Related papers: The Planetary Machine by Johannes Kepler
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun")…
This paper is devoted to exploring how we can discover and study nearby (< 1-2 kpc) planetary and binary systems by observing their action as gravitational lenses. Lensing can extend the realm of nearby binaries and planets that can be…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
With the volume and availability of astronomical data growing rapidly, astronomers will soon rely on the use of machine learning algorithms in their daily work. This proceeding aims to give an overview of what machine learning is and delve…
Gravitational lensing - the deflection of light rays by gravitating matter - has become a major tool in the armoury of the modern cosmologist. Proposed nearly a hundred years ago as a key feature of Einstein's theory of General Relativity,…
In 1755, Kant published his General Natural History and Theory of the Heavens, in which he presented his hypothesis on the formation of the solar system, known as the primitive nebula hypothesis. This original theory of the heavens was…
The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect…
The thoughts expressed in this article are based on remarks made by J\"urgen Ehlers at the Albert-Einstein-Institut, Golm, Germany in July 2007. The main objective of this article is to demonstrate, in terms of plausible order-of-magnitude…
Starting from a suggestion of Einstein on the construction of the concept of space, we elaborate an intrinsic method to obtain space and time transformations between two inertial spaces of reference, mathematically modeled as affine…
A multi-TeraFlop/TeraByte machine will enable the application of the Einstein theory of gravity to realistic astrophysical processes. Without the computational power, the complexity of the Einstein theory restricts most studies based on it…
In 1651 the Italian astronomer Giovanni Battista Riccioli published within his Almagestum Novum, a massive 1500 page treatise on astronomy, a discussion of 126 arguments for and against the Copernican hypothesis (49 for, 77 against). A…
The widespread prevalence of close-in, nearly coplanar super-Earth- and sub-Neptune-sized planets in multiple-planet systems was one of the most surprising results from the Kepler mission. By studying a uniform sample of Kepler "multis"…
A test on quantum mechanics proposed long ago by Karl Popper is reconsidered with further detail and new insight. An ambiguity in the proposal, which turns out to be essential in order to make the test conclusive, is identified and taken…
The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler-11 and Kepler-32, in which ensembles of several planets are found in very closely packed orbits (often within a few percent of an AU of one…
The recent Kepler discovery of KOI-152 reveals a system of three hot super-Earth candidates that are in or near a 4:2:1 mean motion resonance. It is unlikely that they formed in situ, the planets probably underwent orbital migration during…
The Kepler mission is dramatically increasing the number of planets known in multi-planetary systems. Many adjacent planets have orbital period ratios near resonant values, with a tendency to be larger than required for exact first-order…
The heliosphere represents a uniquely accessible domain of space, where fundamental physical processes common to solar, astrophysical and laboratory plasmas can be studied under conditions impossible to reproduce on Earth and unfeasible to…
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…
Although resonant planets have orbital periods near commensurability, resonance is also dictated by other factors, such as the planets' eccentricities and masses, and therefore must be confirmed through a study of the system's dynamics.…
We report on recent refinements and the current status for the rotational state models and the reference frame of the planet Mercury. We summarize the performed measurements of Mercury rotation based on terrestrial radar observations as…