Solar Motion and Lunar Eclipses in Philolaus’ Cosmological System

In this paper, three problems that have hardly been noticed or even gone unnoticed in the available literature in the cosmology of Philolaus are addressed. They have to do with the interrelationships of the orbits of the Earth, the Sun, and the Moon around the Central Fire and all three of them constitute potentially insurmountable obstacles within the context of the Philolaic system. The first difficulty is Werner Ekschmitt’s claim that the Philolaic system cannot account for the length of the day (νυχϑήμερον). It is shown that this problem can be solved with the help of the distinction between the synodic day and the sidereal day. The other two problems discussed in this paper are concerned with two hitherto unnoticed deficiencies in the explanation of lunar eclipses in the Philolaic system. The Philolaic system cannot account for long-lasting lunar eclipses and according to the internal logic of the system, during lunar eclipses the Moon enters the shadow of the Earth from the wrong side. It is almost unbelievable that nobody, from the Pythagoreans themselves up to recent authors, has noticed these two serious deficiencies, and especially the latter, in the cosmology of Philolaus the Pythagorean.

Kinematic study of the association Cyg OB3 with Gaia DR2

ABSTRACT We study the stellar kinematic properties and spatial distribution of the association Cyg OB3 using precise astrometric data from Gaia DR2. All known O- and B-type stars in Cyg OB3 region with positions, parallaxes, and proper motions available are included, comprising a total of 41 stars. The majority of stars are found to be concentrated at a heliocentric distance of 2.0 ± 0.3 kpc. The mean peculiar velocity of the sample after removing Galactic rotation and solar motion is ∼22 km s−1, dominated by the velocity component towards the Galactic centre. The relative position and velocity of the black hole X-ray binary Cyg X-1 with respect to the association suggest that Cyg OB3 is most likely its parent association. The peculiar kinematic properties of some of the stars are revealed and are suggestive of past stellar encounters. The sample includes a previously known runaway star HD 227018, and its high peculiar velocity of ∼50 km s−1 is confirmed with Gaia. We estimated the velocities of stars relative to the association and the star HD 225577 exhibits peculiar velocity smaller than its velocity relative to the association. The star has lower value of proper motion than the rest of the sample. The results suggest a slowly expanding nature of the association, which is supported by the small relative speeds (<20 km s−1) with respect to the association for a majority of the sample stars.

An all-sky proper-motion map of the Sagittarius stream using Gaia DR2

Aims. We aim to measure the proper motion along the Sagittarius stream, which is the missing piece in determining its full 6D phase space coordinates. Methods. We conduct a blind search of over-densities in proper motion from the Gaia second data release in a broad region around the Sagittarius stream by applying wavelet transform techniques. Results. We find that for most of the sky patches, the highest intensity peaks delineate the path of the Sagittarius stream. The 1500 peaks identified depict a continuous sequence spanning almost 2π in the sky, only obscured when the stream crosses the Galactic disk. Altogether, around 100 000 stars potentially belong to the stream as indicated by a coarse inspection of the color-magnitude diagrams. From these stars, we determine the proper motion along the Sagittarius stream, making it the proper-motion sequence with the largest span and continuity ever measured for a stream. A first comparison with existing N-body models of the stream reveals some discrepancies, especially near the pericenter of the trailing arm and an underestimation of the total proper motion for the leading arm. Conclusions. Our study provides a starting point for determining the variation of the population of stars along the stream, the distance to the stream from the red clump stars, and the solar motion. It also permits much more accurate measurement of the Milky Way potential.

Discovery of a nearby 1700 km s−1 star ejected from the Milky Way by Sgr A*

ABSTRACT We present the serendipitous discovery of the fastest main-sequence hyper-velocity star (HVS) by the Southern Stellar Stream Spectroscopic Survey (S5). The star S5-HVS1 is a ∼2.35 M⊙ A-type star located at a distance of ∼9 kpc from the Sun and has a heliocentric radial velocity of 1017 ± 2.7 $\mathrm{\, km\, s^{-1}}$ without any signature of velocity variability. The current 3D velocity of the star in the Galactic frame is 1755 ± 50 $\mathrm{\, km\, s^{-1}}$. When integrated backwards in time, the orbit of the star points unambiguously to the Galactic Centre, implying that S5-HVS1 was kicked away from Sgr A* with a velocity of ∼1800 $\mathrm{\, km\, s^{-1}}$ and travelled for 4.8 Myr to its current location. This is so far the only HVS confidently associated with the Galactic Centre. S5-HVS1 is also the first hyper-velocity star to provide constraints on the geometry and kinematics of the Galaxy, such as the Solar motion Vy,⊙ = 246.1 ± 5.3 $\mathrm{\, km\, s^{-1}}$ or position R0 = 8.12 ± 0.23 kpc. The ejection trajectory and transit time of S5-HVS1 coincide with the orbital plane and age of the annular disc of young stars at the Galactic Centre, and thus may be linked to its formation. With the S5-HVS1 ejection velocity being almost twice the velocity of other hyper-velocity stars previously associated with the Galactic Centre, we question whether they have been generated by the same mechanism or whether the ejection velocity distribution has been constant over time.

A Chinese Innovation Based on Western Methods: The Double-Epicycle Solar Model in the Lixiang kaocheng, 1722

This article attempts to show how an effort was made by Chinese astronomers to improve on the solar model under the auspice of Emperor Kangxi, in circumstances of the merging of Western and Chinese mathematical astronomy. The result of this effort is the Lixiang kaocheng. Different from the eccentric solar model in the previous calendars, Lixiang kaocheng invented a double-epicycle model to describe the solar motion, aiming at bringing computations into agreement with observation. The observational data used for determining the parameters of solar model might be obtained with Tychonic instruments. But it is also possible that these “observational data” might have been derived from Western astronomical tables. Although actual observations did become more accurate, it did not reflect upon the revision of the solar model. The accuracy of the solar model in the Lixiang kaocheng did not increase very much compared with the previous models.

Kinematics of the Milky Way disc from the RAVE survey combined with Gaia DR1

Relying on the complementarity of Gaia proper motions with radial velocities of the RAVE survey, we attempt to constrain the kinematics of the Milky Way disc. Based on the population synthesis model, we simulate the observations, applying the detailed selection functions of the observations. The dynamics is described using a global gravitational potential computed from the mass distribution of the population model, approximated by a Stäckel potential (Bienaymé et al. 2015). We explore a set of free parameters (solar motion, age - velocity dispersion of the disc as a function of age, the velocity gradients, vertex deviation) using a Markov Chain Monte Carlo method. We show that the fitted model reproduces very well the radial velocity and proper motion distributions, allowing to constrain the thin and thick disc secular evolution with time.