the Ptolemaic, Copernican, and Tychonic models of planetary motion. The activities guide students through using open source software to discover important…
After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…
Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural…
The calculation of the trajectories in the Sun-Earth-Mars system will be performed in two different models, both in the framework of Newtonian mechanics. First model is well-known Copernican system, which assumes the Sun is at rest and all…
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…
We present a translation of the German text of an 1874 article by Valentin Rose that concerns the possible school of translators that worked in Toledo, Spain, from about 1150 to 1250. Rose's article relies significantly on the first-hand…
The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the…
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…