Heliocentric models of the Solar System

1. A geocentric universe

1.1 Eudoxus and a geocentric universe

The stars appear to orbit the Earth in a fixed pattern, as if they are attached to a giant sphere that makes one revolution per day. There are seven objects that appear to move independently of this sphere, and that can be seen with the naked eye. These are: the Moon, Mercury, Venus, Mars, Jupiter, Saturn, and the Sun.

Animation showing how the stars move across the night sky.

The night sky at SAAO, Sutherland, South Africa. Image credit: Helen Klus/CC-NC-SA.

Composite photograph showing star-trails, which are created by the star’s movement.

Star trails at SAAO, Sutherland, South Africa. Image credit: Helen Klus/CC-NC-SA.

Ancient Greek astronomer Eudoxus of Cnidus was the first person known to present a mathematical theory of the universe. Eudoxus was born in about 410 BCE and was a student of Plato.

Eudoxus placed the spherical Earth at the centre of the universe, this is known as a geocentric universe. Eudoxus placed the Sun and the planets in giant transparent spheres that orbit the Earth. The Sun's sphere orbits the Earth once every 24 hours, and the stars are attached to a larger sphere beyond this[1].

1.2 Aristotle and a finite, eternal, and geocentric universe

Ancient Greek philosopher Aristotle extended Eudoxus' model of the universe in the 4th century BCE. Aristotle's universe was finite, eternal, and geocentric, with the Sun, Moon, planets, and stars all orbiting the Earth inside of Eudoxus' spheres.

Aristotle believed that space is fundamentally different from the Earth because he thought that objects in space are unchanging and move in perfect circles, which he considered to be the perfect shape. In contrast to this, the Earth is imperfect and constantly changing. Aristotle thought that Comets existed inside of the Earth's sphere, as they clearly do not move in spherical orbits[2][3].

Ancient Greek astronomer Heraclides Ponticus, Aristotle's contemporary, suggested that it would be simpler for the Earth to rotate than for the whole of the sky to orbit around it[4]. Ancient Greek astronomer Aristarchus of Samos, born in 310 BCE, went further and suggested that the Earth revolves around the Sun[5]. These claims were generally dismissed, however, and Aristotle's cosmology remained dominant.

Diagram showing a geocentric universe, with the Sun and planets orbiting the Earth in perfect circles.

A geocentric universe, c. 1470. Image credit: Cristoforo de Predis/Public domain.

Painting showing angels rotating the celestial spheres.

Angels rotating the celestial spheres, c. 1375. Image credit: Breviari d'Amour/British Library/Public domain.

1.3. Ptolemy and epicycles

Roman astronomer Ptolemy developed Aristotle's geocentric theory of the universe in about 150 CE. The Ptolemaic system popularised the use of epicycles to explain why the planets don't appear to orbit in perfect circles around the Earth[6]. Some objects, like Mars, even appear to move backwards before moving forwards again in large loops.

Diagram showing the apparent motion of the Sun and planets from the Earth.

The apparent motion of the Sun and planets from the Earth, depicted in 1777. Image credit: Encyclopaedia Britannica (1777)/Public domain.

Photograph showing the apparent motion of Mars from the Earth

Composite of images taken about 6 days apart from October 2011 (top right) to early July 2012. Image credit: Cenk E. Tezel & Tunç Tezel (TWAN)/Copyrighted, used with permission.

2. A heliocentric universe

2.1 Copernicus and a heliocentric universe

Polish astronomer Nicolaus Copernicus reintroduced the concept of a Sun centred, or heliocentric, universe to Europe in On the Revolutions of the Celestial Spheres, first published in 1543.

Like Ptolemy, Copernicus believed that the planets travel in perfect circles, and so his heliocentric model needed a similar amount of epicycles in order to explain their observed motions.

Painting of a geocentric universe.
Painting of a heliocentric universe.

Geocentric and heliocentric universes, depicted in 1660. Image credit: The Harmonia Macrocosmica of Andreas Cellarius/Public domain.

The Church would not have accepted a realist heliocentric model, and so Copernicus' presented his idea as an instrumental theory. It provided an easier mathematical system for calculating where planets would be, but it was not to be taken literally.

Almost 60 years later, Italian philosopher Giordano Bruno was burned at the stake for heresy after suggesting, among other things, that the Sun is just another star[7].

2.2 Tycho and a changing universe

Danish astronomer Tycho Brahe made some of the most accurate ever observations with the naked eye in the late 1500s. He disproved Aristotle's concept of an unchanging universe when he saw a new star in the constellation of Cassiopeia in 1572. This was later identified as a supernova.

Tycho also proved that Aristotle's transparent spheres do not exist by showing that comets would have to travel through them[8].

2.3 Kepler's laws

Tycho's student, German astronomer Johannes Kepler, first extended Aristotle's theory of spheres by arguing that they are separated by five polyhedrons. Polyhedrons are three-dimensional objects with sides that are all the same shape, like a cube, or a pyramid made of equilateral triangles. All of these shapes can be placed inside of a sphere so that the edges just touch the surface[9][10].

Depiction of a universe composed of a series of shapes nested inside each other.

Kepler's first universe, from Mysterium Cosmographicum, 1596. Image credit: Johannes Kepler/Public domain.

Kepler also suggested that the planets may produce musical notes because they can be described with a frequency. This was based on Ancient Greek mathematician Pythagoras' idea that the universe could be represented in musical terms[11a].

Tycho later assigned Kepler the task of analysing his observations of Mars.

Tycho's data was accurate enough for Kepler to show, in 1609, that Mars' orbit is not circular but fits the shape of an ellipse, centred on a mass determined by the Sun and a second focal point. The second focal point is caused by the mass of all the other planets in the Solar System[12a]. This is Kepler's first law: "The orbit of every planet is an ellipse with the Sun at one of the two foci".

Diagram of Kepler’s first law.

Kepler's first law. Image credit: RJHall/Talifero/CC-SA.

Animation of the movement of Earth and Mars orbiting the Sun. Earth moves faster than Mars because it is closer to the Sun.

Kepler's second and third laws. Image credit: Lookang /Todd K. Timberlake/Francisco Esquembre/CC-SA.

Kepler's second law, published that same year[12b], states that planets move faster when they are closer to the Sun: "a line joining a planet and the Sun sweeps out equal areas during equal intervals of time". This is due to the law of the conservation of angular momentum.

By 1619, Kepler was able to determine the relationship between a planet's distance from the Sun and the time it takes to complete one orbit, its period[11b]. Kepler's third law states that: "the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit".

The loops in Mars' orbit are caused by the Earth passing Mars, which orbits more slowly.

Credit: astrogirlwest.

2.4 Galileo and the telescope

Italian natural philosopher Galileo Galilei, Kepler's contemporary, added further proof to the heliocentric theory in 1610, when he made a number of observations that contradicted Aristotle[13a].

Galileo, like Pythagoras, believed that the universe is composed in the language of mathematics. In 1623, he stated that:

"Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth"[14].

Galileo created one of the first microscopes, and was one of the first people to use the telescope as an astronomical instrument[15]. This allowed him to became the first to observe a number of phenomena, including the moons of Jupiter, the phases of Venus, sunspots, and the depth of the craters on the Moon, which he illustrated by showing the change in shadows across a day.

Galileo showed that not everything in space is perfect and unchanging, and that not everything orbits the Earth or the Sun[13b].

Sketch by Galileo.

Sketch of craters on the Moon by Galileo Galilei, 1610. Image credit: The Galileo Project/Public domain.

Sketches by Galileo.

Sketch of sunspots and Jupiter's moons by Galileo Galilei, 1610. Image credit: The Galileo Project/Public domain.

Galileo's claims were accepted within nine months of their publication, despite the fact that he was extremely secretive about the telescope he used. He did not reveal the size or the focal length, or the type of glass used to make the lens[16a].

Galileo claimed that a 20-power telescope was needed to reproduce his observations, and promised a forthcoming book on the subject, but this was never published. He did distribute several telescopes but these were sent to princes and cardinals, not astronomers or mathematicians.

Galileo was concerned that others would soon learn to build better telescopes, and make all of the possible new discoveries before him. His fears were not unjust, he knew from experience that after receiving a description, a 20-power instrument could be created in four months.

Galileo also knew that these instruments were being constructed in Venice, and that the Jesuits had already turned their telescope into a 34-power instrument[16b].

Galileo's observations were verified three times in 1610. Kepler had already publicly endorsed Galileo's claims, despite not being able to replicate them. He had requested a telescope to further his own project but never received one.

Kepler became the second person to verify Galileo's findings when he received a telescope from Italian astronomer Antonio Santini, the first person to have verified them. The third confirmation was by a Jesuit mathematician who received his telescope from Kepler[16c].

Until 1632, the heliocentric theory was easily dismissed because there was no explanation for why the Earth does not appear to move. Galileo explained this using his principle of relativity, which states that all uniform motion is relative and there is no absolute state of rest.

When you are on a ship, for example, you are at rest with respect to the floor even though you are moving with respect to the sea.

In 1655, Dutch natural philosopher Christiaan Huygens showed that Jupiter is not the only planet with moons, when he discovered Saturn's moon Titan. Huygens was also the first to show that the bulges around Saturn, which had first been observed by Galileo, are actually rings[17].

3. Measuring the universe

3.1 Pythagoras and a spherical Earth

Pythagoras was the first to suggest that the Earth is spherical in about 500 BCE, and this was accepted by most Greek philosophers at the time[18].

3.2 Aristarchus and the distance to the Sun and Moon

Aristarchus was the first person to attempt to calculate the relative distance between the Earth and the Sun. He did this by measuring the angle between the Moon and the Sun during a half moon, and using trigonometry.

Diagram showing how Aristarchus used trigonometry to determine the ratio of the distance to the Earth and Moon (L), and the distance to the Earth and Sun (S), using cos θ equals L divided by S, where θ is the angle.

Diagram illustrating how Aristarchus measured the relative distance between the Earth, Moon, and Sun. Image credit: modified by Helen Klus, original image by andonee/Public domain.

Aristarchus concluded that the Sun is about 20 times further away than the Moon and must be about 20 times larger, since the Moon and Sun appear to be the same size. This is most evident during solar eclipses, when the Moon blocks out the Sun entirely[19].

We now know that the Sun is almost 400 times further away than the Moon, and that it is about 400 hundred times larger.

3.3 Eratosthenes and the circumference of the Earth

Ancient Greek astronomer Eratosthenes, who was the first person to measure the tilt of the Earth in about 240 BCE, also attempted to measure circumference of the Earth.

Eratosthenes knew that the Sun would appear directly overhead in the Egyptian city of Swenet at noon on the day of the summer solstice. This is the longest day of the year, when the Sun is at its highest point in the sky.

Eratosthenes measured the angle of Sun in Alexandria at that same time and found it to be about 1/50 of a full circle. He realised that this meant the distance between Swenet and Alexandria must be 1/50 of the circumference of the Earth, and measured the distance between cities by timing how long it took to ride there by camel.

Diagram illustrating how Eratosthenes measured the length of shadows in order to determine the circumference of the Earth.

Diagram illustrating how Eratosthenes measured the circumference of the Earth. Image credit: The Anome/Gregors/Public domain.

Eratosthenes concluded that the Earth has a circumference of about 252,000 stadia, which became the accepted value[20]. The Greek stadium was about 185 metres, and this leads to a circumference of 46,620 km, an overestimation.

If we assume that Eratosthenes used the Egyptian stadium of about 157.5 metres, however, then the circumference would have converted to 39,690 km, which is very close to the 40,075 km value accepted today[21].

3.4 Bradley and a moving Earth

In 1725, English astronomer James Bradley proved that the Earth moves using a phenomenon known as stellar parallax.

Animation showing the Earth rotating. From our perspective, the stars appear to form a larger sphere around the Earth.

A rotating Earth. Image credit: Tfr000/CC-SA.

Stellar parallax occurs because if the Earth moves around the Sun, then the stars should appear to move as we view them from slightly different positions throughout the year. Those that are closer should appear to move more than those that are very far away.

Diagram showing how the movement of the Earth causes stellar parallax.

Stellar parallax. Image credit: Helen Klus/CC-NC-SA.

Bradley knew that if he could measure the angle that the stars appeared to move, then he could determine how far away they are using trigonometry. Tycho had failed to observe this movement, and Bradley's observations were not able to provide evidence of parallax either, but he did observe stellar aberration[22].

Stellar aberration is caused by the constantly changing angle with which we view the stars as the Earth orbits the Sun. It does not depend on the Earth's change in position, and so it cannot be used to determine the distance to the stars, but it does show that the Earth is accelerating in the way we would expect if it were orbiting the Sun.

3.5 The size of the universe

The size of the known universe doubled in 1781, when British astronomer William Herschel discovered Uranus[23]. It increased by a factor of over 8000 in 1838, when German astronomer Friedrich Bessel became the first to measure stellar parallax. Bessel determined that the star 61 Cygni is about 10.4 light-years away[24].

This was quickly followed by German astronomer Friedrich Georg Wilhelm von Struve's announcement that the star Vega is about 26 light-years away[25]. Both were correct to within one light-year (a light-year is the distance that light travels in 1 year, and is equal to about 9000 billion km).

German astronomer Johann Galle became the first person to observe Neptune in 1846, following calculations made by French mathematician Urbain Le Verrier. British astronomer William Lassell discovered Neptune's largest moon Triton two and a half weeks later[26].

The shape of the universe was refined once again in the 1900s, with the discovery of galaxies beyond the Milky Way, and the expansion of the universe.

4. References

  1. Mazer, A., 2011, 'Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe', John Wiley & Sons.

  2. Aristotle and Stocks, J. L. (trans), 2015 (350 BCE), 'On the Heavens', eBooks@Adelaide.

  3. Dicati, R., 2013, 'Stamping Through Astronomy', Springer Science & Business Media.

  4. Couprie, D. L., 2011, 'Heaven and Earth in Ancient Greek Cosmology: From Thales to Heraclides Ponticus', Springer Science & Business Media.

  5. Africa, T. W., 1961, 'Copernicus' Relation to Aristarchus and Pythagoras', Isis, 52, pp.403-409.

  6. Rabin, S., 'Nicolaus Copernicus', Stanford Encyclopedia of Philosophy, last accessed 15-02-16.

  7. Pogge, R. W., 'The Folly of Giordano Bruno', The SETI League, last accessed 15-02-16.

  8. Ford, D., 2014, 'The Observer's Guide to Planetary Motion: Explaining the Cycles of the Night Sky', Springer.

  9. Kepler, J. and Aiton, E. J. (trans), 1981 (1596), 'The secret of the universe', Abaris Books.

  10. Richeson, D. S., 2012, 'Euler's Gem: The Polyhedron Formula and the Birth of Topology', Princeton University Press.

  11. (a, b) Kepler, J. and Aiton, E. J. (trans) and Duncan, A. M. (trans) and Field, J. V. (trans), 1997 (1619), 'The Harmony of the World', American Philosophical Society.

  12. (a, b) Kepler, J. and Donahue, W. H. (trans), 1992 (1609), 'New Astronomy', Cambridge University Press.

  13. (a, b) Galilei, G. and Van Helden, A. (trans), 2016 (1610), 'Sidereus Nuncius, or The Sidereal Messenger', University of Chicago Press.

  14. Galilei, G., Drake, S. (trans), and Drake, S. (ed), 1957 (1623), 'The Assayer' in 'Discoveries and Opinions of Galileo', New York: Doubleday & Co.

  15. Hilliam, R., 2005, 'Galileo Galilei: Father of Modern Science', The Rosen Publishing Group.

  16. (a, b, c) Biagioli, M., 2000, 'Replication or Monopoly? The Economies of Invention and Discovery in Galileo's Observations of 1610', Science in Context, 13, pp.547-590.

  17. Matson, D. L. and Spilker, L. J., Lebreton, J. P., and Russell, C. T. (ed), 2003, 'The Cassini/Huygens mission to the Saturnian system' in 'The Cassini-Huygens Mission', Springer Netherlands.

  18. Kanas, N., 2012, 'Star Maps: History, Artistry, and Cartography', Springer Science & Business Media.

  19. Heath, T., 2013, 'Aristarchus of Samos, the Ancient Copernicus: A History of Greek Astronomy to Aristarchus, Together with Aristarchus's Treatise on the Sizes and Distances of the Sun and Moon', Cambridge University Press.

  20. Eratosthenes and Roller, D. W. (trans), 2010 (c240 BCE), 'Geography', Princeton University Press.

  21. Pinotsis, A. D., 2006, 'The significance and errors of Erathosthenes' method for the measurement of the size and shape of the Earth's surface', Gibson Bros., Journal of Astronomical History and Heritage, 9, pp.57-63.

  22. Fernie, J. D., 1975, 'The Historical Search for Stellar Parallax', Journal of the Royal Astronomical Society of Canada, 69, pp.222-239.

  23. Schaffer, S., 1981, 'Uranus and the Establishment of Herschel's Astronomy', Journal for the History of Astronomy, 12, pp.11-26.

  24. Bessel, F. W., 1838, 'On the parallax of 61 Cygni', Monthly Notices of the Royal Astronomical Society, 4, pp.152-161.

  25. Kidger, M., 2008, 'Cosmological Enigmas: Pulsars, Quasars, and Other Deep-Space Questions', JHU Press.

  26. Lequeux, J., 2013, 'Le Verrier—Magnificent and Detestable Astronomer', Springer-Verlag New York.

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