History of astronomy

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Astronomy is the branch of physics that studies celestial bodies and the universe as a whole.

From this perspective, the study of celestial bodies can be reasonably said to have begun when at some point humanity looked up and began to observe the moon and the stars and the planets regardless of how they may have thought of them.

These ancient beginnings are often indicated by structures studied by archeologist.[1] Stonehenge, constructed sometime between 3100 to 2000 BC may have constituted an astronomical site, possibly an observatory or the structure may have been designed upon observations previously made. Either way, it seems clear that Stonehenge was meant to take advantage of astronomical phenomena since the "heelstone" in the circle of stones is aligned with the rising Sun on Midsummer's Day (June 21, the Summer Solstice). This represents a true astronomical alignment. Many other Megalithic sites also demonstrate such alignments.[2]

The Megalithic Passage Tomb at Newgrange, built about 3200 B.C. also demonstrates knowledge of astronomical phenomena. The passage and single chamber of the tomb are illuminated by a shaft of sunlight that shines through the roof box over the entrance and penetrates the passage, lighting up the chamber at winter solstice sunrise. This happens at dawn from the 19th to the 23rd of December for 17 minutes.[3]

Earlier evidence of astronomical observations can be found in Vedic India in the Rg Veda which contains a verse observing the winter solstice in the constellation Aries. This would have placed it at around 6500 BC. The Myth of Janus, a four headed god of of the Vedic people of India, presents the possibility of astronomical observations around 4,000 BC. Each head of Janus represented a phase of the moon which in turn represented one of the four seasons: one full moon represented the spring equinox, one full moon represented the autumn equinox, the waning moon the winter solstice and a waxing moon representing the summer solstice.This dating is disputed but it does indicate a very early study of both the constellations and the moon.[4]

Halley's Comet (considered a guest star) was noted by Chinese astronomers as early as 240 BC and perhaps as early as 1059 BC.[2]

Branches and subdisciplines

Celestial mechanics

Celestial mechanics, a subfield of astronomy, began with the application of Newton's theory of mechanics and gravitation (as elucidated in the Principia) to the movement of planets. Eventually Einstein's theory of general relativity and modern computing technology overtook the field of classic physics.[5][6]

Cosmology

Cosmology is defined as the science of the universe,[7] the branch of astronomy which studies the origin, evolution, and structure of the universe,[8] the study of "the contents, structure, and evolution of the universe from the beginning of time to the future",[9] a branch of astronomy that studies the "origin, large-scale properties, and the evolution of the observable universe."[10].

Astronomy underwent significant changes in the period following 1970 when a union of particle physics ("the study of the unbelievably small" ) and astronomy ("the study of the incomprehensibly large") had begun to take place. This has had a significant impact on cosmology. The scope of cosmology arguably begins approximately 10-42 seconds following the origin of the universe when the universe was smaller than a proton.[7]

Planetology

Also referred to as planetary science, this branch of astronomy is involved with the study of other planets, including meteorology, geology, location, orbits, origins. Given the fact that the earth is our primary source of information about other planets, there is a great deal of comparative study of earth and other planets. The primary focus has been on the planets of this solar system but as new planets are discovered, there is a growing amount of data on planets in orbit around other stars.[11]

Radio Astronomy

Astronomy in ancient China

Astronomy in ancient Mesopotamia

Astronomy in ancient India

Astronomy in ancient Greece

Any assertion as to where astronomy began faces the problem of providing dated evidence that supports a reasonable conclusion. With astronomy, there are a great many pieces of evidence in the form of ancient documents and archaeological finds that make such a claim for any place or time difficult to sustain. In other words, it is not really possible to state exactly where astronomy in its earliest forms began. However, it is possible to trace the roots of the study of the skies and the objects visible to the unaided eye with some degree of certainly even if only to establish a theory of its beginnings and where the influences of these early impressions and thoughts eventually spread. For the western world, that is Europe and the European influenced Americas, and the ancient civilisations of North Africa and the Middle East, some of those roots can be traced to the earliest Greek philosophers.[7]

Thales of Miletus (624 B.C. – 547 B.C.)

Thales, either a Milesian or a Phonecian, was an early philosopher, mathematician and engineer. None of his work remains and in fact it may have disappeared by the time of Aristotle. Other sources indicate that he developed a method of navigating by using the constellation Ursa Minor. He is also reputed to have correctly surmised the approximate time of a solar eclipse though there is no evidence that he developed the ability to predict them accurately. At the time of Thales, lunar eclipses were already known and were being predicted. Thales reportedly brought geometry to Greece from Egypt and contributed to the field as well. [12]

Pythagoras of Samos (~580-500 BC)

Aristotle (384 - 322 B.C.)

Aristotle was not alone in the development of the Hellenic foundation of humanity's perspective on the celestial but his name is the most prominent of the early Greeks. He used direct observation and deduction to propose the spherical Earth. He noted that

  • Ships disappear or appear on the horizon as they move away or toward the observer;
  • The shape of the Earth's shadow on the moon is circular;
  • Different stars are visible in the northern and the southern latitudes;
  • Since elephants are found both in India (to the east) and Morocco (to the west), both are a reasonable distance on a moderately sized sphere.

Aristotle rejected the idea that the Earth orbited the Sun, apparently because there was no detectable parallax, which was not, in fact, proved until 1838 by Bessel.[13]

Aristotle's perspective of the cosmos was derived from what he thought things should be, it was an aesthetic view of the cosmos rather than a scientifically derived view. For Aristotle, the Prime Mover set the universe in motion both perfect (in Aristotle’s point of view) and eternal. There was no such thing as vacuum, no emptiness. All the nearby objects, the Sun, the Moon and the planets as well as the far distant were set in eight crystalline spheres that revolved around the Earth. For Aristotle there were the four basic elements we have on Earth, fire, and water, earth and air. In the heavens there was a fifth from which the crystalline spheres were composed, aether--a perfect substance that could neither be changed nor destroyed.[7]

Things moved about Earth, they moved in perfect circles, they were embedded in a perfect substance, they would never stop in their perfect movement--and all of this was based on Aristotle’s vision of perfection.

Aristotle’s view was later incorporated by Ptolemy in Alexandria, North Africa, who made some changes in the Aristotelian perspective to account for anomalies he had observed--the planets occasionally moved in reverse. (Unlike Aristotle, Ptolemy actually observed the phenomena he studied. While he was not the first, this approach to the study of physical phenomena was not required nor evidently even expected of those who made claims about the world.) Ptolemy's work and his writings carried Aristotle’s views forward into the 16th century when Copernicus's work on the calendar led him to make his own changes--in this case a paradigm shift. Copernicus, like Aristotle and unlike Ptolemy, did not make his own observations. However, he did incorporate the work of others and he added his contribution by placing the Sun at the centre of the universe. This heliocentric model of the universe which clearly implied that the Earth itself moved and was not the centre of the universe, was to have a major impact on the study of the celestial, marking the beginning of the end of Aristotelian influence, and the politics of the day.[7][14]

Aristarchus of Samos (approximately 310 B.C. to 230 B.C.)

Aristarchus was a Greek mathematician and astronomer. He is credited as the first in history to propose a Sun-centred universe and for being one of the first to attempt to determine the sizes and distances of the Sun and Moon. Aristarchus and his theory of a heliocentric cosmos is referred to by Plutarch in his work De facie in orbe lunae.[15] Evidently, its contradiction of Aristotle’s perception of the cosmos was ill received. Archimedes credited Artistarchus with the heliocentric model as well as a much larger universe.[16] Aristarchus is credited by Copernicus as the originator of the heliocentric model as well. His work was also to influence Hipparchus and Ptolemy.

Aristarchus made six hypotheses in his work to determine the size of the moon and the sun and their relative distances. He proposed that

  • The Moon receives its light from the Sun, in other words, the moon reflects and does not generate its own light;
  • The Earth is the centre of a sphere in which the Moon orbits or rotates;
  • The phases of the Moon which change as the Moon rotates around the Earth show a darkened circle in our line of sight—we are looking directly at the Moon in the absence of reflected light;
  • Based on Aristarchus' observations, when half the Moon is darkened and appears to be halved, its angular distance from the sun is less 1/30 of a quadrant [17] which means its angular distance is less than 3 degrees, and is therefore equal to 87 degrees;
  • The Width of the Earth’s shadow on the moon is equivalent to twice that of the Moon’s;
  • The moon subtends[18] one fifteenth part of a sign of the Zodiac[19] for an angular diameter of 2 degrees.

He believed that he proved a number of propositions. Some of his most notable were:

  • The distance from the Earth to Sun is eighteen to twenty times that of the distance between the Earth and the Moon. The average distance between the Sun and the Earth is 150 million kilometres and that of the Earth and the Moon is 384,400 kilometres. Either he thought the Moon was much further away or the Sun was closer, but he was off by a significant amount.[20]
  • The diameters of the Sun and Moon have the same ratios as their relative distances between 1:18 and 1:20. Again he was off by a considerable amount. The Sun is about 109 times the diameter of the Earth. The Moon has a diameter of 3,476 kilometres (2,159 miles) or a quarter that of the Earth’s diameter.
  • He also proposed that the relative ratios of the diameters of the Sun and the Earth was between 19:3 and 43:6. It is in fact 109:1.

As inaccurate as they were, these attempts were based on real observations and an attempt to apply the mathematical tools of the period. As such, Artistarchus was a positive step forward in the attempt at a rational explanation of the universe. His work was influential for approximately 2,000 years. [21][22][23][24]

Eratosthenes of Cyrene (276 - 195 B.C.)

Eratosthenes employed observations of the Sun’s shadow and geometry to estimate the circumference of the Earth. By measuring the altitude of the noontime sun at its maximum at Alexandria, North Africa, on Jun 21st and comparing it with the Sun's altitude at the same time at Syene, in southern Egypt,[25] he determined the angle from the zenith to the point where the Sun was at noon. At Syene, the zenith distance was 0 degrees (directly overhead); at Alexandria it was about 7 degrees. Since Eratosthenes knew how far it was between the two cities, he was able to calculate geometrically the difference in zenith angle and thereby the estimated size of the Earth. Eratosthenes also measured the tilt of the Earth axis by 23.5 degrees. It is the tilt of the Earth’s axis that endows the Earth with seasons.[26]

Aglaonike (c. 200 B.C.)

Also known as Aganice of Thessaly and the daughter of Hegetor of Thessaly, she is mentioned as a sorceress in the writings of Plutarch and Apollonius of Rhodes. Possibly the first recorded woman astronomer, she was apparently familiar with the the metonic cycle (periods of the full moon and the cycles of eclipses) because she reportedly developed the ability to predict lunar eclipses. She lived sometime around the early 2nd century B.C., but exact dates are unknown. [27][28][29]

Hipparchus of Nicea (190-120 B.C.)

Hipparchus, an astronomer born in Bithynia, lived on the island of Rhodes where he did most of the work known to us. Rhodes, near the coast of Anatolia, was by that time famous for its schools in philosophy and art. Very little of Hipparchus's work actually survives. Most of what is known about Hipparchus is through other works. Hipparchus’ only remaining work is a commentary written in the third century B.C., the Commentary on the Phainomena of Eudoxus and Aratus.[30] Ptolemy’s work, the Almagest, is the largest source of information on Hipparchus. Ptolemy credits Hipparchus as his most important predecessor.

Hipparchus is possibly the first person in history to use numerical data from observations to construct geometric models to explain astronomical motions. He is credited with discovering the precession of the equinoxes and his work in mathematics was significant. Besides his work in geometry, he is considered the founder of trigonometry.

Hipparchus took a practical approach to his work rather than rely on Aristotelian type models constructed through what he thought things should be. Hipparchus made recorded observations over a period from 147 to 127 BC. He then drew upon earlier works including Apollonius's deferent-epicycle and eccentric, as well as his own to construct the geometric models.

Hipparchus developed or invented some of his instruments used in his observations and models. Ptolemy described an instrument Hipparchus developed called a dioptra and one he may have invented, the planispheric astrolabe, used to tell the time at night from stellar observations.[31][32] John Philoponus (sixth century AD) provided the earliest surviving description of the planispheric astrolabe, a considerable time after Hipparchus. However, the underlying mathematical theory for the stereographic projection used in the astrolabe is found in Ptolemy’s work, the Planispherium.[33]

Hipparchus attempted to determine the distance between the Moon and the Earth by comparing concurrently a solar eclipse as viewed from two positions, a total eclipse in Syene and the other, a partial eclipse in Alexandria. While an observer at Syene observed the total eclipse of the Sun blocked by the Moon, an observer at Alexandria observed that 1/5th of the Sun's disk was visible.[34] This meant that the angular size of the visible Sun observed from Alexandria is 1/10th of a degree (0.1 degree). Expressing this angle in radians and applying the small angle approximation gave the ratio of the Syene-Alexandria distance to the Earth-Moon distance.[35]

Hipparchus also calculated the precession[36] of Earth’s rotational axis. Currently, the North Celestial Pole is closely aligned with the Polaris. At the time of Hipparchus it was not as closely aligned. Five thousand years ago when the pyramids of Egypt were being constructed, it was more closely aligned with the star Thuban in the constellation Draco. In another twelve thousand years it will be more closely aligned with the star Vega in the constellation Lyra. In other words, as the Earth slowly shifts like a spinning gyroscope, the North Star will change as the direction of the Earth’s axis shifts or precesses. The complete cycle or precession back to today’s current alignment with Polaris takes 26,000 years.

Hipparchus also used Babylonian methods and observations in his work. The influence of Babylonian astronomy on Greek is not clear but Hipparchus work does provide a clear historical link between the two cultures. [37][38][39]

Astronomy in ancient Persia

Astronomy in ancient Egypt

Astronomy in Medieval Mesopotamia and the Middle East

Astronomy of the Mayan civilisation

Astronomy of the Aztec civilisation

Astronomy of the Incan civilisation

Claudius Ptolemy (~85-165 AD)

Omar Khayyam (1048-1131)

Nikolas Kopernig (Copernicus, 1473-1543)

Leonard Digges (1520-1559)

Leonard Digges was a writer of mathematics and science in English, one of the first people to popularise work in either field. He was also a surveyor who invented the theodolite, the telescope, the reflecting telescope and possibly the refractive telescope. He published a number of works during his lifetime but his achievements were expanded and revised by his son Thomas and published after Leonard's death, some of the work for the first time.[7][40][41][42]

Thomas Digges (1543-1595)

Thomas Digges's contribution to astronomy is notable for two things: his ability to write for the layman and thereby inform the public of some of the great advances in science; his comprehension of Copernicus's cosmological model that led him to postulate a much larger cosmos than previously perceived.

Digges work, the Perfit Description of the Celestiall Orbes printed in 1576, elaborated, in English, the most important ideas of Book 1 of Copernicus’s De Revolutionibus which had been printed just thirty-three years before in 1543. Digges's historical significance was not widely known until his book, the Perfit Description was reprinted in the 1930's. Since then, Digges has been identified as the first public advocate of Copernicanism in England.

Digges's father Leonard was also an author and had published science and mathematics in English, which was a little unusual at the time. The result being that his works became popular and set the stage, arguably for others to continue to write for the general public. Thomas Digges's family was heavily penalised when his father was sentenced to death for his part in the rebellion of Sir Thomas Wyatt, and then having had his sentence commuted was stripped of all assets and holdings. After his father's death in in 1559, Thomas was raised and educated by philosopher and mathematician John Dee, his guardian and the astrologer to Queen Elizabeth I. Dee had a substantial library and evidently supported Copernicus' view of cosmology although he published nothing on the subject. These resources and perspectives were not lost on Thomas and he read extensively and cooperated with Dee on some work.

In 1571, Thomas published Leonard Digges's book on the telescope, Pantometria, twelve years after his father's death. Panometria was the first publications to discuss the invention of the telescope in English. Thomas had extended, revised and enhanced the book and he wrote the preface.[43] Thomas continued his studies and his research and in 1576 he then published a revised edition of his father's book Prognostication Everlasting. Thomas's revision included the first ever discussion in English of Copernicus's model of the universe. He also asserted that the universe is infinite and he included a diagramme showing a heliocentric universe with the stars stretching into infinity. Apparently this was a leap of imagination fed by the potential capacity of the cosmos provided by his telescopic observations of the Milky Way as well as influence from others. He did not state specifically what led him to this position but he is apparently the first to postulate an infinite universe.

Thomas’s publication, Alae seu scalae mathematicae, in 1573, was a Latin text prompted by the new star of 1572, a supernova.[44] Thomas's observations were employed by Tycho Brahe in his work. The supernova created quite a stir worldwide and certainly in Europe. There was a tremendous increase in astronomical and astrological work and publications. Tycho Brahe's supernova was significant because it encouraged astronomers in the 16th-century to question their perception that the heavans were immutable, that is, unchanging. Thomas's contribution was to determined the nova's postion and his conclusion that its appearance was a challanege to traditional cosmology of the day.

[7][40][45][46][47]

Galileo Galilei (1564-1642)

Johannes Kepler (1571-1630)

Tycho Brahe (1546-1601)

Isaac Newton (1642-1727)

Charles Messier (1730-1817)

Jacobus Kapteyn (1851-1922)

William Herschel

W. H.Pickering and Annie J. Cannon

Albert Einstein

Fred Hoyle (1915-2001)

Edwin Hubble

Georges-Henri Lemaitre

Hans Bethe

George Gamov

Arno Penzias and Robert Wilson

Jocelyn Bell (Burnell) and Anthony Hewish

Conceptual Breakthroughs

The Infinite Universe

The break through in humanity's concept of the size of the universe came in small steps. Copernicus's cosmology provided the rational support for a universe of much greater size.

Thomas Digges (1543-1595)

In 1576, English author and astronomer Thomas Digges proposed the idea of a vast, even infinite, universe. His description, "the orb of stars fixed infinitely up . . . . perpetually shining glorious lights innumerable far excelling our sun both in quantity and quality."Digges spent considerable time with the telescope, had read Copernicus's De Revolutionibus, and was one of the few people who understood at the time the implications of Copernicus's cosmology. [7][40]

Giordano Bruno

A similar proposal was made by a contemporary, Italian monk Giordano Bruno, who asserted that, "there are innumerable suns, and an infinite number of earths revolve around those suns."[7]

Johann Kepler

Johann Kepler is apparently the first to write about the puzzle of the dark night sky. If the number of stars is infinite, and they are uniformly distributed, why is the night sky dark? If they are infinite in number and distributed evenly the night sky should glow brilliantly and possibly create a devastating heat. Kepler concluded that the universe was finite.[7]

Issac Newton

Issac Newton, working from Galileo's data and Kepler's work, provided insight into how Copernicus's cosmology was supported by the laws of motion and his concept of gravity provided a means to determine and predict celestial mechanics. However, Newton's work presented a paradox, If gravity prevailed, then why did the entire universe not fall in on itself? Newton's answer to this was that the stars were uniformly distributed across an infinite space and their mutual gravity kept them suspended as they were. He was not able to explain how these stable stars being pulled upon equally from all directions would maintain the eternal status quo if a star were to deviate from its position and thereby lead to a cascade of stars falling in toward each other. Nor was he able to explain why the night sky was dark.[7]

Heinrich W. M. Olbers

In the early 19th century, nocturnal darkness led Hienrich Olbers proposed that interstellar light was obstructed by clouds of interstellar matter. He may be the first to hypothesis the existence of such phenomena were ever proven.. The question of the nocturnal darkness remained however since Olber was unable to explain how in a infinite universe the clouds themselves had not been heated by the star light and were glowing. This is Olber's Paradox.

  • If the universe is static and infinite and uniform;
  • The every line of sight from Earth must end at a star;
  • And every line of sight would show a point of light and thus the sky would be brilliantly lit and the heat from the stars would be overwhelming.[7]

Edgar Allen Poe

Later, in the 18th century, writer Edgar Allen Poe attempted to resolve Olber's paradox. He proposed that "[The] distance of the invisible background [is] so immense that no ray from it has yet been able to reach us at all." This meant that the age of the universe was finite, it had a beginning and was not eternal.[7]


References

  1. Archeoastronomy is the study of ancient and prehistoric astronomy; methods and interpretations.
  2. 2.0 2.1 A Brief History of Astronomy Gene Smith, University of California, San Diego Center for Astrophysics & Space Sciences
  3. Newgrange Megalithic Passage Tomb
  4. Astronomy of Vedic India Eirik L. Harris, Pamona College
  5. Introduction and Mathematics ReviewCollins, George (1989) The Foundations of Celestial Mechanics
  6. Celestial Mechanics James B. Calvert, Associate Professor Emeritus of Engineering, University of Denver (2003). Mechanics and Thermodynamics
  7. 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 7.11 7.12 Smoot, George, Davidson, Keay (1993). Wrinkles in time: The imprint of creation. London: Abacus Books
  8. Glossary George Mason University
  9. Glossary Contemporary Physics Education Project
  10. Introductory Astronomy Glossary Astronomical Societ of the Pacific
  11. Comparative Planetology University of Washington Astronomy Dept.
  12. Thales University of St. Andrews School of Mathematical and Computational Sciences
  13. Aristotle (384 - 322 B.C.) History of Astronomy, Astronomy, Cornell University
  14. Gribbin, J. (2002) Science: A history. London: Penguin
  15. [1] Plutarch, De facie in orbe lunae , c. 6 “Only do not, my good fellow, enter an action against me for impiety in the style of Cleanthes, who thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the Universe, this being the effect of his attempt to save the phenomena by supposing the heaven to remain at rest and the earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis.” Attributed to Dercyllides, a contemporary of Aristarchus.
  16. Archimedes, Sand-Reckoner, Chapter 1 "Now you are aware that "universe" is the name given by most astronomers to the sphere the center of which is the center of the earth, and the radius of which is equal to the straight line between the center of the sun and the center of the earth; this you have seen in the treatises written by astronomers. But Aristarchus of Samos brought out writings consisting of certain hypotheses, in which it appears, as a consequence of the assumptions just made, that the universe is many times greater than the "universe" just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface."
  17. one quadrant = 90 degrees
  18. be opposite to; of angles and sides, in geometry used to determine dimensions from known quantities
  19. The twelve signs of the Zodiac occupy equivalent portions of 30 degrees each of the 360 degrees of the celestial sphere. So the moon, therefore, has 1/15 of 30 degrees.
  20. The average distance between the Earth and the Sun is about 93,000,000 miles (150 million kilometres). Perihelion, the closest distance, is 91.4 million miles (147.1 million km) away from us. Aphelion, its farthest, is 94.5 million miles (152.1 million km) away. The average distance of the Moon and the Earth is 238,855 miles (384,400 kilometres), the width of 30 Earths. Because of its elliptical orbit, its distance from Earth varies between 225,700 miles (363,300 kilometres) and 252,000 miles (405,500 kilometres).
  21. Aristarchus of Samos University of St. Andrews School of Mathematical and Computational Sciences
  22. Aristarchus of Samos Riley, Kristen (1995) Paper prepared for Greek Science Course taught by Prof. Gregory Crane, Tufts University
  23. How far away is the sun? How far away is the moon? How large is the Sun? How small is the moon compared to Earth? Ask an Astronomer, NASA
  24. Aristarchus Cornell Astronomy
  25. latitude = 23.5 degrees north
  26. Eratosthenes (276 - 195 B.C.) Cornell Astronomy
  27. AGLAONIKE 4,000 years of women in science] Deborah Crocker (University of Alabama), Sethanne Howard (US Naval Observatory retired). University of Alabama, Dept of Physics and Astronomy
  28. Ogilvie, M. B. (1986). Women in Science. The MIT Press.
  29. (2001).Encyclopedia of Astronomy and Astrophysics, Edited by Paul Murdin, Bristol: Institute of Physics Publishing
  30. Hipparchus on a poem Dept. of History and Philosophy of Science, University of Cambridge.
  31. The Astrolabe James E. Morrison, Astrolab.org
  32. Scientific instruments of Medieval and Renaissance Europe Guide to the Astrolabe Museum of the History of Science at Oxford. Site containing a large collection of documents, graphics and explanations on astrolabes of Medieval and Renaissance Europe
  33. Ptolemy used a completely different type of instrument, the 'armillary astrolabe' or star-taker made of rings or bracelets, which he described in the Almagest Book 5, chapter 1 Hipparchus Dept. of History and Philosophy of Science, University of Cambridge.
  34. In other words, 1/5th of 30 minutes of arc of the Sun's disk was visible. The Sun's angular diameter is 30 arc minutes or ½ a degree.
  35. See Hipparchus (190 - 120 B.C.) for an illustration of this.
  36. The Precession of the Earth's Axis Cornell University Dept. of Astronomy
  37. Hipparchus (190 - 120 B.C.) Cornell University Dept. of Astronomy
  38. Hipparchus and the Astrolabe Dept. of History and Philosophy of Science, University of Cambridge.
  39. Mathematical Techniques in Astronomy Dept. of History and Philosophy of Science, University of Cambridge.
  40. 40.0 40.1 40.2 Gribbin, J. (2002) Science: A history. London: Penguin
  41. Thomas Digges: Gentleman and mathematician Stephen Johnston (1994) chapter 2 (pp. 50-106) of, ‘Making mathematical practice: gentlemen, practitioners and artisans in Elizabethan England’ Ph.D. thesis, Cambridge. Available through University of Oxford, Museum of History of Science
  42. Thomas Digges O'Connor, J. J. and Robertson, E. F. (2002) MacTutor History of Mathematics Archive, School of Math and Statistics, University of St. Andrews.
  43. Thomas was publishing his father's work with his contributions which he stated in the text, However, there was an amended section to the book, Mathematical Discourse of Geometrical Solids, a study of Platonic and Archimedean bodies, which was entirley his own work. Refer to PhD thesis, Stephen Johnston cited below.
  44. sometimes referred to as Tycho's Supernova See reference to NASA/ESA Space Telescope cited below.
  45. Thomas Digges: Gentleman and mathematician Stephen Johnston (1994) chapter 2 (pp. 50-106) of, ‘Making mathematical practice: gentlemen, practitioners and artisans in Elizabethan England’ Ph.D. thesis, Cambridge. Available through University of Oxford, Museum of History of Science
  46. Thomas Digges O'Connor, J. J. and Robertson, E. F. (2002) MacTutor History of Mathematics Archive, School of Math and Statistics, University of St. Andrews.
  47. heic0415: Stellar survivor from 1572 A.D. NASA/ESA Space Telescope. On Nov. 11, 1572, Tycho Brahe observed a star in the constellation Cassiopeia as bright as Jupiter which eventually equaled Venus in brightness. It was visible during daylight for about two weeks and eventually faded from unaided view altogether after about 16 months.