Related papers: Learning from Galileo's errors
We consider the Geometria Practica of Christopher Clavius, S.J., a suprisingly eclectic and comprehensive textbook of practical geometry, whose first edition appeared in 1604. Our focus is on four particular sections from Books IV and VI…
All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…
The measurement of the solar diameter is introduced in the wider framework of solar variability and of the influences of the Sun upon the Earth's climate. Ancient eclipses and planetary transits would permit to extend the knowledge of the…
Throughout the early history of Science the heliocentric world model was refused because it contradicted the thoughts of Aristotle and the medieval "Impetus" theory of movement. Even Galileo's sky observations did not lead to any acceptance…
The accuracy of stellar distances inferred purely from parallaxes degrades rapidly with distance. Proper motion measurements, when combined with some idea of typical velocities, provide independent information on stellar distances. Here I…
The Nice model of the dynamical instability and migration of the giant planets can explain many properties of the present Solar System, and can be used to constrain its early architecture. In the jumping-Jupiter version of the Nice model,…
Ancient astronomers faced the problem of dealing with arcs and angles in their observations and predictions without the help of modern trigonometry. The usual method to deal with such problems was the Menelaus Theorem, explicitly discussed…
It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points…
What can physics students learn about science from those scientists who got the answers wrong? Students encounter little science history, and what they have encountered typically portrays scientists as The People with the Right Answers. But…
The second Gaia data release (GDR2) provides precise five-parameter astrometric data (positions, proper motions and parallaxes) for an unprecedented amount of sources (more than $1.3$ billion, mostly stars). The use of this wealth of…
This paper summarises briefly and in English some of the results of the book Hoffmann: Hipparchs Himmelsglobus, Springer, 2017 that had to be written in German. The globe of Hipparchus is not preserved. For that reason, it has been a source…
A selection of astrometric catalogues are presented in three tables for respectively positions, proper motions and trigonometric parallaxes. The tables contain characteristics of each catalogue showing the evolution in optical astrometry,…
The Clementine gnomon has been built in 1702 to measure the Earth's obliquity variation. For this reason the pinhole was located in the walls of Diocletian's times (305 a. D.) in order to remain stable along the centuries, but its original…
For millenia, sailors have used the empirical rule that the elevation angle of Polaris, the North Star, as measured by sextant, quadrant or astrolabe, is approximately equal to latitude. Here, we show using elementary trigonometry that…
The advent of deep, wide, accurate, digital photometric surveys exemplified by the Sloan Digital Sky Survey (SDSS) has had a profound impact on studies of the Milky Way. In the past decade, we have transitioned from a scarcity to an…
Difficulties presented by students on the concept of instantaneous velocity are well known. This is in part due to instantaneous speed being often defined in terms of the notion of mathematical limit, which may not be clear to many students…
Orbital motion in binary and planetary systems is the main source of precise stellar and planetary mass measurements, and joint analysis of data from multiple observational methods can both lift degeneracies and improve precision. We set…
All four giant planets in the Solar system possess irregular satellites, characterized by large, highly eccentric and/or inclined orbits that are distinct from the nearly circular, uninclined orbits of the regular satellites. This…
The changing heavens have played a central role in the scientific effort of astronomers for centuries. Galileo's synoptic observations of the moons of Jupiter and the phases of Venus starting in 1610, provided strong refutation of Ptolemaic…
Construction of a theory of orbits about a precessing oblate planet, in terms of osculating elements defined in a frame of the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine that…