Related papers: Groping Toward Linear Regression Analysis: Newton'…
Exactly 500 years ago, Nicolaus Copernicus drew a lattice of lines on a panel above the doorway to his rooms at Olsztyn Castle, then in the Bishopric of Warmia. Although its design has long been regarded as some kind of reflecting vertical…
Astronomical observations were used as a marker for time and the Calendar from ancient times. A more subtle calibration of epochs is thrown up by an observation of the position of the solstices and equinoxes, because these points shift in…
The principle that celestial bodies must move on circular orbits or on paths resulting from the composition of circular orbits has been assumed as a constant guide in the astronomical thougth of the peoples facing the Mediterranean sea as…
It is known that Sir Isaac Newton suggested a date for the Passion of Christ in the posthumously published "Observations upon the Prophecies of Daniel and the Apocalypse of St. John" (1733). What was not known is that the first attempts to…
The purpose of this note consists of discrete rational reconstruction which took place during the years 1609-1630 and 1630-1666, ie, the year of the publication of their Astronomia Nova and the year of death of the great German astronomer…
Recently much attention has been paid to the discovery of Hubble's law: the linear relation between the rate of recession of the distant galaxies and distance to them. Though we now mention several names associated with this law instead of…
After a brief introduction to the sixteenth and seventeenth century views of the Universe and the nineteenth century paradox of Olbers, we start the history of the cosmic expansion with Hubble's epochal discovery of the recession velocities…
We compute the mean interval between successive returns of the apparent geocentric solar longitude $\lambda$ to a fixed value $L \in \{0^\circ, 45^\circ, 90^\circ, \ldots, 315^\circ\}$, averaged over a multi-millennium window; this gives…
This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's $J_2$ and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane,…
This paper tries to tell the story of the general linear model, which saw the light of day 200 years ago, and the assumptions underlying it. We distinguish three principal stages (ignoring earlier more isolated instances). The model was…
Initially applied in astronomy and geodesy, the linear regression model aimed to find the best estimates for parameters with predefined meanings. E.g., orbital elements, geodetic constants. As its use expanded to other disciplines, often to…
Doubly truncated data are found in astronomy, econometrics and survival analysis literature. They arise when each observation is confined to an interval, i.e., only those which fall within their respective intervals are observed along with…
In 1980 Kowal and Drake found that in December 1612 and January 1613 Galileo observed the planet Neptune. At that time, according to these authors, Galileo was able to measure angular separations with an accuracy of about 10 seconds of arc.…
Precise measurements of the Earth-Moon distance by the lunar laser ranging (LLR), which begun in the early 1970's, contributed significantly to geodesy, geophysics, and lunar planetology, as well as enabled astrophysicists to perform…
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…
This work aims at providing some (further) perspective into the analysis of two well-known datasets in terms of the methods of linear regression. The first set has been taken from Hubble's 1929 investigation of the relation between the…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
The McNish and Lincoln (ML) method, introduced in 1949, was one of the first attempts to produce mid-term forecasts of solar activity, up to 12 months ahead. However, it has been poorly described and evaluated in the past literature, in…
The question of annual stellar parallax is usually viewed as having been a "win-win situation" for seventeenth-century astronomers who subscribed to the Copernican view of universe in which the Earth orbits the Sun and the Sun is one of…
Between the mid-eighteenth and mid-nineteenth centuries, long-haul oceanic voyages of exploration and discovery routinely carried astronomical tent observatories to support land-based longitude determinations using heavy and cumbersome…