The model of the solar system that Johannes Kepler presented in his mature work had dimensions significantly larger than any of the other geocentric, heliocentric, or geo-heliocentric systems on offer in the early part of the seventeenth century. Although by 1630, Kepler’s heliocentric system with its elliptical orbits had become one of the two leading contenders for the correct model of the cosmos, the vast majority of astronomers stayed with the much smaller dimensions, as presented by the Ptolemaic, Copernican and Tychonic systems. Even such an ardent promoter of the Keplerian system as Ismaël Boulliau (1605–1694) preferred his own calculated value of c.1,500 e.r. for the astronomical unit to Kepler’s more than double as large value.
There were however two notable exceptions amongst the Keplerians, but before we look at the first one we need to look briefly at another idea of Kepler’s on the cosmic dimensions that did have a major impact throughout the seventeenth century. Kepler a major fan of Pythagorean harmony theory believed that the sizes of the planets were proportional their distances from the Sun. This concept was immensely popular in the seventeenth century and even extending into the eighteenth; Bode’s Law, which suggests that, extending outward, each planet would be approximately twice as far from the Sun as the one before is just such a concept. This led to increased efforts throughout the seventeenth century to determine both the apparent and the actual sizes of the planetary discs as viewed through telescopes. Before the invention of the micrometer later in the century these efforts produced extremely contradictory results.
In 1631 Pierre Gassendi (1592–1655) became the first person to observe a transit of Mercury, which had been predicted by Kepler in his Rudolphine Tables.
The result of his observations that stirred up the most discussion was the fact that Mercury was very much smaller than had been determined in all previous observation, whether with or without a telescope. This result caused a lot of astronomers to question or even reject Gassendi’s observations.
Kepler had also, correctly, predicted a transit of Venus for 1631, which was however not visible from Europe.
Kepler had, however, not predicted the transit of Venus that was due to take place in in 1639. The young Keplerian astronomer Jeremiah Horrocks (1618–1641), who had bought a copy of the Rudolphine Tables and both corrected and extended them realised that there would be a transit in 1639 and informed his friend and fellow Keplerian astronomer William Crabtree (1610–1644) and the two of them observed the transit. As with Gassendi and Mercury, they observed that Venus was very much smaller than had been previously believed and in his reports on their observations, Horrocks stated that they had vindicated Gassendi. Using similar arguments to those used by Kepler, Horrocks determined the solar parallax to be a maximum of fourteen minutes of arc and the astronomical unit thus 15,000 e.r. Unfortunately, Horrocks died before he could publish his findings and they only became known when published by Johannes Hevelius (1611–1687) in 1662.
Today, less well known that Horrocks is the Flemish, Keplerian astronomer Govaert Wendelen (1580–1667) (also referred to as Gottfried Wendelin).
He had actually used Aristarchus’ half-moon method to determine the astronomical unit in 1626. In a publication on 1644 he used an astronomical unit of c. 14,600 e.r. making him the first to put a value greater than Kepler’s in print.
When he was compiling his astronomical encyclopaedia, Almagestum Novum (1651), the Jesuit astronomer Giovanni Riccioli (1598-1671), a supporter of a semi-Tychonic system, investigated various values for the astronomical unit including Wendelen’s.
Wedelen’s value was, as stated above c. 14,600 e.r. and that of Michel Florent van Langren (1598–1675), another Lowlands astronomer, most well-known for his map of the Moon,
which was c. 3, 400 e.r. Riccioli took an average of these two values and presented as his own value of 7,300 e.r. Following the publication of Horrocks’ work in 1662 both Christiaan Huygens (1629–1695) and Thomas Streete (1621–1689) started arguing for the significantly larger values for the astronomical unit of Kepler and Horrocks but Huygens admitted quite freely that with his value he could err by a factor of three in either direction. As should be very clear, by this point in the century, there was no unity amongst astronomers on the value of the astronomical unit and they were very much groping around in the dark as to the true value.
In 1672 there was a return to Tycho’s attempts to determine the parallax, and thus the distance, of Mars at opposition. Kepler had already calculated the correct relative distances of the planets, so only one correct absolute distance was necessary to determine all of them and both Jean-Dominique Cassini (1625-1712), the director of the French national observatory in Paris,
and John Flamsteed (1646–1719, who would go on to be appointed the first Astronomer Royal,
decided that their best bet lay with determining the parallax of Mars, now they had advanced telescopes with crosshairs and micrometers.
Flamsteed’s observations were a very lowkey effort made from his then home-base in London. Cassini, however, launched a major international programme to observe Mars in opposition, with a whole team of observers in Paris and the dispatch of Jean Richer (1630–1696)
to Cayenne in French Guiana to make observations there. Here we come up against an interesting historical phenomenon. Both Flamsteed and Cassini came up with figures for the solar parallax and the astronomical unit that are reasonable approximations for the correct figures. Flamsteed found the parallax of Mars to be at most fifteen seconds of arc, which made the Sun’s parallax seven seconds of arc and the astronomical unit 29,000 e.r. Cassini’s figures were twenty-five seconds of arc for Mars’ parallax and 22,000 e.r. for the astronomical unit. Richer found the parallax of Mars to have a maximum of perhaps twelve or fifteen seconds of arc. The modern value is c. nine seconds of arc for solar parallax and c. 23,500 e.r. for the astronomical unit, so problem finally solved or? Why is this an interesting historical phenomenon? The answer is quite simple what Flamsteed, Cassini and co. were actually measuring, although they didn’t realise it at the time, was the limit of the measurement accuracy of the instrument that they were using.
On a sidenote, Richer was sent to Cayenne, which is very close to the equator to finally solve the problem of the atmospheric refraction. Since antiquity astronomers had been well aware of the fact that the accuracy of their observational measurements was affected by the light coming from the celestial objects under observation being refracted by the Earth’s atmosphere. From Ptolemaeus onwards they had used an error factor to correct for this, but this factor was at best an informed guess. An observation made directly overhead on the equator is free of refraction, so a comparison of the observations made by Richer in Cayenne and those made in Paris, would and did deliver an accurate figure for the necessary refraction correction.
Cassini was well aware of numerous problems in his measurements and his subsequent calculations and spent a lot of time fudging his figures. A man, who normally rushed into print with his discoveries, he took twelve years to finally publish the results of the 1672 measurements. Despite his own reservations about what exactly he had measured and how reliable those measurements were, he however remained by his conclusion that the astronomical unit lay somewhat over 20,000 e.r.
This twenty thousand plus figure, for the astronomical unit, from Cassini and Flamsteed came to be accepted by almost all European astronomers in the early eighteenth century, including Isaac Newton, who had originally determined a solar parallax of a minimum of twenty seconds of arc, much larger that Flamsteed and Cassini. The one notable exception to this general acceptance amongst astronomers was Edmond Halley (1656–1742), who did not accept the Flamsteed/Cassini determinations of the parallax of Mars and thus the solar parallax and astronomical unit based on those determinations. In his opinion the instruments used were not capable of discerning the angles that they had claimed to have measured.
Halley did not think that the Mars parallax method was fit for purpose and suggested an alternative method for determining the astronomical unit. In 1676, Halley, whilst still a student, was sent by the English government to the South Atlantic island of St Helena to map the southern heavens as a navigation aid for English mariners. Whilst there he observed a transit of Mercury. Up to this point in time, transits of Mercury had only been used to determine the size of the planet, but Halley was aware of a proposal made by the Scottish astronomer, James Gregory (1638–1675), in his Optica Promota (1663).
Gregory outlined how transits could be used to determine solar parallax. Halley was able during his observations of the transit to record the both the moment of initial contact between Mercury of the Sun and the moment of final contact. On his return to England he discovered that the French astronomer, Jean Charles Gallet, in Avignon had also observed the transit. Combining Gallet’s results with his own he determined a parallax for Mercury of one minute six seconds of arc and for the Sun of forty-five seconds of arc. However, he did not regard these results as being very accurate.
Rejecting the Mars parallax method, Halley now became a propagandist for Gregory’s transit method. In 1702, in his Astronomiae physicae et geometricae elementa,
David Gregory, James’ nephew, stated that for an accurate solar parallax measurement people would have to wait for the 1761 transit of Venus but in the meantime, he accepted Newton’s values.
In 1716, Halley published a paper in the Philosophical Transactions of the Royal Society, Dr. Halley’s Dissertation of the Method of Determining the Parallax of the Sun by the Transit of Venus, June 6, 1761, in which he claimed that such a determination would be accurate to one part in five hundred. From this point on he continually drew astronomers’ attention to his proposal, well aware that he wouldn’t live long enough to observe the transit himself.
In 1761 and then again in 1769 astronomers from all over the world travelled to good observation points equipped with the latest in astronomical instrument and telescope technology to observe the transits of Venus. It turned out that for various reasons the observers were not actually able to achieve the accuracy that Halley had forecast not least because of the black drop effect that prevents accurate measurement of the exact moment of first contact.
Despite all of the problems, the Venus transit of 1761 was the first true determination of the astronomical unit. Over the subsequent centuries that determination was continually improved, and it meant that from 1761 the absolute dimensions of the solar system from the Sun out to Saturn were now known if not exactly accurately. The question that remained open was the distance to the fixed stars and it would be some time before that problem was finally solved.