The emergence of modern astronomy – a complex mosaic: Part XLV

The problem of an empirical proof of heliocentricity would occupy astronomers for the next couple of centuries following the publication of Newton’s Principia; the general acceptance of heliocentricity had now been achieved, but people very much wanted concrete assurance of its truth. The Principia actually contained a theoretical proof. Newton showed, assuming the law of gravity and Kepler’s laws of planetary motion, that given the mass of the Sun, the mass of the Earth and the distance between them then it was only possible that the Earth orbited the Sun and not vice versa. This proof was very technical, relied on a heap of assumptions and intelligent estimates, nobody actually knew the real masses of the Sun and Earth or the distance between them, so very few people at the time considered it totally convincing.

What people were looking for was empirical evidence that the Earth was actually moving, both revolving on its own axis and orbiting the Sun; it was providing those proofs that would prove difficult. Many thought that the most likely evidence consisted of the detection of stellar parallax, which should have been visible if the Earth really was orbiting the Sun.

I think most people will have encountered the concept of parallax during their education but just in case, for those who might have forgotten. Parallax is the apparent displacement of an object, due to an actual displacement of the observer. The demonstration you learn at school is to hold a finger up in front of your nose aligned with some point in the background. If you close your right eye your finger appears to move to the right and if you close your left eye to the left. This phenomenon of our binocular vision is how our brain estimates distance, comparing the two offset views that our eyes deliver. Because the distance between out eyes is vey small this only works for fairly close objects, a couple of hundred metres or so. Using technical instruments, we can increase the visual base line and measure greater distances. This is actually the basis of triangulation in surveying.


A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from “Viewpoint A”, the object appears to be in front of the blue square. When the viewpoint is changed to “Viewpoint B”, the object appears to have moved in front of the red square. Source: Wikimedia Commons

The ancient Greeks already realised that one could use parallax to determine the distance of celestial objects. If you view the same object simultaneously from two points on the Earth relatively far apart then they it will appear to align with different stars in the background sphere of fixed star. If you know the distance between the two observation points you can create a triangle and determine the distance of the observed object using a bit of simple trigonometry. Using this method Hipparchus succeeded in determining the distance between the Earth and the Moon. However, despite numerous attempts nobody succeeded in determining the distance to any other celestial object. The distances were too great and the resulting acute angle in the measuring triangle was far too small to determine accurately. This was the case even if one used the entire width of the earth’s sphere (about 13,000km), measuring the position of the desired object from the same point twelve hours apart. This is of course dependent on the daily rotation of the planet but is also valid if one assumes that it is the sphere of the fixed stars that rotate every twenty-four hours rather than the Earth.

With heliocentricity the length of the possible base grows to distance between the aphelion and perihelion of the Earths orbit, its nearest and furthest points from the Sun in its orbit, a distance of about 300 million km, although the exact size of this distance was not known in the Early Modern Period. It was assumed that given this base line it should be possible to measure the parallax and thus the distance of a star.


Stellar Parallax Source: Wikimedia Commons

In fact, in the pre-telescope age all attempts to measure the parallax of a star failed. Even the attempts to measure the parallax of any of the planets failed.


Tycho Brahe depicted sitting in his large mural quadrant at Uraniborg Source: Wikimedia Commons

Tycho Brahe believed he had determined the parallax of Mars, but he was mistaken. Tycho was the best astronomical observer of the sixteenth century with the most accurate instruments, he argued that is the parallax was too small for him to measure this implied for the heliocentric model a distance to the stars that was for him simply unimaginable. He couldn’t conceive a reason why there should be so much empty space between the orbit of Saturn and the nearest stars and so his dismissed the heliocentric model as a fantasy. Little did he realise that the distances involved were much, much larger even than those he had imagined in his wildest speculations. Tycho’s argumentation appeared reasonable to most of the other contemporary astronomers. The invention of the telescope in 1608 appeared, to those trying to measure stellar parallax, to be a game changer but this proved to be an illusion, at least for the next three hundred years.


Justus Sustermans – Portrait of Galileo Galilei, 1636 Source: Wikimedia Commons

Galileo, of course, saw the telescope as a possibility to finally detect and measure the stellar parallax that should be present in a heliocentric model. In his Dialogo (1632) he presents and describes two schemes for measuring parallax with a telescope. The first consists of fixing a telescope to a post, wall, whatever permanently direct at a point in the heavens and taking regular readings of the position of the stars visible through it, over an extended period of time. As we will see a variation of this method was actually utilised at the end of the century and again at the beginning of the eighteenth century with interesting results. The second method introduced the concept of differential parallax. Instead of viewing just one star against the background of the fixed stars, the astronomer observes a so-called binary star, i.e. two stars that appear to be comparatively close to each other, over a period of time looking for systematic variations in the observed distance between them.

Of interest, in particular with reference to the second method, is that in the Dialogo, Galileo presents these methods as something that astronomers could attempt in the future. This is interesting because Galileo actually made extensive efforts to apply the binary star method on various double star with very inconclusive results. In his published works, including the Dialogo, he makes no mention whatsoever of these failed attempts to detect parallax and his observation logs of these attempts remained unknown until discovered in 2004.

Throughout the seventeenth century various astronomers attempted to detect parallax with telescopes and failed. Although, some claimed to have actually observed parallax, all such claims proving to be false. At the end of the century Robert Hooke announced plans to apply Galileo’s first method with a vertical or zenith telescope, arguing, correctly, that this would remove the problem of atmospheric refraction in his observations and measurements. He constructed a large, somewhat ramshackle zenith telescope in his quarters in Gresham College, cutting holes in the roof and intervening floors to accommodate the instrument, which he christened his Archimedean Engine.


Gresham College, engraving by George Vertue, 1740 Source: Wikimedia Commons

As his observation object he chose Gamma Draconis, a not particularly prominent star, but one that is almost directly overhead in London. Hooke only made a total of four observation of Gamma Draconis with his new telescope, the fourth one of which showed the star to be further from the true zenith than the previous three. Hook broke off his observations and claimed that he had detected parallax. Why he broke off after only four observation, he never explained and the value that he claimed to have to observed was fairly obviously false and was not accepted by other astronomers.


Draco constellation map Gamma Draconis on the left at the bottom Source: Wikimedia Commons

As we shall see, to have any hope of success, this type of observational series has to be carried out systematically over a long period of time and all observation carefully controlled for accuracy and possible errors. The men, who realised this and carried out such a programme were the amateur astronomers Samuel Molyneux (1689–1728) and James Bradley ((1692–1762).


James Bradley by Thomas Hudson c. 1744 Source: Wikimedia Commons

Molyneux, a wealthy MP, decided to take up Hooke’s proposed method of detecting stellar parallax. He had a state of the art, precision, zenith telescope constructed by George Graham (1673–1751), London’s leading instrument maker, which he attached the chimney in his mansion in Kew, cutting holes in the roof and between floors to accommodate it.


George Graham artist unknown Source: Wikimedia Commons

He engaged James Bradley, who already had an excellent reputation as an observational astronomer, as his expert advisor and partner. Like Hooke the two started observing Gamma Draconis. Bradley had in advance calculated the expected movement of the star caused by parallax. The star displayed no movement during the first four observation during the first two weeks of December 1725. However, when Bradley observed on 17 December Gamma Draconis had perceptively changed its apparent position but the opposite direction to that expected from parallax. The two men stopped and thoroughly checked their entire technical set up and calculations to eliminate any possible error; they found none.



The two men continued to observe well into 1727 recording 80 observation during which Gamma Draconis appeared to journey south stopped turned and journey back northwards. During an entire year the star travelled a systematic route unrelated to parallax. Puzzled by their observation, Bradley acquired a second smaller zenith telescope with a wider field of view from Graham, which he installed in his deceased uncles house in Wanstead. Bradley’s uncle, James Pound (1669–1724), had also been an astronomer, who had introduced his nephew to the science. With his new telescope Bradley observed a total of about 200 relatively bright stars and confirmed the same behaviour in all of them. He was at a loss to explain the results of his observations.

Molyneux died in 1728 before Bradley solved the puzzle. The solution is said to have come to Bradley during a boat trip on the Thames. When the boat changed direction, he noticed that the windvane on the mast also changed direction. This appeared to Bradley to be irrational, as the direction of the wind had not changed. He discussed the phenomenon with one of the sailors, who confirmed that this was always the case. The explanation is that the direction of the wind vane is a combination of the prevailing wind and the headwind created by the movement of the boat, so when the direction of the headwind changes the direction of the windvane also changes. Bradley realised that the direction of the light coming from the stars was affected in the same way by the movement of the Earth orbiting the Sun. He and Molyneux had discovered stellar aberration and the first empirical evidence of the Earth’s orbit around the Sun. The more common phenomenon used to explain aberration uses rain. When one is standing still the rain appears to fall vertically but when one in walking the rain appears to slant into one’s face at an angle. The same happens to starlight falling onto the moving Earth.



Stellar Aberration: Stars at the ecliptic poles appear to move in circles, stars exactly in the ecliptic plane move in lines, and stars at intermediate angles move in ellipses. Shown here are the apparent motions of stars with the ecliptic latitudes corresponding to these cases, and with ecliptic longitude of 270°. Source: Wikimedia Commons

Bradley wrote up the results of his observations and his interpretation of them in a letter to Edmond Halley, the Astronomer Royal, in 1729, who had the letter published in the Philosophical Transactions of the Royal Society.


Two men set out to measure stellar parallax and failed but instead discovered the till then unknown phenomenon of stellar aberration. The heliocentric theory had acquired its first empirical evidence for the annual orbit of the Earth around the Sun 186 years after Copernicus first published his hypothesis. The world would have to wait somewhat longer for the first indirect evidence of diurnal rotation, one hundred years for the first detection of stellar parallax and somewhat longer than that for the first direct evidence of diurnal rotation. However, after 1729 no serious scientist doubted that the solar system was heliocentric.


Filed under History of Astronomy

9 responses to “The emergence of modern astronomy – a complex mosaic: Part XLV

  1. Just take my hat off to this profound and “short” (with respect to all the literature some has to study) story/summary about the parallax method in astronomy, including its pitfalls, barriers, and outcome – thank you Thony!

  2. Great piece, Thony. But I have reservations about this expression ’empirical proof’ you keep using. I suspect you mean ’empirical support’ or better ‘observational support’. Btw, I think you mean ‘theoretical proof’ in the case of Principia

  3. Todd Timberlake

    Hooke made a weak attempt to explain why he didn’t get more than 4 observations. He said his objective lens broke and after that he got sick and was unable to repair the telescope or take more observations. My impression is that Hooke was never one for extended investigations – his specialty seems to have been the kind of quick demonstrations he could perform at Royal Society meetings in his role as Curator of Experiments.

    What is really interesting, I think, is that Hooke’s four observations, although they aren’t much, almost exactly match the expected pattern from parallax for gamma Draconis. Of course, there is no way he could have actually detected such motions since, if anything, he would have seen aberration, but as you point out the aberration pattern is totally different (shifted by 3 months) from parallax. So either it is a remarkable coincidence that Hooke’s errors just happened to conform to the pattern of parallax, or else Hooke was just willing his data to be what he expected it to be. I suspect observer bias is the answer, and it’s not uncommon when dealing with observations that are just at the edge of what is perceptible. See Adrian van Maanen’s observations of spiral nebula rotations in the early 20th century. Norriss Hetherington has a whole book about such things.

  4. Pingback: The emergence of modern astronomy – a complex mosaic: Part XLV — The Renaissance Mathematicus | Die Goldene Landschaft

  5. adacanalis

    Good read!

    One of the things I find annoying in modern histories is the notion that the ancient astronomers chose geocentric because of human-centered thought, human privilege and religious bias.

    Whereas the truth is they were well aware of parallax, well aware that they could see none and, together with bad physics that had no clear concept of inertia, had absolutely no evidence for a moving Earth.

    The modern narrative of “clever us” vs. “dumb predecessors” is atrocious!

    • Over the years I’ve had numerous disputes with people, who claim that the rejection of heliocentricity in the early 17th century was purely due to religious prejudice. I always ask them to demonstrate, with the knowledge and instruments available at the time, that the Earth actually moves. For some reason none of them has every accepted the challenge.

  6. Phillip Harmsworth

    With regard to measuring the distance between the Earth and Sun, Michel van Biezen has a series of Youtube clips explaining how it was done by Aristarchus (4th c BC), Govaert Wendelen (1630) and Horrocks (1640). (I learn from Wikipedia that Wendelen published a defence of heliocentric astronomy in 1652.)

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s