Cosmology Day July 2018

Lecture 1: Newton’s Cosmology

Professor Robert Iliffe


Professor Iliffe is Professor of History of Science at Oxford, Co-Director of the Oxford Centre for the History of Science, Medicine and Technology, and a General Editor of the Newton Project.


Professor Iliffe’s talk was about the background to Newton’s researches into cosmology, including influences on his early accounts of space, and the development of his thoughts on the nature of the universe and the function of comets.

Professor Illife discussed Newton’s ruminations on a number of the implications of the doctrines of Principa Mathematica, and ended the talk by examining Newton’s late thoughts on the nature of the Milky Way.


There had been major changes in the understanding of cosmology in the century before Newton was born. How many were made in his lifetime? Analysis of his cosmology requires understanding of what went before.

Before Copernicus it was believed that the Earth was the centre of the cosmos.

In astronomy, the geocentric model (also known as geocentrism, or the Ptolemaic system) is a superseded description of the Universe with Earth at the centre. Under the geocentric model, the Sun, Moon, stars, and planets all orbited Earth. The geocentric model served as the predominant description of the cosmos in many ancient civilizations, such as those of Aristotle and Ptolemy.


Ptolemy’s model of the Universe; this drawing is taken form Peter Aplan’s “Cosmographia” (1524)

Nicolaus Copernicus (19 February 1473 – 24 May 1543) was a Renaissance-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the centre of the universe, in all likelihood independently of Aristarchus of Samos, who had formulated such a model some eighteen centuries earlier.


His major work on his heliocentric theory was Dē revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), published in the year of his death, 1543. He had formulated his theory by 1510. “He wrote out a short overview of his new heavenly arrangement [known as the Commentariolus, or Brief Sketch], also probably in 1510 [but no later than May 1514], and sent it off to at least one correspondent beyond Varmia [the Latin for “Warmia”]. That person in turn copied the document for further circulation, and presumably the new recipients did, too..

The Roman Catholic Church, at the time, did not agree with this view as it went against the bible (Aristotle was considered an honorary Catholic).

Leonard Digges (c.1515 – c.1559) was a well-known English mathematician and surveyor, credited with the invention of the theodolite, and a great populariser of science through his writings in English on surveying, cartography, and military engineering. His birth date is variously suggested as c.1515 or c.1520 (but certainly by 1530).

Much of his work was expanded on, annotated, and published by his son, Thomas Digges. His son followed in his footsteps and was a pivotal player in the popularisation of Copernicus’s book De revolutionibus orbium coelestium. Notes written by Thomas Digges in the publication of the book Pantometria in 1570 contain descriptions of how Leonard Digges made use of a “proportional Glass” to view distant objects and people. Some, such as astronomer and historian Colin Ronan, claim this describes a reflecting or refracting telescope built between 1540 and 1559, but its vague description and claimed performance makes it dubious.

The first publication of many by Leonard Digges was A General Prognostication published in 1553, which became a best-seller as it contained a perpetual calendar, collections of weather lore and a wealth of astronomical material, until then largely only obtainable through books published in Latin or Greek. It was revised in 1555 (the earliest surviving edition) and again in 1556 with the title A Prognostication everlasting. Subsequent editions reprint the text from 1556; editions from 1576 and later include additional material by his son.

Thomas Digges (c. 1546 – 24 August 1595) was an English mathematician and astronomer. He was the first to expound the Copernican system in English but discarded the notion of a fixed shell of immoveable stars to postulate infinitely many stars at varying distances. He was also first to postulate the “dark night sky paradox”.


An illustration of the Copernican universe from Thomas Digges’ book

He attempted to determine the parallax of the 1572 supernova observed by Tycho Brahe, and concluded it had to be beyond the orbit of the Moon. This contradicted Aristotle’s view of the universe, according to which no change could take place among the fixed stars.

He went further than Copernicus by proposing that the universe is infinite, containing infinitely many stars, and may have been the first person to do so.

SN 1572 (Tycho’s Supernova, Tycho’s Nova), or B Cassiopeiae (B Cas), was a supernova of Type Ia in the constellation Cassiopeia, one of about eight supernovae visible to the naked eye in historical records. It appeared in early November 1572 and was independently discovered by many individuals.

The remnant of the supernova has been observed optically but was first detected at radio wavelengths; it is often known as 3C 10, a radio-source designation, although increasingly as Tycho’s supernova remnant.


Remnant of SN 1572 as seen in X-ray light from the Chandra X-ray Observatory


Tycho Brahe (14 December 1546 – 24 October 1601) was a Danish nobleman, astronomer, and writer known for his accurate and comprehensive astronomical and planetary observations.


Heliocentric universe of Copernicus (Original Source N/A:

The Italian philosopher Giordano Bruno took the Copernican Principle a stage further in 1584 by suggesting that even the Solar System is not the centre of the universe, but rather a relatively insignificant star system among an infinite multitude of others.

Giordano Bruno (born Filippo Bruno, 1548 – 17 February 1600) was an Italian Dominican friar, philosopher, mathematician, poet, and cosmological theorist. He is known for his cosmological theories, which conceptually extended the then-novel Copernican model. He proposed that the stars were distant suns surrounded by their own exoplanets and raised the possibility that these planets could foster life of their own, a philosophical position known as cosmic pluralism. He also insisted that the universe is infinite and could have no celestial body at its “centre”.


Starting in 1593, Bruno was tried for heresy by the Roman Inquisition on charges of denial of several core Catholic doctrines. He was found guilty and burnt at the stake in Rome’s Campo de’ Fiori in 1600.

In 1605, Johannes Kepler made further refinements by finally abandoning the classical assumption of circular orbits in favour of elliptical orbits which could explain the strange apparent movements of the planets. Galileo’s controversial support of Copernicus’ heliocentric model in the early 17th Century was denounced by the Inquisition but nevertheless helped to popularise the idea. (below left)


Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer. (above right)

Galileo Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Galileo has been called the “father of observational astronomy”, the “father of modern physics”, the “father of the scientific method”, and the “father of modern science”.

This new idea about the universe was seen as dangerous because it threatened to equate God with the universe.

Cartesian Vortex Universe – In 1644, the French philosopher René Descartes outlined a model of the universe with many of the characteristics of Newton’s later static, infinite universe. But, according to Descartes, the vacuum of space was not empty at all, but was filled with matter that swirled around in large and small vortices (no empty space can exist therefore space must consequently be filled with matter.). His model involved a system of huge swirling whirlpools of ethereal or fine matter, producing what would later be called gravitational effects. This fine matter he believed congealed to make up the large bodies in the universe. This fine matter swirled around bodies in “vortices” causing circular motion around the Sun.


Aether vortices around celestial bodies


René Descartes (31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

If there are Suns there must be planets around them.

Initially his ideas influenced Newton, who would later condemn this view as fantasy. Newton objected to the theory because drag must lead to noticeable deviations of the orbits which were not observed. Another problem was that moons often move in different directions, against the direction of the vortex motion. Also, Huygens’ explanation of the inverse square law is circular, because this means that the aether obeys Kepler’s third law. But a theory of gravitation has to explain those laws and must not presuppose them


Henry More (1614–1687) was an English theologian and philosopher and is usually regarded as characteristic of a group of broadly like-minded thinkers, discerned by historians and designated by them as the Cambridge Platonists.

More read Descartes’s Principia philosophiae in 1646, and it had a very profound effect upon him and upon the subsequent development of his own philosophy. He attempted to use the details to establish the existence of immaterial substance.

He criticised Descartes’ vortex theory of celestial motions (which, he pointed out, ought to have given rise to celestial cylinders, rather than spheres).

Christiaan Huygens FRS (14 April 1629 – 8 July 1695) was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution.



Sir Isaac Newton PRS FRS (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a “natural philosopher”) who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), first published in 1687, laid the foundations of classical mechanics.

Newton was admitted to Trinity College, Cambridge in June 1661. At that time, the college’s teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers such as Descartes, and astronomers such as Galileo and Thomas Street, through whom he learned of Kepler’s work. He set down in his notebook a series of “Quaestiones” about mechanical philosophy as he found it. In it he questioned whether the Cartesian system was true. He also linked the world/universe to God.

In a 1675 letter to Henry Oldenburg, and later to Robert Boyle, Newton wrote the following: [Gravity is the result of] “a condensation causing a flow of ether with a corresponding thinning of the ether density associated with the increased velocity of flow.” He also asserted that such a process was consistent with all his other work and Kepler’s Laws of Motion.

Also from 1675 Newton starting linking some of his ideas with theology and alchemy

In 1679, Newton returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler’s laws of planetary motion. His reawakening interest in astronomical matters received further stimulus by the appearance of two great comets in the winter of 1680–1681 (which were also seen in 1618).

In 1681 John Flamsteed proposed that these two great comets were not separate bodies, but rather a single comet travelling first towards the Sun and then away from it. Although Isaac Newton first disagreed with Flamsteed, he later came to agree with him and theorised that comets, like planets, moved around the Sun in large, closed elliptical orbits. Flamsteed argued that this comet turned in front of the Sun due to magnetic repulsion and Newton certainly disagreed with this idea.

Newton argued that the comet’s motions could be accounted for by the same theory of gravity that applied to planetary motions. Anyway burnt magnets stop working.


Isaac Newton demonstrated his universal law of gravitation by showing that a comet visible during 1680 and 1681 followed the path of a parabola. [Adapted from Isaac Newton, 1687. Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy.”)]


John Flamsteed FRS (19 August 1646 – 31 December 1719) was an English astronomer and the first Astronomer Royal.

A great comet is a comet that becomes exceptionally bright. There is no official definition; often the term is attached to comets such as Halley’s Comet, which are bright enough to be noticed by casual observers who are not looking for them, and become well known outside the astronomical community.

Robert Hooke speculated in 1671 that gravitation is the result of all bodies emitting waves in all directions through the aether. Other bodies, which interact with these waves, move in the direction of the source of the waves. Hooke saw an analogy to the fact that small objects on a disturbed surface of water move to the centre of the disturbance.

He wrote to Newton in 1679 about his ideas on cosmology. These included the idea that celestial motions were linked to inertial motion and that there was an inverse law between distance of the object from the centre of the orbit (the central body) and the force of attraction between the object and the central body.

“supposition … that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance.” (Hooke’s inference about the velocity was actually incorrect)

Hooke, however, seemed unable to give a mathematical proof of his conjectures or perhaps unwilling to devote his time to this type of pursuit. However he claimed priority over the inverse square law and this led to a bitter dispute with Newton who, as a consequence, removed all references to Hooke from the Principia.


Posthumous portrait of Robert Hooke (Rita Greer 2004), based on descriptions by Aubrey and Waller; no contemporary depictions of Hooke are known to survive.

Robert Hooke FRS (28 July [O.S. 18 July] 1635 – 3 March 1703) was an English natural philosopher, architect and polymath.

As mentioned earlier Newton initially supported the Cartesian theory of gravity as people wanted a mechanical explanation like that for the water cycle.

Static (or Newtonian) Universe – In 1687, Sir Isaac Newton published his “Principia”, which described, among other things, a static, steady state, infinite universe which even Einstein, in the early 20th Century, took as a given (at least until events proved otherwise). In Newton’s universe, matter on the large scale is uniformly distributed, and the universe is gravitationally balanced but essentially unstable.

Newton used Kepler’s laws of planetary motion to derive his law of universal gravitation. Newton’s law of universal gravitation was the first law he developed and proposed in his book Principia. The law states that any two objects exert a gravitational force of attraction on each other. The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them. Along with Newton’s law of universal gravitation, the Principia also presented his three laws of motion. These three laws explain inertia, acceleration, action and reaction when a net force is applied to an object.


Title page of Newton’s ‘Philosophiæ Naturalis Principia Mathematica’, first edition (1687)

Discussions about the inverse-square law continued throughout the 1680s. In 1684 Edmond Halley asked Newton what law of motion gave rise to elliptical orbits.


Edmond Halley, FRS (8 November [O.S. 29 October] 1656 – 25 January 1742 [O.S. 14 January 1741]) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.

During 1684 to 1686 Newton worked on his three laws of motion:

First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

Second law: In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant.)

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

After 1687 Newton viewed comets as the source of water for planets. He wondered what was in the comet’s tail. It has been suggested that Newton thought Noah’s flood was caused by a comet.

During the 1690’s Newton corresponded with Richard Bentley, one of England’s leading theologians, about the connection between natural science and God.

In modern terms, the role that emerged was to provide initial conditions, boundary conditions, and divine interventions to account for those aspects of the Universe that could not be understood with the physics of Newton’s day. Among other questions, Bentley asked why some matter in the Universe formed the luminous Sun and other matter became the dark planets, whether the motions of the planets could arise from natural causes, whether the lower densities of the outer planets were caused by their distance from the Sun, and what produced the inclination of the Earth’s axis. The implication of these questions was that Newton’s physics could offer no complete explanation, and so Newton, who was basically theistic, agreed that these phenomena were evidence for the deity.


Richard Bentley (27 January 1662 – 14 July 1742) was an English classical scholar, critic, and theologian. He was Master of Trinity College, Cambridge.

By 1710 Newton considered the universe as infinitely large and empty, like dust on a fingertip. He made a case that objects can move through a vacuum where there is nothing to stop them. His view was that the only cause was God himself.

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