Three pre-telescopic star catalogues contain about a thousand star magnitudes
each (with magnitudes 1, 2, 3, 4, 5, and 6), with these reported brightnesses
as the original basis for what has become the modern magnitude scale. These
catalogues are those of Ptolemy (c. 137, from Alexandria at a latitude of
31.2), Al Sufi (c. 960, from Isfahan at a latitude of 32.6), and Tycho Brahe
(c. 1590, from the island of Hven at a latitude of 55.9). Previously, extensive
work has been made on the positions of the catalogued stars, but only scant
attention has been paid to the magnitudes as reported. These magnitudes will be
affected by a variety of processes, including the dimming of the light by our
Earth's atmosphere (atmospheric extinction), the quantization of the
brightnesses into magnitude bins, and copying or influence from prior
catalogues. This paper provides a detailed examination of these effects.
Indeed, I find all three catalogues to report magnitudes that have near-zero
extinction effects, so the old observers in some way extinction corrected their
Ever since Flinders Petrie undertook a theodolite survey on the Giza plateau
in 1881 and drew attention to the extraordinary degree of precision with which
the three colossal pyramids are oriented upon the four cardinal directions,
there have been a great many suggestions as to how this was achieved and why it
was of importance. Surprisingly, given the many astronomical hypotheses and
speculations that have been offered in the intervening 130 years, there have
been remarkably few attempts to reaffirm or improve on the basic survey data
concerning the primary orientations.
This paper presents the results of a week-long Total Station survey
undertaken by the authors during December 2006 whose principal aim was to
clarify the basic data concerning the orientation of each side of the three
large pyramids and to determine, as accurately as possible, the orientations of
as many as possible of the associated structures. The principal difference
between this and all previous surveys is that it focuses upon measurements of
sequences of points along multiple straight and relatively well preserved
structural segments, with best-fit techniques being used to provide the best
estimate of their orientation, as opposed to simple triangulation between
directly identified or extrapolated corners.
Our results suggest that there is only a very slight difference in
orientation (c. 0.5 arc minutes) between the north-south axes of Khufu's and
Khafre's pyramids, that the sides of Khafre's are more perfectly perpendicular
than those of Khufu's, and that the east-west axis is closer to true
cardinality in both cases. The broader context of associated structures
suggests that the east-west orientation in relation to sunrise or (in one case)
sunset may have been a, or even the, key factor in many cases.
The present work provides an outline of the history of the efforts to map the topography of the surface of the moon, from the days of pre-telescopic astronomy to the present. The first part of the book covers the time span from 1600 to 1960 and reproduces numerous examples of this early, earth-based selenographic work. The manned lunar missions in the 1960's revolutionized the science of lunar mapping with their high-resolution, close-range photography of the moon. In 1959, a comprehensive lunar mapping program was initiated by two DOD mapping agencies - the U.S. Air Force Aeronautical Chart and Information Center (ACIC) and the U.S. Army Map Service (AMS). In the course of this program, the cause of lunar mapping enlisted for the first time the services of professional cartographers; the outcome of their efforts speedily relegated all previous work into absolescence. The methods and results of this work are described, and the underlying principles of physical selenodesy are set forth, including the definition of lunar coordinates and the methods for a determination of three-dimensional coordinates of lunar features. A section is included on lunar mapping in the U.S.S.R.
The present paper deals with the methods proposed and the values achieved for the eccentricity and the longitude of apogee of the (apparent) orbit of the Sun in the Ptolemaic context in the Middle East during the medieval period. The main goals of this research are as follows: first, to determine the accuracy of the historical values in relation to the theoretical accuracy and/or the intrinsic limitations of the methods used; second, to investigate whether medieval astronomers were aware of the limitations, and if so, which alternative methods (assumed to have a higher accuracy) were then proposed; and finally, to see what was the fruit of the substitution in the sense of improving the accuracy of the values achieved. In Section 1, the Ptolemaic eccentric orbit of the Sun and its parameters are introduced. Then, its relation to the Keplerian elliptical orbit of the Earth, which will be used as a criterion for comparing the historical values, is briefly explained. In Section 2, three standard methods of measurement of the solar orbital elements in the medieval period found in the primary sources are reviewed. In Section 3, more than twenty values for the solar eccentricity and longitude of apogee from the medieval period will be classified, provided with historical comments. Discussion and conclusions will appear in Section 4 (in Part 2), followed there by two discussions of the medieval astronomers' considerations of the motion of the solar apogee and their diverse interpretations of the variation in the values achieved for the solar eccentricity.
Earlier orbit determinations (by Douwes and Olbers) based on a very
short arc of observations by Peter Apian did yield ambiguous results.
While the uncertainty involved was already obvious to Olbers, the
Chinese records which became subsequently available were not even
remotely compatible with either solution. While this was well known
already in 1875 (and documented in ''Nature'', presumably by J. R.
Hind), no adequate orbit correction was possible due to the absence of
hard quantitative data. The introduction of an up to now unknown series
of 10 observations (by Achilles P. Gasser of Lindau) covering one full
month now made a straightforward orbit determination possible. The
resulting retrograde parabola satisfies all known European and East