Related papers: Variational Principle for Planetary Interiors
Over the past several decades, thousands of planets have been discovered outside of our Solar System. These planets exhibit enormous diversity, and their large numbers provide a statistical opportunity to place our Solar System within the…
Many recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20% of the known extrasolar planetary systems are associated with one or more stellar companions. The orbits of…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
Planetary systems can evolve dynamically even after the planets themselves have fully formed, and there is circumstantial evidence that most planetary systems become unstable after the disappearance of the gaseous protoplanetary disk.…
Having a massive moon has been considered as a primary mechanism for stabilized planetary obliquity, an example of which being our Earth. This is, however, not always consistent with the exoplanetary cases. This article details the…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by…
The hundreds of exoplanets that have been discovered in the past two decades offer a new perspective on planetary structure. Instead of being the archetypal examples of planets, those of our Solar System are merely possible outcomes of…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by \textit{Kepler} and \textit{K2}. We propagated 21,400 simulated planetary…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
We regard the background of space-time as a physical system composed of discrete volume elements at the Planck scale and get the internal energy of space-time by Debye model. A temperature-dependent minimum energy limit of the particles is…
Planetary systems with multiple transiting planets are beneficial for understanding planet occurrence rates and system architectures. Although we have yet to find a solar system analogue, future surveys may detect multiple terrestrial…
Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods,…
Uncovering the formation process that reproduces the distinct properties of compact super-Earth exoplanet systems is a major goal of planet formation theory. The most successful model argues that non-resonant systems begin as resonant…
We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are…
Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…