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Some discoveries need a large telescope. The first observed transit of Venus needed a small one, a sheet of paper and a young man who trusted his own calculations more than the published tables. This post covers how Jeremiah Horrocks predicted and observed the 1639 transit, works through the measurements he recorded, and looks at what his reasoning got right and wrong.
Who was Jeremiah Horrocks?
The historian Allan Chapman's paper for the International Astronomical Union, Jeremiah Horrocks, William Crabtree, and the Lancashire observations of the transit of Venus of 1639, is the clearest modern account. Horrocks studied at Emmanuel College, Cambridge, and was "no more than 21 or 22 years old at most in 1639". Chapman argues that he was probably too young to be the curate of Much Hoole, as legend says, and more likely worked there as a schoolmaster or tutor while assisting in church.
He was already an original astronomer. By 1638, when he was about 20, he had correctly worked out that the Moon's orbit is an ellipse. His friend William Crabtree, a cloth dealer in Salford, had realised that the published astronomical tables were unreliable and that serious work meant observing and measuring the sky for yourself.
How did he predict the transit?
Kepler had predicted transits of Mercury and Venus in 1631 and believed that Venus would not cross the Sun again for 130 years. Chapman explains that by mid-October 1639, from his own observations of Venus and the disagreements between tables, Horrocks concluded that Kepler was mistaken and that a transit would occur on 24 November 1639 (4 December in the modern calendar). The trouble lay in the numbers in the tables; our post on Kepler's laws of planetary motion covers the laws themselves.
What did he see?
Horrocks projected the Sun's image through a small telescope onto a 6-inch circle drawn on paper and divided into 360°. To be safe he watched on 23 November too. On the day itself, clouds and duties kept interrupting. In the 1859 English translation of his account, he writes that at about fifteen minutes past three in the afternoon "the clouds, as if by divine interposition, were entirely dispersed", and a perfectly round spot had already entered the Sun's disc.
He made three measurements of the distance between the centres of Venus and the Sun before sunset:
3.15 p.m.: 14′ 24″
3.35 p.m.: 13′ 30″
3.45 p.m.: 13′ 0″
Crabtree, in Salford, glimpsed the planet through a short break in the clouds. Chapman notes that both men found Venus perfectly round and black, an opaque body rather than a glowing one.
How big did Venus look? A worked example
Horrocks wrote that the Sun's diameter was to Venus's "as 30′ to 1′ 12″". Work in arcseconds: 30′ = 1,800″ and 1′ 12″ = 72″.
Ratio. 72 ÷ 1,800 = 0.04, so Venus looked one twenty-fifth as wide as the Sun.
Modern check. The NASA Venus fact sheet gives an equatorial radius of 6,051.8 km and a mean distance of 41.39 million km at inferior conjunction. Angle = diameter ÷ distance = 12,103.6 ÷ 41,390,000 = 2.92 × 10⁻⁴ rad. Multiply by 206,265″ per radian: about 60″. NASA lists 60.0″.
Compare. Horrocks's 72″ is about 20% too large. In his letter to Crabtree of 26 October 1639, quoted in the 1859 book, Horrocks noted that Kepler gave Venus's diameter as 7′, or 420″, seven times too large, and Lansberg 11′. His direct measurement was far closer.
Rate of approach. From 3.15 to 3.45 the distance between centres shrank from 864″ to 780″, that is 84″ in 30 minutes, or 2.8″ per minute.
Then the solar parallax, the angle Earth's radius makes as seen from the Sun. Chapman records that Horrocks arrived at 14″, though by a line of reasoning now known to be false.
Distance from parallax. Distance = Earth's radius ÷ parallax in radians. 14″ = 14 ÷ 206,265 = 6.79 × 10⁻⁵ rad, so the distance is 1 ÷ 6.79 × 10⁻⁵ ≈ 14,700 Earth radii. Chapman gives "15 000 Earth radii". The true value, from the NASA Earth fact sheet, is 149.6 million km ÷ 6,371 km ≈ 23,500 Earth radii.
Common mistakes: mixing arcminutes and arcseconds (1′ = 60″), forgetting to convert to radians before using a small-angle formula, and reading step 4 as Venus's full speed, when it is only the rate at which the gap between centres closed.
If small-angle problems trip you up, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
What happened to his work?
Chapman records that Horrocks wrote up the observations in Venus in Sole Visa and then died suddenly on 3 January 1641. The manuscript passed through several hands until Johannes Hevelius printed it in 1662. It was later astronomers, starting with Edmond Halley's idea of timing transits from distant stations, who used transits to measure the Sun's distance. Our post on Friedrich Bessel and stellar parallax continues the parallax story.
What can a student take from Horrocks's way of working?
Check the source. He found the error by comparing tables, not by accepting one.
Prepare for the worst day. He watched a day early and used every gap in the clouds.
Record numbers, not impressions. Three timed measurements let others recompute his results centuries later.
Separate data from theory. His measured size of Venus held up; his theory-based parallax did not.
Try it now: convert Crabtree's measured diameter of 1′ 3″ to a fraction of the Sun's 30′ and compare it with NASA's 60″.
