The predictions of the Venus and Mercury transits in front of the Sun requires a good knowledge of the orbital movements of interior planets. It was possible starting from the beginning of the XVIIth century thanks to the work of Johannes Kepler (1571-1630) and to the publication in 1627 of the Rudolphines Tables named thus by Kepler in homage to its former protector, the emperor of Germany Rodolphe II of Habsbourg (1552-1612). Kepler predicts the Mercury transit of November 7, 1631 and the Venus transit of December 7, 1631 that it could not observe. It also found a period approximately of 120 years recurrence for the observation of the Venus transits. The Mercury transit of November 7, 1631 was observed in Paris by the astronomer Pierre Gassendi (1592-1655) "Le rusé Mercure voulait passer sans être aperçu, il était entré plustôt qu'on ne s'y attendait, mais il n'a pu s'échapper sans être découvert, je l'ai trouvé et je l'ai vu; ce qui n'était arrivé à personne avant moi, le 7 novembre 1631, le matin". This passage was also observed by three other people Remus Quietanus in Rouffach (Haut-Rhin, Alsace), the father Cysatus in Innsbrusck (Tyrol) and an anonymous Jesuit in Ingolstadt (Bavaria). The Venus transit was not observed because of the inaccuracies of the tables Rudolphines, the transit was to occur in Europe in the night from the 6 to December 7, 1631, actually the end of the passage was visible from the Central Europe.

The english father Jeremiah Horrocks (1619-1641) predicted the following transit of Venus for Sunday December 4, 1639 at 3 hours of the afternoon (November 24, 1639 of the Julien calendar); this prediction was in contradiction with the 120 years period found by Kepler. It observed this passage from its village of Hoole (close to Preston) by projecting the image of the Sun on a graduated paper and thus carried out the first measurement of a Venus transit in front of the Sun. Actually, it could not observe all the phenomenon, having stopped its observation to be occupied with its religious obligations. Using this observation, Horrocks calculated the position of the node of the Venus orbit; it estimated that the apparent Venus diameter was not to be higher than the minute of arc and that the value of the solar parallax was not to exceed 14", which corresponds to a distance Sun-Earth of approximately 14700 terrestrial radii (either approximately 94 million kilometers). His Venus in sole visa, in which he describes his observation, will be published by J. Hevelius in 1662. Other parts of his work on Venus will be published by John Wallis in 1672. This transit was also observed by William Crabtree (1610 - 1644) in Manchester. William Crabtree was a friend of Horrocks. He was so amazed by the observation that he did not make any measurement...

Determination of the solar parallax

The last law of Kepler makes it possible to know the size of the solar system except for a scale factor. The knowledge of only one distance between planets or a planet and the Sun is enough to calculate all the others. The solar parallax is the angle under which one sees the radius of the Earth from the Sun, the knowledge of the parallax is thus equivalent to the knowledge of the distance Earth-Sun. The measurements and calculations carried out since the antiquity largely underestimated the actual value of this distance. The following table gives the various known values:

The last three values were calculated using measurements of the parallax of Mars at the time of its opposition of September 1672.

The transits of Venus and Mercury

In 1677, on the island of Sainte-Hélène, Edmond Halley (1656-1742) observed the Mercury transit which took place on November 7. It then imagines a method to determine the solar parallax, therefore the distance Sun-Earth. It excluded the transits of Mercury, because the Mercury parallax is too small and its passages are more difficult to observe. His method is founded on the comparison of the times of the transit of Venus measured from several sites located at different latitudes. The difference between the times of transits observed gives access to the Venus parallax, then to the parallax of the Sun. The following Venus transits occurring in 1761 and 1769, Halley left to his successors the care to carry out the observations and to apply his method. His predictions and recommendations were published in the Philosophical transactions of the Royal Society in 1691, 1694 and 1716. The method of Halley consisted in measuring the time elapsed between the first and the last interior contact of the planet Venus with the solar disc in at least two sites having the greatest possible variation in latitude. For that, one has to go often very far and one was to carry out in these sites the preliminary observations in order to determine with accuracy their geographical coordinates, the latitude to deduce from it the parallax from planet and the longitude to synchronize the observations. By this method, Halley hoped to determine the solar parallax with an accuracy of 1/500 if the observation of the contacts were made with a precision of two seconds of time. The french astronomer Joseph-Nicolas Delisle (1688-1768) proposed, since 1722, another method relating to the observation of a single phase of the passage (first or last interior contact); this method allowed to increase the list of the possible sites of observations by adding all the locations where only one phase is observable. But he asked for a very good knowledge of the longitudes of the sites of observations, that was difficult to obtain in this middle of the XVIIIth century.

Note 1:

"the Mercure crafty one wanted to pass without being seen, it had entered sooner that one did not expect it, but it could not escape without being discovered, I found it and I saw it; what had arrived to nobody before me, November 7, 1631, the morning"