Abstract
The year is 1692, and the reverend Richard Bentley, Master of Trinity College, Cambridge, has just asked Isaac Newton a deep and troubling question. An acclaimed theologian, Bentley was preparing to deliver the first of the newly endowed Robert Boyle Lectures. Open to the public, this series of eight lectures was to be delivered from the pulpit of St. Martin’s Church, London, and the talks were to consider the role of Christian theology and the requirement of an active deity within the framework of natural philosophy (what we now call science) and specifically within the quest to understand the workings of the universe.
There, in the night, where none can spy,
All in my hunter’s camp I lie,
And play at books that I have read
Till it is time to go to bed
—R. L. Stevenson
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Notes
- 1.
Halley specifically found that the positions of the bright stars Sirius, Arcturus, and Aldebaran had moved over half a degree on the sky since the compilation of the star catalog by Hipparchus circa 135 b.c.
- 2.
There is little doubt that Stonehenge was primarily constructed to accommodate the religious and funerary practices of a specific Stone Age society. It was not an astronomical observatory, although its geometry does indicate alignments with the rising and setting locations of the solstice Sun.
- 3.
This problem is usually described under the guise of Olber’s Paradox [3]. And, this paradox is only resolved under the constraint that we live in a universe of finite age.
- 4.
It is clear from Galileo’s correspondence of the time that he intended the Latin word nuncius to mean message as opposed to messenger, and indeed, it is via the former term that Galileo refers to his work when describing it in his native Italian. The tradition of referring to the booklet as the Sidereal Messenger was apparently started by Johannes Kepler in his Dissertatio cum nuncio sidereo (published April 19, 1610).
- 5.
From Genesis 1:14, which would have been Wright’s overriding authority, we have, on the fourth day, “Let there be luminaries in the vault of the sky.”
- 6.
It was in 1785 that William Herschel began the construction of what was to be his great 40-foot telescope—an instrument that utilized a 47-inch diameter mirror to capture starlight. This giant telescope was paid for with funds provided by King George III, and saw first light on February 19, 1787, when Herschel observed the Orion Nebula—object number 42 in Messier’s catalog (Fig. 1.1a).
- 7.
Isaac Newton in his 1687 Principia Mathematica estimated that Sirius was 615,670 AU from Earth.
- 8.
A supplement to Herschel’s catalog was published by John Dreyer in 1878. The New General Catalog (NGC) was additionally compiled by Dreyer in 1888, with further supplements appearing in the Index Catalog (IC) in 1895 and 1908. The NGC catalog describes 7840 objects, with the IC documenting a further 5386 nebulae.
- 9.
Although C/1758 appears to have been independently discovered by Messier, his first recognized new cometary catch occurred some 2 years later, with his detection of C/1760 B1 (Messier). Over the ensuing 38 years, 12 additional new comet discoveries were to follow.
- 10.
Although M 1 was recorded by Bevis in 1731 and marked on copper plates engraved between 1748 and 1750, the actual sky charts were not published until 1786, at which time Bevis’s posthumous Atlas Celeste appeared.
- 11.
Odd among stars in general, the Wolf-Rayet stars show strong emission lines in their spectrum (see Chap. 2). First described by Charles Wolf and Georges Rayet in 1867, the Wolf-Rayet stars are now known to be pre-supernova stars.
- 12.
The phrase ‘common nova’ is now no longer in use, and the hyphen in the original spelling by Baade and Zwicky has also been dropped.
- 13.
Many supernovae have been seen in other galaxies, and the inferred supernova rate for a galaxy like our own is of the order one every 50 years. The fact that the observed rate is on average about 1 every 350 years is entirely due to the effects of interstellar dust—as will be described later in Chap. 3.
- 14.
The Bonner Durchmustering all-sky star catalog was compiled at Bonn Observatory between 1859 and 1903. The final catalog provides data on the position and apparent magnitude of 325,000 stars down to a limiting apparent magnitude of +10.
- 15.
Mitchell is one of those greatly under-appreciated pioneers of modern science. He not only speculated upon the possibility of some cosmic objects having an escape velocity greater than the speed of light, a black hole in modern vernacular, he also developed the experimental technique behind the famed Cavendish experiment to determine the mean density of Earth.
- 16.
In terms of other probabilities, our analysis results are comparable to the 1 in 20 million odds of an individual eventually being canonized, and the 1 in 500 chance of being born with an extra finger or toe.
- 17.
The Hyades cluster is so close to the Sun, in fact, that its distance can be determined through the observed proper motion of its members—by the so-called moving cluster method. Direct parallax distances have also been determined for individual stars in the cluster with the Hubble Space Telescope.
- 18.
Huggins’s home at 90 Upper Tulse Hill no longer stands, the building being demolished, along with the homes of its neighbors, to make way for the modern housing estate of Vibart Gardens, Brixton.
- 19.
This was the first outburst of the recurrent nova T Corona Borealis. A second nova outburst from the system was recorded in 1946 [12].
- 20.
In a delightful, but short communication to the Astrophysical Journal (volume 8, 1898) Margaret additionally suggested coronium, nephium and asterium as possible names.
References
Halley investigated the possibility that the observed magnetic field variations across the Earth’s surface might be mapped-out and thereby used as a means of determining longitude at sea. Unfortunately, as Halley discovered, the magnetic field variations were highly variable. Halley suggested in a paper read before the Royal Society of London in 1692 that the anomalous variations in the geomagnetic field could be explained if the Earth was composed of a series of concentric shells. Each shell was envisioned as having its own magnetic field and independent rotation. The magnetic field at the Earth’s surface was then expressed as a combination of the time and position varying magnetic fields associated with the rotating shells.
If all stars had the same luminosity (L), then their distances (d) could be gauged directly from their observed brightness – or more precisely their measured energy flux (F) at the Earth’s surface. The three quantities being related through an inverse square law in the distance, such that the measured flux F = L / (4 π d 2) - see Appendix I in this book.
There is a long history of trying to solve Olbers Paradox, even before Heinrch Olbers brought it to popular attention in the 1820s. At issue is the contention that if in every line of sight direction that one could possible see on the sky there was a star, then the entire sky should be aglow with light. The paradox is to explain why this is observably not the case. The answer to this paradox entails the fact that the universe is not infinite in extent or age, and that the universe is additionally expanding – the consequence of the latter condition being that as spacetime expands, so light is redshifted to longer and longer wavelengths. It is this latter effect, specifically, that accounts for the fact that at the present epoch the light produced during the Big Bang moment of creation of the universe is observed in the microwave part of the electromagnetic spectrum – that is as the cosmic microwave background radiation. As the universe continues to expand, so the cosmic background radiation will peak at successively longer and longer wavelengths.
Halley deduced the fact that the bright stars Arcturus, Aldebran and Sirius had shifted relative to the companion constellation stars by comparing contemporary positional data against that provided in several historical star catalogs.
The multiverse is a hypothetical set of infinitely many universes. The origins of this concept lie within the currently favored philosophical formulations of quantum mechanics and cosmology, and they attempt to explain the many fine-tuning issues that seem to apply to the observable universe. For a highly readable discussion of these topics see the recent book by Max Tegmark, Our Mathematical Universe: my quest for the ultimate nature of reality (Alfred A. Knopf, New York, 2014).
From the translation of Lacaille’s notes – see the (highly recommended) Students for the Exploration and Development of Space (SEDS) web page: http://messier.seds.org/xtra/history/lac1755.html.
Messier’s first 1774 catalog contained 45 objects. By 1781 the number of objects cataloged by Messier had increased to 80, and by 1784 the number had risen to 102. Additional objects have been added to Messier’s catalog over the years, the last one being the dwarf elliptical galaxy M 110 (a satellite galaxy to M 31) by Kenneth Jones in 1967. Some of the objects in Messier’s catalog might reasonably be excluded as being neither a physical grouping of stars (a galactic or globular cluster) nor a true nebulous cloud – M 24, M 40, M 73 are really just star asterisms. There is additionally, no present-day entry for object M 102, which is thought to have been a duplicate entry for M 101.
Key to the expanding nebula method working is the calculation of the actual expansion distance D in time interval T: this, in fact, is simply D = T V exp , where V exp is determined by the Doppler shift method (see note 13) With D determined the distance to the nebula will be d = D / φ (radians), where φ is the observed angular expansion, expressed in radians, of the nebula in time T.
Taking the number of stars per unit volume to be constant, the number of stars counted in two surveys, one out to a distance R 1 and the other out to a distance R 2 > R 1, will be N 1 / N 2 = (R 1 / R 2)3. Since, additionally, the brightness of a star falls off as the inverse distance squared, we can relate the brightness of the faintest stars observed in each survey as B 1 / B 2 = (R 2 / R 1)2 where B 1 is the brightness of the faintest star seen in the survey out to a distance of R 1 , and B 2 is the brightness of the faintest star seen in the survey out to a distance of R 2. We now eliminate R 1 and R 2 from these two expressions and find B 1 / B 2 = (N 2 / N 1 )2/3. At this stage it will be convenient (from a modern perspective) to introduce the idea of the magnitude scale of stellar brightness. The magnitude scale (see Appendix I) is based upon the measured brightness (more specifically, the measured energy flux) at the observer’s telescope. If the measured energy flux from a specific star is f* (joules per square meter per second), then the magnitude m* is expressed as m* = −2.5 Log (f*). This formulation and conversion was introduced by British astronomer Norman Pogson in the mid-1850s. If we now take the logarithm of the ratio B 1 / B2 we obtain the result that Log (B 1 / B 2) = (2 / 3) log (N 2 / N 1 ). Now in accordance to the manner in which Pogson’s scheme is set up, the magnitude difference (m 1 – m 2) between two stars of brightness B 1 and B 2 is, m 1 – m 2 = −2.5 log (B 1 / B 2), and so m 1 – m 2 = −2.5 log (B 1 / B 2) = −2.5 (2/3) log (N 2 / N 1 ). Finally, if we ‘fix’ our surveys so that the faintest stars observed in the survey to distance R 2 is one magnitude fainter than the faintest stars observed in the survey out to R 1, then log (N 2 / N 1 ) = 1 / (2.5 x 2 / 3) = 0.6, which can be expressed yet more simply as (N 2 / N 1 ) = 100.6 = 3.981. That is, what our initial assumptions of uniform star distribution and constant star luminosity imply is that if we conduct two star-count surveys, one to a limiting magnitude of m and the other to a limiting magnitude of m + 1, then N m+1 / N m ≈ 4)
From Table 1.1, we see that our all-sky count for stars brighter than +5 is N 5 = 2,724, and the final step is to calculate the μ parameter, which is given as the ratio of N 5 / N A, where N A corresponds to the total number of cluster areas A C = π (φ / 2)2 that would be required to cover the entire sky: N A = 41,253 / A C, where the 41,253 number corresponds to the number of square degrees over the entire sky. The probability that the star groupings in these two cluster came about purely by random can now be evaluated as P = N A P(r, μ) x100. The multiple by N A in the probability comes about because we do not specifically care which area AC we are looking at on the sky. For counting experiments such as we are considering, where events occur at a random rate μ, the probability of recording r events in a particular trial is give by the Poisson distribution: P(r, μ) = (μ r / r!)e -μ, where r! is the r-factorial product r(r-1)(r-2)….3.2.1.
Sir David Brewster (1781 – 1868) specialized in optics, and is credited with the invention of the binocular camera, the stereoscope, various polarimeters and the kaleidoscope. He was one of the founders of the British Association for the Advancement of Science, a long time editor of the Edinburgh Philosophical Journal, and he edited the first 16 volumes of the Edinburgh Encyclopedia from 1824 to 1830. The proof that Brewster offered in his More Worlds than One (published in 1854), is a classic example of incorrect but precise logic. In short he offered an inductive proof for the resolvability of all nebulae into star clusters. He argued that each time a new and larger telescope is constructed, so more and more nebulae are resolved in to stars. Taking the Orion nebula as an example, Brewster noted that Galileo in the early 1600s failed to see it at all with his telescope, William Herschel in the mid-1700s saw it as a diffuse nebula, but Lord Rosse (erroneously as we now know) in the mid-1800s resolved it into stars. Accordingly, so argued Brewster by inductive logic, those nebulae seen by Rosse must ultimately be resolved into star clusters when new and larger telescopes are brought to bear on them. The logic seems impeccable, but it is entirely based upon the unarticulated premise that all nebulae must be star clusters.
The star T Corona Borealis is a member of that group of variable outburst stars known as cataclysmic variables. Such binary systems are comprised of two stars that are sufficiently close to each other that mass transfer from one star to the other can take place. If the accreting star is an evolved white dwarf object an accretion disk can form around it, and this disk may, at times, become unstable. A disk instability episode can result in the rapid and massive accumulation of matter on the surface of the white dwarf, and this in turn can result in the sudden onset of fusion reactions, triggering a nova outburst. During a nova outburst the brightness of the system increases dramatically, and much of the material that accumulated on the surface of the white dwarf will be ejected into the surrounding interstellar medium.
The Doppler Effect is concerned with the apparent change in the observed wavelength of an emission or absorption line feature due to the relative motion between the star and the observer. The difference between the observed wavelength λ obs and the expected wavelength λ if the star and observer were at rest is related to the radial velocity V R as: (λ obs - λ) / λ = V R / c, where c is the speed of light. Austrian physicist Christian Doppler first described the basis of the phenomena named after him in 1842, although in the original publication he incorrectly attributed the different colors observed for the stars as being due to their relative motions towards or away from the Earth – these color difference are now known to be associated with the different temperatures of stars (a consequence, in part, explained by Wien’s law – see chapter 5 [2]).
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Beech, M. (2017). Reading the Sky. In: The Pillars of Creation. Springer Praxis Books(). Springer, Cham. https://doi.org/10.1007/978-3-319-48775-5_1
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