Astronomers From England

"The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity. It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties."

"The solution... was found only after the rise of nuclear physics, and, strange to relate, was not known to Eddington when he developed his celebrated theory of stellar structure between 1916 and 1924. Indeed, it is one of the most intriguing facts in the history of science that the two most influential theories concerning the stars—Newton's theory of gravitation and Eddington's theory of stellar construction—were each developed so successfully although Newton was ignorant of the origin of gravitation and Eddington of the origin of stellar energy."

"It became clear that our Galaxy is only one system among many, and that the universe is far vaster than the particular stellar system to which the Sun and planets belong. Since then developments have been more rapid than at any time since the days of Copernicus, Digges and Bruno when the geocentric hypothesis of the cosmos received its death-blow."

"One of the few authors to have explicitly connected the physical issue of the expansion of the universe with the philosophical topic of the metaphysical status of space is Gerald James Whitrow."

"By combining prodigious scholarship from the ancient Greeks to modern physicists, he argued persuasively in more than 100 academic papers and a string of books that an integrated, interdisciplinary understanding of time should be possible."

"Whether the stars were all at the same distance, or whether they were scattered throughout infinite space, or whether they formed a finite system of vast but limited depth, were questions that could not be answered until towards the end of the eighteenth century. Until then, stellar astronomy was a field left to the unaided imagination."

"Our conscious appreciation of the fact that one event follows another is of a different kind from our awareness of either event separately. If two events are to be represented as occurring in succession, then—paradoxically—they must also be thought of simultaneously."

"Although the classic theoretical foundation of distance measurement in physics is the 'rigid rod', nearly all distances in surveying, whether terrestrial or celestial, are made to depend on the properties of light. The two simplest properties so employed are the principle of propogation in straight lines and the principle that the intensity of light diminishes inversely as the square of the distance."

"Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem)."

"Although the peculiarly fundamental nature of time in relation to ourselves is evident as soon as we reflect that our judgments concerning time and events in time appear themselves to be 'in' time, whereas our judgments concerning space do not appear themselves in any obvious sense to be in space, physicists have been influenced far more profoundly by the fact that space seems to be presented to us all of a piece, whereas time comes to us only bit by bit. The past must be recalled by the dubious aid of memory, the future is hidden from us, and only the present is directly experienced. This striking dissimilarity between space and time has nowhere had a greater influence than in physical science based on the concept of measurement. Free mobility in space leads to the idea of the transportable unit length and the rigid measuring rod. The absence of free mobility in time makes it much more difficult for us to be sure that a process takes the same time whenever it is repeated."

"Galileo had raised the concepts of space and time to the status of fundamental categories by directing attention to the mathematical description of motion. The midiaevel qualitative method had made these concepts relatively unimportant, but in the new mathematical philosophy the external world became a world of bodies moving in space and time. In the Timaeus Plato had expounded a theory that outside the universe, which he regarded as bounded and spherical, there was an infinite empty space. The ideas of Plato were much discussed in the middle of the seventeenth century by the Cambridge Platonists, and Newton's views were greatly influenced thereby. He regarded space as the 'sensorium of God' and hence endowed it with objective existence, although he confessed that it could not be observed. Similarly, he believed that time had an objective existence independent of the particular processes which can be used for measuring it."

"Let us suppose that an explosion occurs on Mars, which is observed by an astronomer on earth, who records the instant when he sees the flash. If light travelled instantaneously with an infinite velocity, this instant would coincide with the time... recorded by the... observer on Mars. In this way a meaning could be attached automatically to absolute time and the simultaneity of events at different places; indeed, the classical theory is now regarded as the limiting form of Einstein's theory when the velocity of light becomes infinite. But as there is a mass of experimental evidence supporting the view that light takes a finite time to travel... the terrestrial observer must correct the time recorded on his watch. This correction... will depend on assumptions concerning the velocity of light and the measurement of distance. Thus the concept of a world-wide simultaneity ceases to be a primitive idea."

"Consider an event, for example the outburst if a nova... Suppose this event is observed from two stars in line with the nova, and suppose further that the two stars are moving uniformly with respect to each other in this line. Let the epoch at which these stars passed by each other be taken as the zero of time measurement, and let an observer A on one of the stars estimate the distance and epoch of the nova outburst to be x units of length and t units of time, respectively. Suppose the other star is moving toward the nova with velocity v relative to A. Let an observer B on the star estimate the distance and epoch of the nova outburst to be x units of length and t units of time, respectively. Then the Lorentz formulae, relating x to t, arex' = \frac {x-vt}{\sqrt{1-\frac{v^2}{c^2}}} ; \qquad t' = \frac {t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}} These formulae are... quite general, applying to any event in line with two uniformly moving observers. If we let c become infinite then the ratio of v to c tends to zero and the formulae becomex' = x - vt ; \qquad t' = t."

"[Time is not] a mysterious illusion of the intellect. ..It is an essential feature of the universe."

"In developing his theory of gravitation, Newton assigned to every material body another property which is called its gravitational mass. Gravitational mass determines the force exerted by the body on other bodies, and so its function appears to be quite distinct from that of inertial mass. Nevertheless, the two are found to be identical in magnitude. Newton made experiments to verify this remarkable equality by swinging a pendulum with a bob which could be made with different materials. The period of the swing depended on the ratio of the inertial and gravitational masses of the pendulum, but in all cases it was found to be the same... In 1890 Eötvös made a much more refined test with the aid of a... torsion balance. Repeated experiments showed that inertial mass and gravitational mass were equal to within one part in 100 million. Einstein suggested that this was because inertia and gravitation are identical."

"Much of Dr. Whitrow's work is concerned with problems in cosmology and relativity. ...He has been editor of The Observatory Magazine and the Monthly Notices of the Royal Astronomical Society."

"Minkowski made a remarkable discovery concerning the Lorentz formulae. He showed that, although each observer has his own private space and private time, a public concept which is the same for all observers can be formed by combining space and time as a kind of 'distance' by multiplying it by the velocity of light, c; in other words, with any time interval we can associate a definite spatial interval, namely the distance which light can travel in empty space in that period. If, according to a particular observer, the difference in time between any two events is T, this associated spatial interval is cT. Then, if R is the space-distance between these two events, Minkowski showed that the difference of the squares of cT and R has the same value for all observers in uniform relative motion. The square root of this quantity is called the space-time interval between two events. Hence, although time and three-dimensional space depend on the observer, this new concept of space-time is the same for all observers."

"According to the Special Theory of Relativity, the velocity of a moving body is always less than the velocity of light. Since the energy of motion of a body depends on its inertial mass and its velocity, it follows that if the energy of a body is increased indefinitely by the continual application of a force, the inertial mass of the body must be increased too; for, if not, the velocity would ultimately increase indefinitely and exceed the velocity of light. Einstein found that, corresponding to any increase in the energy content of a body, there is an equivalent increase in its inertial mass. Mass and energy thus appeared to be different names for the same thing, the energy associated with a mass M being Mc2, where c is the velocity of light; and the mass M of a body moving with velocity v he found to be given by the following formulaM = \frac {m}{\sqrt{(1 - \frac {v^2}{c^2}}}"

"I will add another thing which I also had from Dr. Bentley himself. Mr. Halley was then thought of for successor, to be in a mathematick professorship at Oxford; and bishop Stillingfleet was desired to recommend him at court; but hearing that he was a sceptick, and a banterer of religion, he scrupled to be concern'd; 'till his chaplain, Mr. Bentley, should talk with him about it; which he did. But Mr. Halley was so sincere in his infidelity, that he would not so much as pretend to believe the christian religion, tho' he thereby was likely to lose a professorship; which he did accordingly; and it was then given to Dr. Gregory: Yet was Mr. Halley afterwards chosen into the like professorship there, without any pretence to the belief of christianity. Nor was there any enquiry made about my successor Mr. Sandersons christianity, even when the university of Cambridge had just banished me for believing and examining it so throughly, that I hazarded all I had in the world for it."

"s production was not without drama. ... ... The had promised to publish the work, but now pulled out, citing financial embarrassment. The year before the society had backed a costly flop called ', and they now suspected that the market for a book on mathematical principles would be less than clamorous. Halley, whose means were not great, paid for the book's publication out of his own pocket. Newton, as was his custom, contributed nothing. To make matters worse, Halley at this time had just accepted a position as the society's clerk, and he was informed that the society could no longer afford to provide him with a promised salary of £50 per annum. He was to be paid instead in copies of The History of Fishes."

"In the mean time, those that desire to know how to construct Geometrically the Orb of a Comet, by Three accurate Observations given, may find it at the End of the Third Book of Sir Isaac Newtons Principles of Natural Philosophy, entituled De Systemate Mundi, in the Words of its renowned Inventor. Which have since been more fully explained by my very worthy Collegue Dr. Gregory, in his Learned Work of Astronomia Physica & Geometrica."

"Hitherto I have consider'd the Orbits of Comets as exactly Parabolick; upon which Supposition it wou'd follow, that Comets being impell'd towards the Sun by a Centripetal Force, descend as from Spaces infinitely distant, and by their Falls acquire such a Velocity, as that they may again run off into the remotest Parts of the Universe, moving upwards with such a perpetual Tendency, as never to return again to the Sun. But since they appear frequently enough, and since none of them can be found to move with an Hyperbolick Motion, or a Motion swifter than what the... Comet might acquire by its Gravity to the Sun, 'tis highly probable they rather move in very Excentrick Orbits, and make their Returns after long Periods of Time: For so their Number will be determinate, and, perhaps, not so very great. Besides, the Space between the Sun and the fix'd Stars is so immense, that there is Room enough for a Comet to revolve, tho' the Period of its Revolution be vastly long."

"By comparing together the Accounts of the Motions of these Comets, 'tis apparent, their Orbits are dispos'd in no manner of Order; nor can they, as the Planets are, be comprehended within a Zodiack, but move indifferently every Way, as well Retrograde as Direct; from whence it is clear, they are not carry'd about or mov'd in 'Vortices'. Moreover, the Distances in their Perihelium's are sometimes greater, sometimes less; which makes me suspect, there may be a far greater Number of them, which moving in Regions more remote from the Sun, become very obscure; and wanting Tails, pass by us unseen."

"The principal Use therefore of this Table of the Elements of their Motions, and that which induced me to construct it, is, That whenever a new Comet shall appear, we may be able to know, by comparing together the Elements, whether it be any of those which has appear'd before, and consequently to determine its Period, and the Axis of its Orbit, and to foretell its Return. And, indeed, there are many Things which make me believe that the Comet which Apian observ'd in the Year 1531, was the same with that which Kepler and Longomontanus took Notice of and describ'd in the Year 1607, and which I my self have seen return, and observ'd in the Year 1682."

"5. From these Things given (by the very same Rules that we find the Planets Places, from the Suns Place and Distance given) we may obtain the Apparent or Geocentrick Place of the Comet, together with the Apparent Latitude. And this it may be worth while to illustrate by an Example or two."

"These necessary Things premis'd, let it be propos'd to compute the apparent Place of any one of the mention'd Comets, for any Given Time."

"After this manner... the Astronomical Reader may examine these Numbers, which I have calculated, with all imaginable Care, from the Observations I have met with. And I have not thought fit to make them publick before they have been duly examin'd, and made as accurate as 'twas possible, by the Study of many Years. I have publish'd this Specimen of Cometical Astronomy, as a Prodromus of a designed future Work, left, happening to die, these Papers might be lost, which every Man is not capable to retrieve, by reason of the great Difficulty of the Calculation."

"All the Elements agree, and nothing seems to contradict this my Opinion, besides the Inequality of the Periodick Revolutions: Which Inequality is not so great neither, as that it may not be owing to Physical Causes. For the Motion of Saturn is so disturbed by the rest of the Planets, especially Jupiter, that the Periodick Time of that Planet is uncertain for some whole Days together. How much more therefore will a Comet be subject to such like Errors, which rises almost Four times higher than Saturn, and whose Velocity, tho' encreased but a very little, would be sufficient to change its Orbit, from an Elliptical to a Parabolical one."

"The Astreonomical Elements of the Motions in a Parabolick Orb of all the Comets that have been hitherto duly obferv'd. ...This Table needs little Explication, since 'tis plain enough from the Titles, what the Numbers mean. Only it maybe observ'd, that the Perihelium Distances, are estimated in such Parts, as the Middle Distance of the Earth from the Sun, contains 100000."

"Wherefore (following the Steps of so Great a Man) I have attempted to bring the same Method to Arithmetical Calculation; and that with desired Success. For, having collected all the Observations of Comets I could, I fram'd this Table, the Result of a prodigious deal of Calculation, which, tho' but small in Bulk, will be no unacceptable Present to Astronomers. For these Numbers are capable of Representing all that has been yet observ'd about the Motion of Comets, by the Help only of the following General Table; in the making of which I spar'd no Labour, that it might come forth perfect, as a Thing consecrated to Posterity, and to last as long as Astronomy it self."

"A General Table for Calculating the Motions of Comets in a Parabolical Orbit."

"At length, came that prodigious Comet of the Year 1680, which descending (as it were) from an infinite Distance Perpendicularly towards the Sun, arose from him again with as great a Velocity. This Comet, (which was Seen for Four Months continually) by the very remarkable and peculiar Curvity of its Orbit (above all others) gave the fittest Occasion for investigating the Theory of the Motion. And the Royal Observatories at Paris and Greenwich having been for some time founded, and committed to the Care of most excellent Astronomers, the apparent Motion of this Comet was most accurately (perhaps as far as Humane Skill cou'd go) observ'd by Mrs. Cassini and Flamsteed."

"Next, Hevelius (a Noble Emulator of Ticho Brahe) following in Keplers Steps, embraced the same Hypothesis of the Rectilinear Motion of Comets, himself accurately observing many of them. Yet, he complain'd, that his Calculations did not perfectly agree to the Matter of Fact in the Heavens: And was aware, that the Path of a Comet was bent into a Curve Line towards the Sun."

"Not long after, that Great Geometrician, the Illustrious Newton, writing his Mathematical Principles of Natural Philosophy, demonstrated not only that what Kepler had found, did necessarily obtain in the Planetary System; but also, that all the Phænomena of Comets wou'd naturally follow from the same Principles; which he abundantly illustrated by the Example of the aforesaid Comet of the Year 1680, shewing, at the same time, a Method of Delineating the Orbits of Comets Geometrically; wherein he (not without the highest Admiration of all Men) solv'd a Problem, whose Intricacy render'd it worthy of himself. This Comet he prov'd to move round the Sun in a Parabolical Orb, and to describe Area's (taken at the Center of the Sun) proportional to the Times."

"The Construction and Use of the general Table.As the Planets move in Elliptick Orbs, so do the Comets in Parabolick ones, having the Sun in their common Focus, and describe equal Areas in equal Times. But now because all s are similar to one another, therefore if any determinate Part of the Area of a given Parabola, be divided into any Number of Parts at Liberty, there will be a like Division made in all Parabolas, under the same Angles, and the Distances will be proportional: And consequently this one Table of ours will serve for all Comets."

"[I]n the Year 1456, in the Summer time, a Comet was seen passing Retrograde between the Earth and the Sun, much after the same Manner: Which, tho' no Body made Observations upon it, yet from its Period, and the Manner of its Transit, I cannot think different from those I have just now mention'd. Hence I dare venture to foretell, That it will return again in the Year 1758. And, if it should then return, we shall have no Reason to doubt but the rest must return too: Therefore Astronomers have a large Field to exercise themselves in for many Ages, before they will be able to know the Number of these many and great Bodies revolving about the common Center of the Sun; and reduce their Motions to certain Rules."

"[I]n the Year 1472, which being the swiftest of all, and nearest to the Earth, was observ'd by Regiomantanus. This Comet (fo frightful upon the Account both of the Magnitude of its Body,and the Tail) mov'd Forty Degrees of a great Circle in the Heavens, in the Space of one Day, and was the first, of which any proper Observations are come down to us."

"Yet almost all the Astronomers differ'd from this Opinion of Seneca; neither did Seneca himself think fit to set down those Phænomena of the Motion, by which he was enabled to maintain his Opinion: Nor the Times of those Appearances, which might be of use to Posterity, in order to the Determining these Things. And indeed, upon the Turning over very many Histories of Comets, I find nothing at all that can be of Service in this Affair, before, A.D. 1337, at which time ', a Constantinopolitan Historian and Astronomer, did pretty accurately describe the Path of a Comet amongst the Fix'd Stars, but was too laxe as to the Account of the Time; so that this most doubtful and uncertain Comet, only deserves to be inserted in our Catalogue, for the sake of its appearing near 400 Years ago."

"But all those that consider'd Comets, until the Time of Ticho Brahe (that great Restorer of Astronomy) believ'd them to be below the Moon, and so took but little Notice of them, reckoning them no other than Vapours."

"So that 'tis to the Greeks themselves as the Inventors (and especially to the Great Hipparchus) that we owe this Astronomy, which is now improv'd to such a Heigth. But yet, amongst these, the Opinion of Aristotle (who wou'd have Comets to be nothing else, but Sublunary Vapours, or Airy Meteors) prevailed so far, that this most difficult Part of the Astronomical Science lay altogether neglected; for no Body thought it worth while to take Notice of, or write about, the Wandring uncertain Motions of what they esteemed Vapours floating in the Æther; whence it came to pass, that nothing certain, concerning the Motion of Comets, can be found transmitted from them to us."

"Wherefore, if, according to what we have already said, it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman."

"But Seneca the Philosopher, having consider'd the Phænomena of Two remarkable Comets of his Time, made no Scruple to place them amongst the Cœlestial Bodies; believing them to be Stars of equal Duration with the World, tho' he owns their Motions to be govern'd by Laws not as then known or found out. And at last (which was no untrue or vain Prediction) he foretells, that there should be Ages sometime hereafter, to whom Time and Diligence shou'd unfold all these Mysteries, and who shou'd wonder that the Ancients cou'd be ignorant of them, after some lucky Interpreter of Nature had shewn, in what Parts of the Heavens the Comets wander'd, and how great they were."

"But in the Year 1577, (Ticho seriously pursuing the Study of the Stars, and having gotten large Instruments for the Performing Cœlestial Mensurations, with far greater Care and Certainty, than the Ancients cou'd ever hope for) there appear'd a very remarkable Comet; to the Observation of which, Ticho vigorously applied himself; and found by many just and faithful Trials, that it had not a Diurnal Parallax that was at all perceptible: And consequently was not only no Aireal Vapour, but also much higher than the Moon; nay, might be plac'd amongst the Planets for any thing that appear'd to the Contrary; the cavilling Opposition made by some of the School-men in the mean time, being to no Purpose."

"Perhaps the most important of Whitrow's books was The Natural Philosophy of Time. He showed that time can be studied independently of its magnitude. ...Whitrow's historical work included a paper on Robert Hooke."

"The shift toward a linear time conception, a confutation against (instead of a development from) the age-old cyclic time conception, did not occur suddenly and lasted well into the nineteenth century. ...Attention had clearly drifted away from seeking an eternally valid order toward a focus on change; truth had now ceased to lie in an unchanging order of things—rather, it tended to be regarded as dependent on process. Gerald Whitrow has put the matter succinctly, that in the nineteenth century " interest was transferred from the 'thing completed' to the genetic process, that is, from 'being' to 'becoming.' ""

"Next to Ticho, came the Sagacious Kepler. He having the Advantage of Tichos Labours and Observations, found out the true Physical System of the World, and vastly improv'd the Astronomical Science. For he demonstrated that all the Planets perform their Revolutions in Elliptick Orbits, whose 'Plains pass thro' the Center of the Sun, observing this Law, That the Area's (of the Elliptick Sectors, taken at the Center of the Sun, which he proved to be in the common Focus of these Ellipses) are always proportional to the Times, in which the correspendent Elliptical Arches are describ'd. He discover'd also, That the Distances of the Planets from the Sun are in the Ratio [3:2] of the Periodical Times, or (which is all one) That the Cubes of the Distances are as the Squares of the Times. This great Astronomer had the Opportunity of observing Two Comets, one of which was a very remarkable one. And from the Observations of these (which afforded sufficient Indications of an Annual Parallax) he concluded, That the Comets mov'd freely thro' the Planetary Orbs, with a Motion not much different from a Rectilinear one; but of what Kind, he cou'd not then precisely determine."

"Professor Gerald Whitrow, who has died aged 87, wrote The Natural Philosophy of Time (1960) a tour de force that examined the subject from every side—mathematical, cosmological, historical, biological and psychological. ...As an opening for his talks, he would sometimes recount one of his favourite stories on time. It concerned the Russian poet Samuel Marshak, on a visit to London before 1914. Marshak's English was not too good and when he asked a man in the street "Please, what is time?", he received the surprised response, "But that's a big question. Why ask me?""

"I design to treat of all these Things in a larger Volume, and contribute my utmost for the Promotion of this Part of Astronomy, if it shall please God to continue my Life and Health."

"Astronomy is probably the oldest of all the sciences. It differs from virtually all other science disciplines in that it is not possible to carry out experimental tests in the laboratory."

"Bertrand, Darboux, and Glaisher have compared Cayley to Euler, alike for his range, his analytical power, and, not least, for his prolific production of new views and fertile theories. There is hardly a subject in the whole of pure mathematics at which he has not worked."