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We review the mathematical models available for relativistic astrometry, discussing the different approaches and their accuracies in the context of the modern experiments from space like Gaia and GAME, and we show how these models can be…
When a structure displays dependence on distance and azimuthal angle from a center (for example the spiral arms of galaxies or the diffraction spikes of stars), projecting the pixels to polar coordinates greatly simplifies their study. This…
We consider the role of deuterium as a potential marker of location and ambient conditions during the formation of small bodies in our Solar system. We concentrate in particular on the formation of the regular icy satellites of Jupiter and…
Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the…
By basing on observations of skeletal structures of the Sun and assuming that some of them are located inside of star, and also that a filamentary (linear) matter (whose a model earlier was put forward by B.U. Rodionov) is in basis of these…
The data of 2012 transit of Venus are compared with the ones of 2004. The thickness of the atmosphere of Venus, its aureole and the effect of oblateness and other asphericities in the figure of the Sun are taken into consideration, as well…
We present variational characterizations of frozen planet orbits for the helium atom in the Lagrangian and the Hamiltonian picture. They are based on a Levi-Civita regularization with different time reparametrizations for the two electrons…
In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the…
In-order to understand the results of recent observations of exoplanets, models have become increasingly complex. Unfortunately this increases both the computational cost and output size of said models. We intend to explore if…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…
We constrain the angular momentum architecture of VHS J125601.92-125723.9, a 140 $\pm$ 20 Myr old hierarchical triple system composed of a low-mass binary and a widely-separated planetary-mass companion VHS 1256 b. VHS 1256 b has been a…
The irregular satellites of the giant planets are believed to have been captured during the evolution of the solar system. Knowing their physical parameters, such as size, density, and albedo is important for constraining where they came…
This report provides some closed form solutions -- and their inversion -- to a satellite's bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the $J_{2}$ spherical zonal harmonic. The equatorial track of…
Several different controlled vocabularies have been developed and used by the astronomical community, each designed to serve a specific need and a specific group. The Unified Astronomy Thesaurus (UAT) attempts to provide a highly structured…
The study of Julia sets gives a new and natural way to look at fractals. When mathematicians investigated the special class of Misiurewicz's rational maps, they found out that there is a Julia set which is homeomorphic to a well known…
This paper presents the analytical solution of the inverse ray tracing problem for photons emitted by a star and collected by an observer located in the gravitational field of the Solar System. This solution has been conceived to suit the…
We offer a simple direct proof of the unitarity of the Julia operator associated to a contraction $A$, from which follow the intertwining identity $(I - A A^*)^{1/2} A = A (I - A^* A)^{1/2}$ and the unitarity of Halmos dilations.
IAU 2000 resolutions on the reference frames set up a solid theoretical foundation for implementing general relativity in astronomical data processing algorithms and for unambiguous interpretation of measured relativistic effects. We…
In the planning of some Chinese towns we can see an evident orientation with the cardinal north-south direction. However, other features reveal a possible orientation with the sunrise/sunset azimuth on solstices too, as in the case of…