# Distance to the Sun

##### Class Practical

A Greek method and a more modern method, using data from a transit of Venus, to calculate the distance from Earth to the Sun.

#### Apparatus and materials

Data from the transit of Venus

#### Health & Safety and Technical notes

#### Procedure

Data from observations of the transit of Venus from observers at different latitudes on the Earth can be used to estimate the diameter of the Sun and hence the distance from Earth to Sun.

The method for using this data can be downloaded from the NASA website. This website has information about transits of Venus.

#### Teaching notes

**1** A modern version of finding the Sun’s distance from the Earth is to observe the transit of Venus. This observation is only for a privileged few as it has a cycle of over a century but then two transits happen in 8 years. Data is freely and publicly available from the transit that took place on 8 June 2004. The next transit of Venus will be on 5-6 June 2012. The next, after that, will not be until 2117.

**2** When the Moon seems to be exactly at half Moon to an observer on the Earth, the directions from the Moon to the Sun and to the Earth must make 90º. If you know the direction of the Sun and the Moon at that instant, you have the data for a right angle triangle with a right angle at the Moon and almost 90º at the Earth. A scale diagram can be drawn to find the ratio of ES to EM.

It is very difficult to fix the exact instant so the Greek estimate of 87º was far from right. (It was nearer to 89.85º, so much nearer to 90º, and so the distance was wrong by a factor of 20). It yielded, by simple geometry, the result that the Sun is 20 times further away than the Moon. We now know that the ratio is about 400.These early estimates therefore assumed that the Sun was quite small, because it appeared to be so near.

**3** See also the article by Arkan Simaan called *Transit of Venus* which was originally published in Volume 85 of the School Science Review in March 2004 but can now be viewed on the Venus 2004 website.

*This experiment was safety-checked in July 2007*