Related papers: Uffenbach's "Zeitweiser" published 1598
In the historical literature there has been an extended discussion on the question, whether the report of Sartorius von Waltershausen about C. F. Gauss checking the largest triangle of the geodetical measurement campaign in the kingdom of…
One of the oldest methods for constructing integrable Hamiltonian systems, proposed by Jacobi, recently is being presented as a novel St\"{a}ckel lift construction related with Haantjes geometry. It may cause some confusion.
In this short note, we construct an example of spiraling conformal geodesic in Euclidean signature in dimension $3$, answering the question posed by Helmuth Friedrich and Paul Tod, if such objects exists. Our example is not real analytic,…
The century long (1914-2007) $H_{\alpha}$ (656.28 nm) spectroheliograms from Kodaikanal Solar Observatory (KSO) have been recently digitised. Using these newly calibrated, processed images we study the evolution of dark elongated on disk…
We introduce a coordinate system that complements the Kruskal--Szekeres extension. Like the standard construction, it covers the maximally extended Schwarzschild manifold in its entirety, while offering an additional advantage of expressing…
Einstein's early calculations of gravitational lensing, contained in a scratch notebook and dated to the spring of 1912, are reexamined. A hitherto unknown letter by Einstein suggests that he entertained the idea of explaining the…
We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and…
For several decades a portrait of Johannes Kepler has been widely circulating among professional astronomers, scientific and academic institutions, and the general public. Despite its provenance and identification having been questioned in…
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based…
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825).…
We determine all Finsler metrics of Randers type for which the Riemannian part is a scalar multiple of the Euclidean metric, on an open subset of the Euclidean plane, whose geodesics are circles. We show that the Riemannian part must be of…
A Platonic surface is a Riemann surface that underlies a regular map and so we can consider its vertices, edge-centres and face-centres. A symmetry (anticonformal involution) of the surface will fix a number of simple closed curves which we…
Monthly averages of the sunspot number visible on the sun, observed from 1749, Zurich Observatory, and from 1848 other observatories, have been analyzed. This time signal presents a frequency power spectra with a clear $1/f^\alpha$ behavior…
One of the most exciting results of the Spitzer era has been the ability to construct longitudinal brightness maps from the infrared phase variations of hot Jupiters. We presented the first such map in Knutson et al. (2007), described the…
The great development of astrometric accuracy since the observations by Hipparchus about 150 BC was documented in 2008 in the first version of the present report. This report was updated in H{\o}g (2017d), e.g. with recent information on…
The first result of the paper (Theorem 1.1) is an explicit construction of unimodal maps that are semiconjugate, on the post-critical set, to the circle rotation by an arbitrary irrational angle $\theta\in(3/5,2/3)$. Our construction is a…
1973 Schinzel proved that the standard logarithmic height h on the maximal totally real field extension of the rationals is either zero or bounded from below by a positive constant. In this paper we study this property for canonical heights…
An N-parameter Brownian sheet in R^d maps a non-random compact set F in R^N_+ to the random compact set B(F) in \R^d. We prove two results on the image-set B(F): (1) It has positive d-dimensional Lebesgue measure if and only if F has…
Ratnatunga et al. (1995) have recently proposed that an object, HST 14176+5226, in the "Groth-Westphal" HST survey strip is an "Einstein cross" gravitational lens. By chance, this object has been previously observed in the Canada-France…
Sunspot positions from various historical sets of solar drawings are analysed with respect to the tilt angles of bipolar sunspot groups. Data by Scheiner, Hevelius, Staudacher, Zucconi, Schwabe, and Spoerer deliver a series of average tilt…