The transit of Venus, trigonometry, and the size of the solar system.

[Jim__]

Everybody knows that Venus will transit the sun on June 5 - 6 (you need eye protection to watch). I did not know that Venus' transit is what was originally used to compute the size of the solar system. Wikipedia ( http://en.wikipedia.org/wiki/Transit_of_Venus ) describes the technique used for this computation (actually the computation of the distance of the earth from the sun - then using already known AU distances, the size of the solar system falls out):

Aside from its rarity, the original scientific interest in observing a transit of Venus was that it could be used to determine the distance from the Earth to the Sun, and from this the size of the solar system, by employing the parallax method and Kepler's third law. The technique involved making precise observations of the slight difference in the time of either the start or the end of the transit from widely separated points on the Earth's surface. The distance between the points on the Earth was then used as a baseline to calculate the distance to Venus and the Sun via triangulation.[12]

Although by the 17th century astronomers could calculate each planet's relative distance from the Sun in terms of the distance of the Earth from the Sun (an astronomical unit), an accurate absolute value of this distance had not been determined.

In 1627, Johannes Kepler became the first person to predict a transit of Venus, by predicting the 1631 event. His methods were not sufficiently accurate to predict that the transit would not be visible in most of Europe, and as a consequence, nobody was able to make arrangements to observe the phenomenon.

The first good estimates weren't obtained until the 1874 - 1882 transits, so the actual astronomical problem must be more difficult than the simple trigonometric description. Modern technology obviates the use of the technique described.

More details on the trig problem can be found here.

[longship]

1. Gladly R&K a Trig post

[eppur_se_muova]

2. A reminder that geometry means "earth measurement" ...

though it was originally meant in the sense of surveying.