About the Work
This is a summary of Edmond Halley’s A Synopsis of the Astronomy of Comets, a foundational scientific treatise first published in London in 1705 by John Senex. The work was originally printed at Oxford and was written by Halley in his capacity as Savilian Professor of Geometry at Oxford and Fellow of the Royal Society. The edition described here is sourced from the Dibner Library of the History of Science and Technology at the Smithsonian Institution Libraries. The book represents a landmark in the history of astronomy, as it compiles and analyzes all known comet observations up to that time, presents a systematic method for computing comet positions, and famously predicts the return of a specific comet—now known as Halley’s Comet—around the year 1758. The text is technical and mathematical in nature, intended for an audience of astronomers and natural philosophers, and it synthesizes the work of earlier astronomers while advancing a new theoretical framework based on Newtonian physics.
Context
The book emerges from a critical period in the history of science, when the understanding of comets was undergoing a fundamental transformation. For centuries, the dominant view, derived from Aristotle, held that comets were sublunary vapors or airy meteors—atmospheric phenomena rather than celestial bodies. This opinion prevailed for so long that the study of comets was neglected, and nothing certain about their motion was transmitted from antiquity. The ancient Egyptians and Chaldeans, according to Diodorus Siculus, could predict comet apparitions through long observation, but because they also prognosticated earthquakes and tempests, their knowledge was judged to be astrological calculation rather than astronomical theory. The Greeks, who conquered these peoples, found little other learning among them, and it is to the Greeks—especially the great Hipparchus—that astronomy is owed.
The work of Tycho Brahe in 1577 marked a turning point, as he used large instruments to observe a remarkable comet and found no perceptible diurnal parallax, proving it was higher than the Moon and possibly among the Planets, despite opposition from the School-men. This observation laid the groundwork for later theoretical advances. Johannes Kepler, using Tycho’s labors, discovered the true physical system of the planets, demonstrating that they move in elliptical orbits with the Sun at the common focus, with areas proportional to times and distances in sesquialtera ratio of periodical times. However, Kepler’s understanding of comets remained incomplete, as he concluded they moved freely through planetary orbs with nearly rectilinear motion. The prodigious comet of 1680, which descended perpendicularly toward the Sun and rose with great velocity, was observed for four months by Cassini and Flamsteed at the Paris and Greenwich observatories, providing crucial data. It was Isaac Newton who, in his Mathematical Principles, demonstrated that Kepler’s findings hold in the planetary system and that all comet phenomena follow from the same principles, illustrating with the 1680 comet and proving it moved in a parabolical orb, describing areas proportional to times. Halley’s book applies and extends Newton’s methods, bringing them to arithmetical calculation and creating a comprehensive framework for understanding comets.
Structure of the Book
The book is organized as a systematic treatise on cometary astronomy, progressing from historical background through computational methods to physical conclusions and predictions. The opening sections provide a historical survey of comet observations from antiquity to Halley’s own time, establishing the state of knowledge and the contributions of key figures such as Hipparchus, Seneca, Tycho Brahe, Kepler, Hevelius, and Newton. The middle sections present Halley’s mathematical methods for computing comet positions, including the construction of a General Table for parabolic orbits and detailed worked examples demonstrating the application of these methods to specific comets. The later sections address the physical nature of comets, the question of whether their orbits are parabolic or elliptical, and the identification of periodic comets. The book concludes with Halley’s famous prediction regarding the return of a comet in 1758 and his arguments about the nature of comet tails as vapors. Throughout, the text combines theoretical exposition with practical computational instructions, making it both a scientific argument and a practical manual for astronomers.
Detailed Section-by-Section Summary
The book opens with a historical account of comet observations, beginning with the ancient Egyptians and Chaldeans, who could predict comet apparitions through long observation but whose knowledge was judged to be astrological calculation rather than astronomical theory. The Greeks, particularly Hipparchus, are credited with advancing astronomy, but Aristotle’s opinion that comets were sublunary vapors or airy meteors prevailed, causing this difficult part of astronomy to be neglected. Seneca the Philosopher, considering two remarkable comets of his time, placed them among celestial bodies, believing them to be stars of equal duration with the world, though he admitted their motions were governed by unknown laws. He predicted future ages would unfold these mysteries, yet almost all astronomers disagreed with him, and he did not record the phenomena or times of appearance. Nothing useful is found in comet histories before A.D. 1337, when Nicephorus Gregoras, a Constantinopolitan historian and astronomer, described a comet’s path among fixed stars but was lax about time.
The next comet of note was in 1472, observed by Regiomontanus; it was the swiftest and nearest to Earth, moving forty degrees of a great circle in one day, and was the first with proper observations. Until Tycho Brahe, all considered comets below the Moon. In 1577, Tycho, using large instruments, observed a remarkable comet and found no perceptible diurnal parallax, proving it was higher than the Moon and possibly among the Planets, despite opposition from the School-men. Next came Kepler, who used Tycho’s labors to find the true physical system, demonstrating planets move in elliptical orbits with the Sun at the common focus, areas proportional to times, and distances in sesquialtera ratio of periodical times. Observing two comets, he concluded they moved freely through planetary orbs with nearly rectilinear motion. Hevelius, following Kepler, embraced rectilinear motion but found calculations imperfect, aware the path bent toward the Sun. The prodigious comet of 1680, descending perpendicularly toward the Sun and rising with great velocity, was observed for four months by Cassini and Flamsteed at the Paris and Greenwich observatories.
Newton, in his Mathematical Principles, demonstrated Kepler’s findings and that comet phenomena follow from the same principles, illustrating with the 1680 comet, proving it moved in a parabolical orb, describing areas proportional to times. Halley, following Newton, brought the method to arithmetical calculation, collecting observations and framing a table representing all observed comet motions. The table’s perihelium distances are estimated in parts where the Earth’s mean distance from the Sun is 100,000. The construction of the table is based on the principle that comets move in parabolick orbs with the Sun at the common focus, describing equal areas in equal times. All parabolas are similar, so one table serves all comets. The velocity of a comet in a parabola is to a planet’s circular velocity at the same distance as the square root of 2 to 1. A comet at the Earth’s distance would describe a quadrant in 109 days, 14 hours, 45 minutes. Rules are given for computing a comet’s apparent place: find the Sun’s place, the time difference from perihelion, add constant log 9.960128, and use the table to find the mean motion, angle from perihelion, and distance from the Sun, adjusting for direct or retrograde motion and time before or after perihelion.
The computational method continues with instructions for finding the comet’s position given the place of the node, the comet’s place in its orbit, and the inclination of the plane. One finds the comet’s distance from the node, then by common rules of trigonometry obtains the comet’s place reduced to the Ecliptic, the heliocentric latitude, and the logarithm of the curtate distance. From these, using the same rules by which planets’ places are found from the Sun’s place and distance, one obtains the apparent or geocentric place and apparent latitude. Two worked examples are provided to demonstrate the method. The first example is the comet of 1664, for which Halley provides the full logarithmic computation, including the log. dist. perihel. 0.011044, log. sesquialt. 0.016566, comp. arith. 9.973434, log. temp. 1.980862, log. med. mot. 1.981211, medius motus 85.001, perihelion in Leo 10.41.25, angle corrected 83.38.07, comet in orbit in Pisces 17.3.10, ascending node in Aries 21.00.00, comet from node 34.15.40, reduced to ecliptic in Pisces 19.07, comet heliocentric in Pisces 18.54.55, inclination north 11.46.50, log. curtate distance 0.257117, comet’s place viewed in Aries 21.44.45, comet visible in Taurus 22.53.30, latitude visible 5.38.15. The second example is the comet of 1682, with its own detailed computation yielding medius motus 44.498, perihelion in Sagittarius 25.29.30, comet in orbit in Aquarius 28.42.10, descending node in Leo 23.00, comet from node 35.19.10, comet heliocentric in Pisces 28.11.30, inclination north 35.2.00, comet visible in Gemini 5.11.50, latitude north 28.52.00.
Halley verifies these computations against actual observations. At the first example’s specified instant, the comet of 1664 was observed at London applying to the Second Star of Aries, found 9 minutes more northerly and 3 minutes to the east, according to Mr. Hook’s observation. At the second example’s time, Halley himself, near London with the same instruments he formerly used for southern constellations, found the comet of 1682 at Gemini 5.50.11 with 28.52 minutes north latitude, agreeing exactly with the Greenwich observation at nearly the same moment. The comet of 1680 required special treatment, as it came almost to the Sun itself, its perihelion being not above one-sixth of the Sun’s semi-diameter from its surface. Its latus rectum being so small, it could hardly be contained within the General Table’s limits due to the excessive velocity of mean motion. For this comet, after finding the mean motion, one uses the equation z cubed minus 3z equals 2/3 of the mean motion to obtain the tangent of half the angle from perihelion and the logarithm for distance from the Sun.
Halley then addresses the reliability of observations, noting that his five first comets—the third and fourth observed by Peter Apian, the fifth by Paulus Fabricius—and the tenth seen by Maestlin in 1596 are uncertain, as they were observations made without fit instruments or due care, disagreeing with themselves. The 1684 comet was only noticed by Blanchin at Rome, and the 1698 comet was seen only by those at Paris who determined its course in an uncommon way; it was very obscure and moved swift, coming near Earth, yet Halley’s party saw nothing of it. He omitted two remarkable comets from November 1689 and February 1702 for lack of observations, as they directed their courses toward southern parts, scarce conspicuous in Europe. If anyone brings accurate observations from India or southern parts, Halley will represent their orbits.
Comparing the motions of comets shows that their orbits are disposed in no order; they cannot be comprehended within a Zodiac as planets are, but move indifferently every way, retrograde and direct—hence not carried in Vortices. Perihelion distances vary, suggesting many more comets exist in remote regions, obscure and lacking tails, passing unseen. Halley has considered orbits as exactly parabolic, implying comets descend from infinite distances and recede forever. But since comets appear frequently and none moves with hyperbolic motion—swifter than gravity to the Sun would give—they likely move in very eccentric orbits with long periods. The latus rectum of an ellipse is to that of a parabola with the same perihelion distance as the aphelion distance is to the whole axis; velocities are in subduplicate ratio. In very eccentric orbits this approaches equality.
The principal use of the table is stated: when a new comet appears, compare elements to determine if it appeared before, determine its period and axis, and forecast its return. Halley then presents his famous identification of periodic comets. He suspected that the comets of 1607, 1682, and one other from 1531 were the same, making its third revolution in an ellipse. Finding differences and deeming Apian’s and Kepler’s observations too inaccurate, he first published this opinion in 1705 with probability, advising watch for return about 1758. Later, he found a method for computing motions in any ellipse and discovered three more comets in 1305, 1380, and 1456, giving six total: 1305, 1380, 1456, 1531, 1607, 1682. He substituted elliptic tables for the 1682 comet and tested against Flamsteed’s observations, which were made with a large accurate sextant and corrected for refractions. Two periods amount to 151 years, alternately 56 and 55 years. Applying Newton’s Principia, Book 1, Prop. 15, his theory gave the comet’s place on August 30, 1682 as Libra 15 degrees 35 minutes 58 seconds, while the observation was Libra 15 degrees 34 minutes 42 seconds; the latitude was 17 degrees 24 minutes 42 seconds in theory versus 17 degrees 25 minutes 27 seconds observed—differences of only 1 minute 16 seconds and 45 seconds.
For the 1607 comet, Kepler and Longomontanus observed it at Prague on September 16, 1607, old style, at 9 PM, finding it in Leo 18 degrees 30 minutes with latitude 35 degrees 4 minutes. Correcting Tycho’s false star places, the apparent place at London was Leo 21 degrees 49 minutes 00 seconds, while Halley’s computation gave Leo 21 degrees 55 minutes 50 seconds—a difference of 6 minutes 56 seconds. The latitude observed was 36 degrees 12 minutes 0 seconds, computed 36 degrees 20 minutes 4 seconds—a difference of 8 minutes 4 seconds. Twelve observations showed little difference after correcting errors. Halley notes that one revolution exceeding another by over a year is like Saturn’s revolutions differing by 13 days, a consequence of Newton’s gravity laws; this irregularity is greater in a comet emerging four times higher than Saturn, possibly making the next return more than 76 years—end of 1758 or beginning of 1759.
For the 1531 comet, Apian’s observations were made with a small azimuth instrument for showing the tail’s ascent and were imperfect. Halley procured Apian’s Astronomicon Cæsareum, dedicated to Emperor Charles V. Correcting star longitudes and refractions, he found that on August 13, 1531, the true place was Leo 20 degrees 16 minutes 0 seconds versus Apian’s Leo 19 degrees 15 minutes 0 seconds, and on August 23, Libra 3 degrees 49 minutes 0 seconds versus Libra 1 degree 23 minutes 0 seconds—differences of 1 degree 1 minute and 2 degrees 26 minutes. Halley concludes that agreement with three different comets in 1531, 1607, and 1682 makes it “next to a miracle” if not the same comet’s third revolution in an ellipse; if it appears about 1758, posterity must allow this an Englishman’s discovery. This comet is “as it were the Mercury of Comets,” revolving in the smallest orbit.
The book concludes with a discussion of comet tails. Halley argues that tails are subtle vapors exhaled by the Sun’s heat, like steam from water. Newton argues that the Earth would be exhausted of moisture by vegetation unless supplied; comet tails, dilating as they ascend, scatter through planetary regions and are gathered by planets attracting bodies, entering Earth’s atmosphere to renovate things and supply humidity lost to putrefaction and vegetation—far from portending mischief. Evidence that tails are vapors includes the fact that the Earth is more than half the year closer to the Sun than the 1664 and 1665 comets were at nearest approach, yet Earth, Mercury, and Venus emit no tails. Newton’s computation shows that a one-inch globe of air carried to one Earth-semidiameter height would rarity to fill all planetary regions to Saturn’s sphere and beyond. Regarding the brightness objection, Newton observes that the most refulgent tails hardly appear brighter than a sunbeam through a one-inch hole into a dark room, and the smallest fixed stars are visible through them without sensible diminution.
Main Arguments
The central argument of the book is that comets are celestial bodies governed by the same physical laws as the planets, moving in orbits around the Sun, and that their motions can be precisely computed and predicted. Halley establishes this by building on the work of his predecessors, particularly Tycho Brahe’s demonstration that comets are above the Moon, Kepler’s discovery of elliptical planetary orbits, and Newton’s proof that comet phenomena follow from the same principles of gravity. A key argument is that comets move in parabolic or elliptical orbits with the Sun at the focus, describing equal areas in equal times, and that their apparent motions can be calculated using a general table applicable to all comets. Halley argues against the older view that comets are sublunary vapors, showing instead that they are distant celestial objects whose tails are subtle vapors exhaled by the Sun’s heat.
Another major argument is that comets do not move in vortices, as their orbits are disposed in no order and they move indifferently every way, both retrograde and direct, unlike planets which are confined to a Zodiac. Halley argues that since comets appear frequently and none moves with hyperbolic motion, they likely move in very eccentric elliptical orbits with long periods rather than true parabolas. The most famous argument is the identification of the comets of 1531, 1607, and 1682 as the same comet returning periodically, with a predicted return around 1758. Halley supports this with detailed comparisons of computed and observed positions, showing close agreement after correcting for errors in earlier observations. He also argues that comet tails are not portents of mischief but natural phenomena—vapors that scatter through planetary regions and may even supply moisture to the Earth, contributing to the renewal of things lost to putrefaction and vegetation.
Key Concepts
The book introduces and develops several key concepts in cometary astronomy. The first is the idea that comets move in parabolic orbits with the Sun at the common focus, describing equal areas in equal times, a principle derived from Newton’s work. All parabolas are similar, so one general table serves all comets, allowing astronomers to compute a comet’s position given its perihelion distance and time since perihelion. The velocity of a comet in a parabola is to a planet’s circular velocity at the same distance as the square root of 2 to 1, and a comet at the Earth’s distance would describe a quadrant in 109 days, 14 hours, 45 minutes. The computational method involves finding the Sun’s place, the time difference from perihelion, adding a constant logarithm, and using the table to find the mean motion, angle from perihelion, and distance from the Sun.
Another key concept is the distinction between parabolic and elliptical orbits. While Halley initially considers orbits as exactly parabolic, implying comets descend from infinite distances and recede forever, he argues that since comets appear frequently and none moves with hyperbolic motion, they likely move in very eccentric elliptical orbits with long periods. The latus rectum of an ellipse is to that of a parabola with the same perihelion distance as the aphelion distance is to the whole axis, and velocities are in subduplicate ratio. This leads to the concept of periodic comets, where the same comet returns at regular intervals. Halley identifies six appearances of one comet—1305, 1380, 1456, 1531, 1607, 1682—with two periods amounting to 151 years, alternately 56 and 55 years.
The concept of the General Table is central to the book’s practical utility. The table’s perihelium distances are estimated in parts where the Earth’s mean distance from the Sun is 100,000. The table allows astronomers to compute a comet’s apparent place through a series of steps: find the Sun’s place, the time difference from perihelion, add constant log 9.960128, and use the table to find the mean motion, angle from perihelion, and distance from the Sun, adjusting for direct or retrograde motion and time before or after perihelion. For comets very close to the Sun, such as the 1680 comet, a special equation is used: z cubed minus 3z equals 2/3 of the mean motion, to obtain the tangent of half the angle from perihelion and the logarithm for distance from the Sun.
The book also develops the concept of comet tails as vapors. Halley argues that tails are subtle vapors exhaled by the Sun’s heat, like steam from water, and that they dilate as they ascend, scattering through planetary regions where they are gathered by planets attracting bodies. These vapors may enter Earth’s atmosphere to renovate things and supply humidity lost to putrefaction and vegetation. Evidence includes the fact that the Earth is more than half the year closer to the Sun than the 1664 and 1665 comets were at nearest approach, yet Earth, Mercury, and Venus emit no tails. Newton’s computation shows that a one-inch globe of air carried to one Earth-semidiameter height would rarity to fill all planetary regions to Saturn’s sphere and beyond. The most refulgent tails hardly appear brighter than a sunbeam through a one-inch hole into a dark room, and the smallest fixed stars are visible through them without sensible diminution.
Themes
A prominent theme is the progression of scientific knowledge, as Halley traces the history of comet observations from the ancient Egyptians and Chaldeans through the Greeks, Seneca, Tycho Brahe, Kepler, Hevelius, and Newton. This historical narrative emphasizes how erroneous theories, such as Aristotle’s view of comets as sublunary vapors, delayed progress, and how the accumulation of accurate observations and theoretical insights gradually led to a correct understanding. The theme of observation versus theory is central, as Halley repeatedly emphasizes the importance of accurate instruments and careful measurements, while also showing how theoretical frameworks like Newton’s gravity are necessary to interpret observations correctly.
Another theme is the reliability of data and the need for correction. Halley notes that many earlier observations were made without fit instruments or due care and disagree with themselves, such as those by Apian, Fabricius, and Maestlin. He corrects star longitudes and refractions in earlier observations, showing how errors can be identified and rectified. This theme extends to the practical challenges of observation, as some comets were seen only in southern parts and scarce conspicuous in Europe, and Halley calls for accurate observations from India or southern parts to represent their orbits.
The theme of prediction and verification runs throughout the book, culminating in the prediction of the comet’s return around 1758. Halley’s identification of the comets of 1531, 1607, and 1682 as the same comet is based on close agreement between computed and observed positions, and he frames this as a testable prediction that posterity can verify. The theme of comets as natural phenomena rather than portents is also significant, as Halley argues that tails are vapors that may even benefit the Earth by supplying moisture, far from portending mischief. This represents a shift from astrological to astronomical understanding, echoing the book’s opening distinction between the astrological calculations of the Egyptians and Chaldeans and true astronomical theory.
The Author’s Conclusions
Halley concludes that comets are celestial bodies moving in orbits around the Sun, governed by the same laws of gravity that govern the planets. He demonstrates that their motions can be computed with precision using parabolic or elliptical orbit models, and he provides a general table and computational methods for this purpose. He concludes that comets do not move in vortices, as their orbits are disposed in no order and they move indifferently every way, both retrograde and direct. He argues that since comets appear frequently and none moves with hyperbolic motion, they likely move in very eccentric elliptical orbits with long periods.
The most significant conclusion is the identification of the comets of 1531, 1607, and 1682 as the same comet, making its third revolution in an ellipse. Halley finds the agreement among these three appearances to be “next to a miracle” if not the same comet, and he predicts its return about 1758, possibly at the end of 1758 or the beginning of 1759, noting that the period may be more than 76 years due to irregularities caused by gravitational perturbations. He describes this comet as “as it were the Mercury of Comets,” revolving in the smallest orbit. Halley also concludes that comet tails are subtle vapors exhaled by the Sun’s heat, which scatter through planetary regions and may be gathered by planets, entering Earth’s atmosphere to renovate things and supply humidity lost to putrefaction and vegetation—far from portending mischief.
Significance
The significance of this work lies in its transformation of cometary astronomy from a neglected and mysterious subject into a precise, predictable science. By applying Newton’s principles of gravity to comets and developing a general table for computing their positions, Halley provided astronomers with a practical tool for understanding and predicting comet appearances. The identification of the periodic comet now known as Halley’s Comet was a landmark achievement, demonstrating that comets could be the same object returning at regular intervals and that their appearances could be forecast. The prediction of the comet’s return around 1758 was a bold statement that invited verification by future generations, and its fulfillment would confirm the validity of Newtonian physics and the power of mathematical astronomy. The book also contributed to the understanding of comet tails as natural vapors rather than portents, reinforcing the shift from astrological to astronomical interpretations of celestial phenomena. By collecting and analyzing observations from across Europe and correcting errors in earlier data, Halley established a foundation for future cometary research and demonstrated the value of collaborative and cumulative scientific inquiry.
