The Fantastic Life Of Tycho Brahe

The brilliant 16th century astronomer who built Uraniborg: a renaissance masterpiece and the astronomical wonder of the world

On the 14th Dec 1546 a boy was born who would grow up to be the greatest observer of the skies who had ever lived. His name was Tycho Brahe.

Tycho’s great achievement was to make observations of the stars and planets (including a supernova and several comets) that were so accurate that they ended up overthrowing previous held beliefs:

· that the Earth was the centre of the Universe

· that the planets moved around the Earth in perfect circles, embedded in perfect crystalline spheres

· that there could be no change in the skies beyond the orbit of the Moon

Tycho himself was not responsible for the Sun-centred model of the Solar System — that was due to Copernicus. But his superbly accurate observations of Mars allowed the German astronomer Kepler to deduce that the orbit of Mars around the Sun (Kepler was an enthusiastic supporter of Copernicus) was an ellipse, to a very high degree of accuracy.

He also removed the belief in crystalline spheres by showing that comets crossed the orbits of planets, and also the belief that there could be no change beyond the orbit of the Moon by his observations of a bright new star (what we now call a supernova) that appeared in 1572.

Tycho’s work significantly advanced astronomy, laying the ground work for Newton’s great theory of Universal gravity in the late 17th century.

This is the story of his amazing life.

Tycho (most scholars pronounce his name ‘Teeko’) Brahe’s family were the most senior members of the Danish nobility; they occupied positions on the Council of the Realm that effectively co-ruled Denmark with King Frederick II.

Tycho Brahe, wearing the apparel of a Dutch nobleman as he did in every portrait. Around his neck are the chains of the Danish Order of the Elephant, the highest honour in Denmark, bestowed on him by Frederick II in May 1580. Oil on canvas, 1596, artist unknown. Wikimedia Commons

But Tycho’s path was to be very different to that of a Brahe, and one which started in a most unexpected way. For when Tycho was ‘in his earliest youth’ (as Tycho would write later) he was kidnapped by his uncle Jorgen “without my parents’ knowledge … and brought me up and thereafter generously supported me during his lifetime, and always treated me as his own son”.

One would have thought that the result was a permanent family rift and the reclaiming of Tycho by his natural parents, but happily tempers cooled and Tycho was allowed to stay with Jorgen Brahe and his wife Inger Oxe.

From the ages of 12 to 15 Tycho attended Copenhagen University to study Latin and Greek, logic and rhetoric, and possibly some Hebrew. The Latin inscription of the University translates as “He looks up to the light of heaven” — there is no-one who entered the university for whom this was more appropriate than Tycho Brahe.

Already, at this early age, Tycho was developing an interest in astronomy which he taught himself. We know, for example, that he purchased Sacrobosco’s medieval text On the Spheres, and the more advanced Cosmography by Peter Apian and Trigonometry by Regiomontanus. He also bought tables compiled by Giovanni Carelli and Johannes Stadius that predicted the positions of the planets over time according to Ptolemy and Copernicus respectively, and he would compare their predictions.

After Copenhagen University, Tycho followed the tradition of the Oxe, not the Brahe, family where he would go on a Grand Tour of the universities of Europe.

So, at the age of 15, Tycho, accompanied by his 19-year-old tutor, Anders Vedel, travelled to Leipzig University in 1562 where they stayed for two years. It was here that Tycho was taught a curriculum of languages and classical culture, but secretly bought and read books on astronomy. He also bought a celestial sphere and the star maps of Albrecht Durer.

The 1515 star maps of Albrecht Durer, one of several texts that Tycho Brahe bought secretly when a student at Leipzig University to learn the principles of astronomy

A key moment was when he checked the actual position of the planets against the tables of Carelli and Stadius. He did so by lining up a planet and two stars using a taut string and estimated the position of the planet from the same two stars on his celestial globe. He soon realised that the predictions of planetary positions by Ptolemy and Copernicus were inaccurate.

In 1563 he witnessed the conjunction of Jupiter and Saturn, and again found that although the Copernican predictions were superior, their errors were still easily detectable by a 16-year-old.

Tycho realised that to improve this state of affairs he would need a substantial body of more accurate observations of the stars and planets over time than had previously been attained.

This would be his life’s work.

On 4th Jun 1565, Tycho’s foster father Jørgen Brahe was with King Frederick II when the latter was thrown from his horse on Højbro Bridge near the royal castle in Copenhagen.

Jørgen jumped into the water and saved him, but later died himself from the experience.

Thus the king felt he owed the Brahe family a debt of gratitude which would turn out to be very fortuitous for Tycho.

After a year back in Copenhagen, Tycho travelled first to Wittenberg University — which he left after five months due to a pandemic — and then subsequently to Rostock University where he matriculated on 14th Sept 1566, aged 19.

Just 8 weeks later, disaster struck.

On Dec 29th 1566 Tycho (now 20) and a fellow student and nobleman named Manderup Parsberg, were having an argument. Ostensibly about who was the best mathematician — but perhaps also because Parsberg may have been making fun of Tycho after he’d cast a horoscope of Suleiman the Magnificent predicting his death when in fact he’d died 6 weeks beforehand — the argument swiftly escalated into a duel with swords.

Tycho received an appalling wound from Parsberg’s sword which had hacked away the bridge of his nose and he was disfigured for life. From then on, he wore a flesh-coloured nosepiece kept in place with an adhesive salve.

Fortunately Tycho was not mortally wounded, and he and Parsberg overcome this episode and remained good friends for the rest of their lives.

Tycho left Rostock and travelled to several cities in Europe conversing with various people of learning on astronomy and astrology, but also developing his skills in what would be the mainstay of his life: cultivating relationships with learned individuals and the building of astronomical (though pre-telescopic) instruments of unprecedented accuracy.

In Basel he worked with Hugo Blotius on a quadrant that was 1–1.5m in radius, when normally such instruments were hand-held. In Freiberg he saw celestial models that demonstrated planetary motions according to the theories of Ptolemy and Copernicus. In Lauingen he visited and stayed with the mathematician Cyprianus Leoveticus and in Ingolstadt he met Philip Apian, son of the mathematician Paul Apian whose textbook Tycho had used to teach himself astronomy.

Tycho then stayed at Augsberg for 14 months where he built, in collaboration with Paul Hainzel, an enormous quadrant with a radius of 5.5m which had a brass scale calibrated to one minute of arc (1/60th of a degree).

The vast quadrant that Tycho and Paul Hainzel built in the grounds of Hainzel’s estate in Göggingen. It took 20 men to hang the instrument from its frame. Astronomiæ instauratæ mechanica

Tycho’s path in life was now set: he would commit himself to being an astronomer, and measure the skies with instruments of his own design, fashioned by the best artisans of the day.

From 1571 (?) Tycho spent his time at Herrevad Abbey (now in Sweden) which was owned by his maternal uncle Steen Bille. It had extensive buildings, grounds, a substantial financial income from thirteen parishes and a material one from the vast resources of grain, livestock, dairy products and honey paid annually by nearly three hundred farmers.

Tycho continued to develop his skills in the design of astronomical instruments for which the Abbey was ideal, since it had an iron works as well as iron-smiths, brass-founders and cabinet makers. With these he built a sextant to rival in size the one he had built in Augsberg, carefully experimenting with its performance and developing a table of corrections due to the position of the eye being slightly behind its fulcrum.

Tycho was not only deeply interested in astronomy (and astrology) but also spagyric alchemy, that is to say the use of alchemy for making medicinal remedies rather than turning base metals into gold (which he found vulgar and beneath his noble station — presumably he had sufficient gold of his own anyway). Tycho developed an alchemical laboratory at Herrevad Abbey, supplied with initially with equipment from Copenhagen and then from a glassworks, also the Abbey, established by Steen Bille.

Herrevad Abbey was in many ways the model for Uraniborg, the observatory and alchemical laboratory that Tycho would later build for himself in 1576.

On Nov 11th 1572, whilst at Herrevad Abbey, Tycho was astonished to look up and notice that a bright star had appeared in the constellation Cassiopeia were there was none previously — so much so that he felt compelled to his alchemical assistants whether his senses had not deceived him.

It is hard to exaggerate the impact this event, for it overturned the almost universally believed doctrine of Aristotle that held that there could be no change in the skies beyond the ‘sub-lunary sphere’ (i.e. beyond the Moon’s orbit around the Earth).

Tycho observed the star with his sextant to determine whether it showed any daily parallax, i.e. movement with respect to the background stars due to the rotation of the observer around the Earth as any object would do. Night after night he observed it, yet despite being the most accurate observer of his day, Tycho could not detect any parallax. It must be a true star.

We now know that it was an exploding star, called a supernova, but of course no-one in the 16th century knew that (nor would they until the 20th century). Bright naked eye supernovae are extremely rare: about 10 or so have appeared in the last 2000 years and although Kepler’s supernova appeared just 34 years later in 1604, there have been none since (supernova 1987A was temporarily visible to the naked eye, but it occurred in a neighbouring galaxy and was much dimmer than Tycho and Kepler’s supernovae).

Tycho wrote and published a book on the new star called de Stella Nova, and it made him famous. It contained Latin poems by Vedel and Professor Pratensis, as well as astrological predictions of great political and religious change. In it he expressed his belief that we were placed in the centre of the universe to study the work and wisdom of its Creator. He presented his evidence that the new star was in the eighth sphere amongst the fixed stars and not in the sub-lunary sphere or those of the planets. As a result of the new star’s appearance he made astrological predictions of great political and religious change, as well as periods of abundance, peace, war, pestilence, sorrow and death.

Page from Tycho’s Brahe’s 1573 publication De Stella Nova, with the position of the new star (I) that appeared in 1572 amongst the stars of the constellation Cassiopeia. Tycho observed the star with his sextant for night after night for months, repeatedly checking whether it moved with respect to the other bright nearby stars. If it was nearer than the Moon then as the Earth (and therefore Tycho’s position) rotated around the Earth’s centre during the night, then the star would appear to move with respect to the background stars. Since he could detect no such motion he correctly concluded that it must be farther away than the Moon. This contradicted Aristotle who’d asserted that there could be no change in the heavens beyond the orbit of the Moon. De nova stella.

At the end Tycho wrote an ‘Elegy to Urania’ which he wrote in the style of Ovid and where he described himself wandering through beautiful countryside where his Uncle Steen had dismissed barbarism and introduced fine Venician crystalline glass and also paper.

Most significantly for science, however, was Tycho’s realisation that multiple observations and data reduction techniques were essential for astronomy to progress, something that we take for granted but at the time were unprecedented.

After a period of travel in Germany where he sought out craftsmen for King Frederick II’s Kronberg castle project and met astronomical and other learned friends, Tycho presented himself to the King at Sorø Abbey, recommending the sculptor Schardt and the fountain builder Labenwolf. He also came with news from the courts of Regensburg, Kassel and Venice.

The King was pleased and offered Tycho the command of a variety of castles. But Tycho hesitated; the courtly life was not for him and would leave little time for his passions. Subsequently on 11th Feb 1576 he was again summoned to King Frederick’s court. The King said that he had been informed by Steen Bille that Tycho planned to live in Germany. He said he would much rather Tycho lived in Denmark, and went on to offer him the island of Hven (now Ven) in the Sound where ‘it would be very suited to your experiments in astronomy and distillation, because it his high and has an isolated location … if you want to live on the island, I will gladly grant it to you’.

The island of Ven in The Sound between Denmark and Sweden, the gift from King Frederick II on which Tycho would build Uraniborg. Credit: Bjørn Christian Tørrissen

Tycho was stunned; this was his heart’s desire — an isolated place where he could build his temple to Urania and live as a natural philosopher measuring the skies and experimenting with alchemy in peace. After consulting friends and family, he accepted the King’s offer, which included not only the island but an annual pension and a lump sum to build a residence.

On 23rd May 1576 the island was his.

Never one to hesitate once he had decided on a course of action, Tycho was standing on the island of Ven 4 days later. In the following months and years he conceived of and built an elaborate Renaissance villa which under his direction became the first research institute and the model for future ones.

Far more than merely an observatory, the building and its gardens was a synthesis of Tycho’s obsessions: astronomy, astrology, alchemy, poetry, architecture, allusions to the ancient world, instrument making and printing. It was a temple to Urania, the muse of astronomy, and a reflection of Tycho’s view of himself as the successor to Hipparchus, Ptolemy and Copernicus.

On passing through the gatehouse the visitor would have walked between an avenue fruit and nut trees and then though the botanical gardens containing a wide variety of herbs, a recreation of the Garden Of Eden.

The house would then appear with its elaborate tripartite Venician gable, domes with their statues representing the four seasons, and central cupola on top of which was a gleaming golden statue of Pegasus.

Uraniborg, as imagined in a 19th century painting by Constantin Hansen, based upon Tycho’s own diagrams in his Orthographia Praecipuae Domus Arcis Uraniburgi. The windows at ground level are those of the cellars which contained the alchemical laboratories. The ground floor window to the left of the main door belongs to the Winter room. The circular tower to the right contains the kitchens, above and to the side of which are two circular towers which house astronomical instruments. Their conical towers are removable to expose the night sky. The same arrangement of circular and astronomical towers is found on the other side of the building, with the first floor circular tower housing Tycho’s museum with its 3000 books and rare manuscripts, great brass globe and Copernicus’ precious triquetrum

On entering Uraniborg, the visitor could take steps down and into the cellars where 16 alchemical furnaces burned. These were below the round tower to the south of the main square building. Ascending the steps of this tower led to the Museum, a circular library which contained over 3000 books and precious rare manuscripts as well as Tycho’s Great Brass Globe, a nearly perfect sphere 1.3 m in diameter and etched with the positions of 777 stars (made up to a round 1000 shortly before he left Uraniborg). The library also contained the precious triquetrum of Copernicus, a gift from the dean of Frombork Cathedral, automata and clocks, portraits of mathematicians, astronomers and philosophers.

Walking back into the main building one could see the room containing the Mural Quadrant and also the Winter Room, the main hub of activity where Tycho and his familia ate their meals, discussed projects, were entertained with dance, music and by Jeppe, Tycho’s dwarf jester. This was also the room where Tycho and his wife slept and where they conceived no less than 6 children (though presumably not during supper). In the centre of this floor at the crossroads of its corridors sat an elaborate fountain whose maker (Georg Labenworf) also create an hydraulic system that carried running water throughout the building.

On the floor above was the Summer banqueting room where special guests (including Queen Sophie of Denmark and King James VI of Scotland — later James I of England and Ireland) were entertained and the red, blue and yellow rooms where they slept. From there one could walk around and into the towers to the north and south where Tycho’s fabulous astronomical instruments were kept. Aviaries of birds could also be seen and heard nearby.

The Uraniborg site as it would have appeared in 1591, with the previously straight ramparts remodelled to incorporate the 4 semicircles that each enclosed a pavilion within an orchard of three hundred fruit and nut trees. The four corners of the ramparts are aligned with the four cardinal points, with North to the right. The north building was the servants lodgings and the south building the printing office, each a mini version of the central building. The main entrance is the eastern gatehouse at the bottom of the diagram. The botanical gardens inside of the orchard consisted of parterres of medicinal, herbal and floral plans and were probably designed by Tycho’s sister Sophie. Astronomiæ instauratæ mechanica

Tycho surrounded himself at Uraniborg with what he referred to as his familia: nearly 100 friends, academics, artisans and artists who came to live and work at Uraniborg and with whom he discussed ideas for research projects, observed the skies, made medicinal recipes in the alchemical laboratories, designed and built instruments, fountains, statues, painted murals and the buildings and gardens of Uraniborg itself.

He designed, built and housed at Uraniborg the most sophisticated astronomical instruments that had ever been made. They are too numerous to all be discussed here (though fortunately they are described by Tycho himself in his Astronomiæ instauratæ mechanica) so I have selected three that are illustrated and briefly described in the figures below.

The instrument for which Tycho is perhaps best known: The Mural Quadrant. This instrument was fixed to the west wall of the SW room adjacent to the Winter Room. Made in 1582 it consisted of a solid brass arc, 194cm in radius. Around the quadrant were painted views representing the alchemical laboratories, museum and observatory of Uraniborg itself in harmony with its surroundings. Tycho was particularly pleased with the rendering of himself as he points to the aperture through which the observer measures the heavens. Note the contrast between the sleeping dog and the industry of Tycho’s helpers. Astronomiæ instauratæ mechanica
Tycho’s Great Celestial Globe, covered with seamless brass plates and engraved with the positions of 777 stars as determined by his observations (made up to a round 1000 just before Tycho left Uraniborg), as well as the equatorial and ecliptic, was the pride of Uraniborg’s ‘Museum’, along with Tycho’s library of over 3000 books, precious manuscripts, automata and painted portraits. Astronomiæ instauratæ mechanica
Tycho’s Triangular Sexant mounted on a ball-and-socket of Tycho invention, which he installed in Stjerneborg. Left: From the Astronomiæ instauratæ Mechanica. Right: Modern reproduction at Benatky Castle outside Prague (Photo: Gudrun Wolfschmidt)

Around 1583 Tycho realised that he needed more space and to secure his instruments to the ground so that they would be stable enough to achieve the sub-arc minute accuracy that he desired. And so he built an underground observatory called Stjerneborg, or ‘Star Castle’, 80m to the south of the Uraniborg site which consisted of series of circular crypts in which he installed new and substantial instruments.

Stjerneborg, the underground observatory that Tycho built just outside Uraniborg and where he could fix his largest instruments to the ground, protect them from the elements, and so achieve greater stability. The entrance is through the portal to the left in front of the grass covered mound topped with a statue of Mercury. This was the roof of the warming room with its inscriptions and paintings, that the visitor entered first. From the warming room were entries to five circular crypts that contained the great equatorial armillary, the large azimuth quadrant, the zodiacal armillary, the largest azimuth quadrant of steel and the trigonal sextant on a ball-and-socket mounting. Astronomiæ instauratæ mechanica

One entered Stjerneborg via its ionic portal with its three lions and arms of Brahe and Bille. Descending its steps, one walked past inscriptions in Latin and portraits of famous astronomers including Tycho himself who pointed to his model of the Solar System on the ceiling and saying Quid si sic? (“Is This it?”).

From the main square room, one could enter the various hemispherical crypts containing its astronomical instruments: the great equatorial armillary, large azimuth quadrant, zodiacal armillary, largest azimuth quadrant of steel and the trigonal sextant.

Tycho published books of his astronomical findings, theories and details of his instruments using the Uraniborg’s printing press in his Astronomiæ instauratæ mechanica in 1598, and which made his name as the greatest observer of his day.

Frederick II died in 1588, and his son and successor, Christian IV, although much taken with a visit to Uraniborg when he was 15 in 1592, began to question the enormous sums that the crown was paying to Tycho.

The following year Christian IV had paid a visit to the Chapel of the Three Holy Kings at Roskilde Cathedral that held the tomb of his father, which Tycho, as part of his obligations to the crown had agreed to maintain, but had failed to do so, leaving the chapel in a very poor state of repair. He sent a courier to Uraniborg demanding to know immediately when the repairs would be made, which Tycho, very unwisely, ignored. This, combined, with Christian’s determination to stamp his authority on over-mighty aristocrats meant that the crown’s financial support for Tycho and Uraniborg was removed.

Tycho left Uraniborg on 11th Apr 1597. After spending short periods in Copenhagen, Rostock and Hamburg he obtained a commendation from Duke Ernest of Bavaria to the Holy Roman Emperor Rudolph II in Prague. In 1599 the Emperor became Tycho’s enthusiastic patron and made him his Imperial Mathematicus.

Meanwhile Tycho invited Johannes Kepler to work with him at his residence at Benatky Castle, 43 km from Prague, where Tycho had created an observatory and alchemical library. Tycho wanted Kepler for his mathematical skills and assigned him the problem of the orbit of Mars based upon Tycho’s meticulous observations of the planet. It was from these observations that Kepler was able to deduce his 3 laws of planetary motion, published in his Astronomia Nova in 1609 (1st and 2nd Laws) and Harmonices Mundi in 1619 (3rd law).

Johannes Kepler (1571–1630). Tycho recognised Kepler’s genius from his publications and their correspondence, and asked him to make sense of his observations of Mars. In one of the most famous collaborations in science, Kepler used Tycho’s Mars data to determine his 3 laws of planetary motion. Kepler would also go on to publish tables of the positions of the planets based on Tycho’s data, named by Tycho the Rudophine Tables after Rudolph II, The Holy Roman Emperor, in 1627. Wikimedia Commons.

In June 1600 Tycho was summoned to Prague by Rudolph II and moved into a palace on the Loreta Plaza where he started a new observatory: The New Imperial Uraniborg. Tycho and Kepler have an audience with Rudolph II who commissioned them to compile a new set of planetary tables, The Rudolphine Tables, based upon Tycho’s observations.

On Oct 13th 1601 Tycho and Baron Ehrenfried von Mickwitz attended a feast at the palace of Peter Vok von Rosenberg, during which Tycho consumed vast quantities of food and drink. Etiquette prevented him from being excused and when he returned home, found he could not urinate and was in intense pain. This continued for 5 days and nights. Delirium set in with Tycho softly repeating the phrase “Let me not have lived in vain”.

The delirium then passed, and he urged Kepler to complete new planetary tables (the Rudolphine tables) using Tycho’s observations and based on his model (Earth centred, with the other planets orbiting the Sun) of the solar system and not the Copernican (Sun-centered) one.

Around 9pm on Oct 24th 1601 Tycho died in the arms of Count Erik Brahe and in the presence of Kepler who later said: “I saw the greatest of all men expire”.

Tycho Brahe life’s work was the ‘restoration’ of astronomy: to observe the stars and planets with the highest possible precision that was humanly possible, so that we might understand the universe and its workings better.

There is no question that he achieved his goal.

Rawlins (1993) states that ‘Tycho Brahe’s … “Thousand Star Catalog” published in 1598 … was one of history’s outstanding attempts at mass-perfectionism … it is of far greater magnificence than is now generally realised. In it Tycho realised, on a mass scale, a precision far greater than earlier catalogues. It represents an unprecedented confluence of skills: instrumental, observational and computational, all of which combined to enable Tycho to place most of the hundreds of recorded stars to an accuracy of 1 arcmin” (1/60th of a degree).

All this has sometimes created the impression that Tycho was ‘merely’ an observer (as if somehow observations are less significant than theories — except that theories are nothing without observations).

But he also thought deeply about how the universe worked. He had his own theory of the Solar System and of the motions of the Moon. And he made several important discoveries. From his observations of the new star of 1572 and several comets he demolished the Aristotelian views that there could be no change in the heavens farther than the Moon and that the planets were carried along in their orbits by perfect crystalline spheres. He was the first to realise that the tail of a comet always points away from the Sun, and that the direction of the Moon’s axis changes over time (nutation).

Tycho made enormous strides in scientific instrumentation. He carefully specified each of his instruments, employing many new innovations of his own as he did so, such as the traversal dots to sub-divide angular spacings and parallel sightings instead of pin-holes to minimise errors. He separated his observers into different teams using different instruments so as to compare their results, constantly making refinements to improve results. The enormous size of several of his instruments sometimes produced problems of their own such as being cumbersome to handle or being vulnerable to the wind, so he worked to overcome these by modifying their design and by building an underground observatory to house them. He was inventor of the sextant.

He was the first person to understand the importance of taking multiple measurements of the same object, the first to understand the role of measurement error, and invented techniques to reduce his data that are still used today. These are so fundamental to modern science that we take them for granted. Yet before Tycho they were unheard of.

Perhaps most impressive was Tycho’s enormous capacity for bringing to bear the diverse talents of so many people to the realisation of his life’s work, and over such a long period (1574–1601). This is in striking contrast to, say, Copernicus, Galileo and Kepler whose achievements involved, at most, a few other people. In so doing, Tycho created the world’s first research institute: Uraniborg, and the model for ’Big Science’ which he effectively invented.

Tycho was fond of writing inscriptions which were dotted all over Uraniborg. Perhaps this one is the most appropriate with which to end:

Neither wealth nor power, but only knowledge, alone, endures.

Brahe, T. (1598) Astronomiæ instauratæ mechanica, Wansbeck

Brahe, T. (1573) De nova stella

Christianson, J. R. (2002) On Tycho’s Island, Cambridge University Press

Christianson, J. R. (2020) Renaissance Lives: Tycho Brahe and the Measure of the Heavens, Reaktion Books, London

Dreyer, J. L. E. (1890) Tycho Brahe, A Picture of Scientific Life and Work in the Sixteenth Century

Rawlins, D. (1993) Tycho’s Star Catalog, DIO 3

Thoren, V. & Christianson, J.R. (1990) The Lord Of Uraniborg, Cambridge University Press

Wesley, W. G. (1978) The Accuracy of Tycho Brahe’s Instruments, Journal for the History of Astronomy, Vol. 9, p42

Architect for the Lunar Pathfinder mission at SSTL. Masters in Radio Astronomy (Jodrell Bank, UK) and Natural Sciences with Physics and Astronomy (OU, UK).

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