During a stay on the
"We therefore recommend again and again, to the curious investigators of the stars to whom, when our lives are over, these observations are entrusted, that they, mindful of our advice, apply themselves to the undertaking of these observations vigorously. And for them we desire and pray for all good luck, especially that they be not deprived of this coveted spectacle by the unfortunate obscuration of cloudy heavens, and that the immensities of the celestial spheres, compelled to more precise boundaries, may at last yield to their glory and eternal fame."
Halley prophesied that his paper would be "immortal", and indeed it was. His exhortations and detailed plans, projected beyond the grave, caused well-equipped expeditions to set out to far flung corners of the Earth to observe the 1761 and 1769 transits.
In 1761, Charles Mason and Jeremiah Dixon observed from
Having got there eventually, he decided to stay 8 years to make sure of
seeing the 1769 transit. Tragically, he missed this one too, because in an
otherwise cloud-free month a cloudy morning managed to totally obscure the
transit. To add insult to injury, when he returned to
An even greater number of expeditions set out to monitor the 1769 transit.
Amongst these was the famous voyage of Captain James Cook, which set up
an observing station in
A summary of the results of some of these expeditions is shown in Figure 10. As can be seen, the timings of ingress and egress permitted different chords to be plotted.
From the perpendicular distance between these chords, relative to the known angle subtended at the Earth by the diameter of the Sun, it is possible to compute the solar parallax .
In Figure 11, D = d . Lv/(LE - Lv ) (from similar triangles)
the ratio Lv / LE however was known from Kepler's Third Law. In cruder terms, it was equal to sin θ (where θ was the angle of greatest eastern elongation of Venus - see Figure 4)
Therefore, D = d . sin θ. LE/(LE( 1 - sin θ)) = d . sin θ/( 1 - sin θ)
Consequently, from the ratio D / H (based on Figure 10), H (the diameter of the Sun) can be calculated and hence the solar parallax and the distance to the Sun.
Figure 10: The Observed Tracks of Venus across the Face of the Sun during the Transits of 1761 and 1769
Halley had pointed out that the duration of the transit of Venus would be of the order of 7 hours. Venus would make approximately 1 arcsecond of progress per 14 seconds of time (for a central transit, given that the angle subtended by the Sun was about 31' 30" ). He reckoned that an error of 3 seconds in the measurement of time would produce only a 1% error in the parallax.
The results were not as good as expected. It proved difficult to discern exactly when the moments of contact took place (due to the 'black-drop' effect) and also the longitude of some of the observing stations was not known with sufficient accuracy. Nevertheless, the accuracy of the measurements represented a great achievement.
Figure 11: Halley's Method for computing the Solar Parallax
When all the results were fed back, the calculated solar parallax varied between 8.55" and 8.88". The modern accepted value is 8.794148".
It can be truly said, that the real distance from the Earth to the Sun - the 'Astronomical Unit' - was at last discovered. Kepler's laws had already enabled the relative distances of the planets from the Sun (in Astronomical Units) to be determined. Now - as a result of the selfless efforts and dedication of numerous astronomers, explorers, surveyors and sailors - the absolute dimensions of the Solar System could be fathomed.
Note : Or, at least, so say some books!
This story is given by A.Pannekoek 'A History of Astronomy',
Note : Please note that this simple
explanation is only intended to show that geometrical
relationships exist which allow the solar parallax to be determined by
measuring durations of the Transit of Venus at different locations. In
practice, Halley's method of durations requires the use of quite complex
trigonometry. To see how exactly this is done, old textbooks on spherical
astronomy need to be consulted - e.g "A Treatise on Spherical
Astronomy" by R.S.Ball (1908,