Claudius Ptolemy is one of the most influential individuals in the history of astronomy. Ptolemy is recognized for developing a model of the heavenly sphere and solar system ( Timberlake , 2013 ). This system was particularly important due to its role in refining the models that other astronomers had developed previously. In particular, Ptolemy’s model was used in explaining the movement of heavenly bodies with more accuracy compared to other models ( Timberlake , 2013 ). Due to this attribute, the model was adopted for use in fostering an accurate understanding of the solar system and its structure. Similar to previous models, the Ptolemaic model was anchored on the assumption that the earth formed the center of both the solar system and the whole universe. This conceptualization of the earth as the center of the universe was the basis of the geocentric theory. Against this background, the most pertinent question is the extent to which the Ptolemaic model influenced astronomical history. Overall, the model was an indispensable element of astronomical history.
Background: Astronomy and Cosmology according to the Ancient Greeks
Astronomy was developed out of people’s quest to understand the movement of stars across the sky. The science was also aimed at fostering an understanding of the stars’ position in the context of the larger universe. In a bid to fill this gap in knowledge, civilizations have come up with different systems for understanding and ordering the universe throughout history. The first astronomers to develop these systems were from Egypt and Babylon ( Graham & Hintz , 2016; Kelley & Milone , 2011 ). These systems formed the basis for the subsequent development of Greek astronomy. Other systems were developed by astronomers from China, India, and the Americas. Documentation of the work of ancient Greek astronomers has been made possible by the fact the Greek tradition of inquiry was furthered by Islamic astronomers who were then succeeded by early modern European astronomers. This passing down of information enabled the preservation of various astronomical ideas possible.
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The Earth as a Sphere
Conceptualization of the earth as a sphere began in the 5 th Century B.C. Arguments in support of earth's spherical nature in this century were advanced by two Greek philosophers, namely Anaxagoras and Empedocles ( Kelley & Milone , 2011 ). This notion was informed by the manifestation of the lunar eclipse. The two philosophers reckoned that the earth's shadow was located on the moon when the earth was placed between the moon and sun. The fact that the shadow moving across the moon was round confirmed the earth’s spherical nature. Sailors also provided evidence of the spherical nature of the earth. In particular, when a ship is approaching from the horizon, sailors confirmed that only a ship’s top appears first, illustrating that the earth is indeed round. For instance, if the earth were instead flat, one would expect to see the whole ship once it becomes visible. The sailors' take on the shape of the earth was necessary since the occurrence of a lunar eclipse was rare.
The lunar eclipse was used in developing yet another vital piece of information regarding the earth. In the 3 rd Century B.C, Greek astronomer Aristarchus reckoned that he could estimate earth's size using information gathered from the manifestation of a lunar eclipse. The astronomer argued that when the Earth occurs between the moon and the sun, it results in the occurrence of a lunar eclipse ( Graham & Hintz , 2016) . In this regard, part of the information he thought was important in calculating the earth's size was a measurement of the size of the earth's shadow as it occurred on the moon. Nevertheless, estimation of the earth's size was done by yet another Greek astronomer, Eratosthenes, around the 240 B.C ( Kelley & Milone , 2011 ). In contrast to Aristarchus, Eratosthenes measured the shadows that were cast in Syene and Alexandria in a bid to calculate their angle relative to the sun. Despite the emergence of disputes regarding the accuracy of these calculations, the measurement made was found to be comparative close to the earth's actual size. Based on the above, it is clear that the Greeks made extensive use of mathematics in their efforts to theorize their understanding of the earth and the world around them. They also held various beliefs regarding the world and nature and grounded these beliefs using an empirical exploration of what could easily be reasoned from the evidence gathered.
Aristotle’s take on Astronomy and Cosmology
According to Aristotle, the universe was comprised of four key elements, namely earth, water, air, and fire ( Granada, 2004 ) . This argument supported the arguments of other philosophers, namely Empedocles and Plato. Aristotle also reckoned that a void space did not exist ( Timberlake , 2013 ). Instead, all space was comprised of a combination of these different elements. Likewise, these elements could further be grouped into two sets of qualities, namely, wet and dry or cold and hot. Aristotle also argued that each quality could be replaced by its opposite. This system was used as the basis of understanding how change on earth happens. He used the example of water, which, when heated, changes into steam, which interestingly resembles air. This understanding of the universe as comprising four principal elements played a crucial role in Aristotle's conceptualization of cosmology.
Aristotle's understanding of cosmology was based on the fact that each of the four elements of the universe had a certain weight. The earth was deemed the heaviest, followed by water, while fire and air were the lightest. The philosopher reckoned that while the lighter elements moved from the center of the universe, the heavier ones, in contrast, settled in the middle ( Couprie , 2011; Kelley & Milone , 2011 ). As they sort themselves to comply with this order, these elements are bound to assume mixed identities. Thus, apart from the four elements, Aristotle argued that anything else that occurred in the world should be viewed as a mixture of the elements. This implied that change and transition in the world were as a result of the mixing of the different elements. Accordingly, based on these elements, Aristotle argued that the terrestrial ought to be a place of death and birth, while the heavens are separate and governed by a different set of rules.
The celestial region, in contrast to the terrestrial, featured a distinctively different nature. Ancient Greeks generally supported the notion that the celestial region featured two critical types of objects, namely, wandering stars and fixed stars ( Kelley & Milone , 2011 ). For instance, they observed that the majority of the visible celestial objects tended to move at the same speed. The objects also assumed the same arrangement every day. Due to these features, the objects were branded the fixed stars and appeared to move together as a group. Other objects were observed to behave differently, and each followed its system. The Greeks named these objects the wandering stars and included the sun, moon, and planets Juniper, Mercury, Saturn, Mars, and Venus. The universe, in this system, was deemed to be part of one sphere that was split into an inner terrestrial realm and an outer celestial one ( Couprie , 2011 ). The moon’s orbit was deemed to be responsible for separating the two realms. While the heavens never changed, the earth was characterized by constant change ( Couprie , 2011) .
Aristotle further argued that there was a fifth substance that was quintessential. It is this substance that formed the heavens. Also, the heavens, according to Aristotle, were characterized by spherical motion of objects that proceeded perfectly. This account is contained in Aristotle’s On the Heavens ( Granada, 2004 ) . It is vital to note that during this time, the amount of observational evidence available was limited. However, there was an explanation for the existence and behavior of objects in the heavens. In particular, the celestial spheres were deemed to be overseen by a set of movers that were responsible for the movement observed amongst the wandering stars. Each wandering star was assumed to be characterized by an ‘unmoved mover’ which determined its movement in the heavens. The Greeks believed that the ‘unmoved mover’ was synonymous with god.
The Ptolemaic Model
Ptolemy's Almage st
Ptolemy is known to have accumulated immense astronomical knowledge in Alexandria, his home in Egypt. This information was obtained from many years of observation by his predecessors, namely Eudoxus and Hipparchus. He also relied on data that had been collected by the Babylonians. Using all this information, Ptolemy came up with a system that could be used in predicting the motion of stars. This model was published in Almagest , which contained his most important astronomical work ( Carman , 2009; Goddu, 2006 ). During the process, Ptolemy successfully synthesized and refining the existing astronomical ideas, while improving others where necessary. As a result, Almagest was highly acclaimed and became the most popular astronomy book for the subsequent one thousand years.
Almagest was used as a tool for aiding in the prediction of the location of various stars. In contrast to previous books on astronomy, Almagest served as an important tool as opposed to providing another system that could be used to describe the nature of the heavens ( Goddu, 2006 ). Ptolemy's quest to foster accuracy in predicting the location of stars over extended periods led to the creation of a more complex model.
Development of the Ptolemaic Model
During Ptolemy’s era, Greek astronomers had already pointed the need to add circles on the circular orbits of such wandering stars like the sun, moon, and the planets. These circles were deemed necessary in explaining the motion of the wandering stars and were referred to as epicycles ( Carman , 2009 ). According to the Greek tradition, the heavens exhibited perfect circular motion. The addition of circles was thus done to account for this perfection. The inclusion of stars resulted in the creation of somewhat confusing illustrations.
Ptolemy came up with several new concepts in a bid to resolve the complications that came with the use of the high number of circles. The astronomer resorted to the use of eccentric circles in describing planetary motion more accurately ( Carman , 2009; Goddu, 2006 ). Using an eccentric circle meant that the center of the planets’ orbit would be at a different point rather than the earth. To address this issue, Ptolemy put the epicycles on a separate set of circles referred to as deferents ( Carman , 2009) . This move meant that the planets moved on circles that also moved on circular orbits. Further, Ptolemy introduced equants. These tools ensured that as planets moved around the circles, they moved at different speeds. The resultant model, despite being complicated, had more predictive ability.
Overall, the Ptolemaic model was used as a means of accounting for the motion of planets. This is mainly through the assumption that each planet moved on a small circle or sphere referred to as an epicycle, which also moved on a much large circle or sphere known as deferent ( Carman , 2009). On the other hand, it was assumed that stars moved on a celestial sphere that occurred outside of the planetary spheres.
Impact of t he Ptolemaic Model o n Islamic , Medieval a nd Renaissance European Astronomy
Islamic astronomers produced extensive astronomical work from the 8 th to the 15 th century. These astronomers anchored their efforts on the Ptolemaic framework, in which case they made improvements to and refined the Ptolemaic system. The Islamic astronomers, besides developing better tables, came up with superior instruments that enhanced the capacity to make more accurate observations. These astronomers also brought the weaknesses inherent in the Aristotelian and Ptolemaic systems to light. A notable Islamic astronomer, in this case, was al-Farghani, who was also known as Alfraganus . In Elements of Astronomy on the Celestial Motions , Alfraganus presented Ptolemy’s Almagest in a non-mathematical manner and included revised values obtained from works of other Islamic astronomers (Unat, 2007). Besides being translated into Latin, Alfraganus ' book was used extensively in the Islamic world. It also became an essential source of reference for European scholars.
In Doubts on Ptolomey , Ibn al-Hatheym critiqued Ptolemy's work and converted the mathematical models presented by Ptolemy into a physical representation of movement in the heavens. Al-Sufi, in The Book of the Fixed Stars, combined Arabic astronomical traditions with Ptolemy’s work on mapping of constellations ( Hafez et al., 2011) . The book also illustrated each constellation from a terrestrial perspective as well as from outside the fixed stars’ sphere. Al-Sufi’s work was widely circulated and translated in Europe. Al-Mashar was yet another crucial Islamic astronomer. This astronomer focused on understanding the meaning of movement of stars, and their impact on future human events. Al-Mashar also translated Aristotle's works and disseminated his ideas in not only the Islamic world but also in Europe. Likewise, his work was translated into Latin from Arabic in the 12 th century and was widely adopted by both Renaissance and Medieval intellectuals. Through the works of these Islamic astronomers, the Ptolemaic model was widely embraced in medieval cosmology.
Other astronomers that disputed the Ptolemaic model were Nicolaus Copernicus and Johannes Kepler . While Ptolemy's planetary motion was widely accepted, the equant point was marred with controversy. Some astronomers objected to the existence of an imaginary point. However, Copernicus objected to Ptolemy's argument that elementary rotation in the heavens had speed variations. In On the Revolutions of the Heavenly Spheres, Copernicus contradicted Ptolemy by arguing that the sun occurs at the center of the universe ( Goddu , 2006 ). He also reckoned that the earth is one of the planets and moves across the heavens. The astronomer suggested the existence of a heliocentric universe and supported this using astronomical tables and mathematical evidence. Through his argument, Copernicus introduced a more sophisticated order for the universe.
Kepler, informed by the equant, developed an elliptical model that was articulated by the philosopher’s laws of planetary motion. In particular, Kepler came up with mathematical models to explain elliptical orbits, in the process, challenging some critical assumptions of the Aristotelian cosmology. In Astronomia Nova , Kepler fine-tuned the planets’ movements and demonstrated that Mars moved in a manner whose best description was an ellipse ( Goddu , 2006 ). He mathematically described the ellipses that closely fit the paths of planets in the heavens. Ultimately, Kepler’s take on elliptical orbit enhanced the understanding of the cosmos.
The role of the Ptolemaic model in advancing astronomy cannot be overstated. Anchored on mathematics, this model was particularly crucial in the prediction of the motion of heavenly bodies. The model was accepted widely by society, which indicated its importance. By remaining unchallenged for more than a thousand years, the Ptolemaic model was an essential element of astronomical history and continues to influence the field to date.
References
Carman, C. C. (2009). Rounding numbers: Ptolemy's calculation of the Earth-Sun distance. Archive for history of exact sciences , 63 (2), 205-242.
Couprie, D. L. (2011). Heaven and earth in ancient Greek cosmology: From Thales to Heraclides Ponticus (Vol. 374). Springer Science & Business Media.
Goddu, A. (2006). Ptolemy, Copernicus, and Kepler on linear distances. Proceedings of the2nd ICESHS, Cracow, Poland .
Graham, D. W., & Hintz, E. (2010). An ancient Greek sighting of Halley’s comet. Journal of Cosmology , 9 , 2130-2136.
Granada, M. A. (2004). Aristotle, Copernicus, Bruno: centrality, the principle of movement and the extension of the universe. Studies in History and Philosophy of Science Part A , 35 (1), 91-114.
Hafez, I., Stephenson, R., & Orchiston, W. (2011). Abdul-Rahman al-Sufi and his Book of the Fixed Stars: a journey of re-discovery. W. Orchiston, T. Nakamura, & R. Strom , 121-138.
Kelley, D. H., & Milone, E. F. (2011). Exploring ancient skies: A survey of ancient and cultural astronomy . Springer Science & Business Media.
Timberlake, T. (2013). Modeling the History of Astronomy: Ptolemy, Copernicus and Tycho. Retrieved from https://arxiv.org/ftp/arxiv/papers/1301/1301.2119.pdf
Unat, Y. (2007). Alfraganus and the Elements of Astronomy. Retrieved from https://muslimheritage.com/uploads/Alfraganus2.pdf
