D) Observations that you can make in 2004

1) Single observations that are quick and easy to make

Make plans to record an image of the transit when Venus is on the mid-line of the face of the Sun (point A'). You then need to share your results with another observer who is located on the same longitude (meridian) and who will observe at more or less the same time (point B').

You have to measure the distances DA and Db (from the centre of the Sun CA and CB) as shown in the diagram. Obviously the diagrams must be adjusted to be the same size to allow DA and Db to be compared.

To obtain the highest accuracy you will need to take a photograph or make a still video image.

You can try to make a pencil sketch of a projected image but the problem will be that the image will drift across your screen as the Earth turns. This will make it difficult but not impossible to be precise.

We suggest you try a combination of methods in case one of them lets you down!

To calculate Db you need to measure the diameter of the image D, and DA and DB to the same scale. Then taking the angular diameter of the Sun, seen from the Earth as 30' (minutes of arc)

Db = (p / 360)((DB - DA) / D) = ........... radians

then

bs = 0.38248 Db = ........... radians

and the distance AB is

AB = 2 . 6378 . sin ((j1 - j2) / 2) = ...........  km

where j1 and j2 are the latitudes of the observers and the radius of the Earth, R = 6378 km. If the observers are in opposite hemispheres, the angle is (j1 + j2) / 2.

and finally the Earth-Sun distance

re = AB / bs =...........  km

If you want, you can find your own value for the angular diameter of the Sun but you will need to know the focal lengths of your telescope's eyepiece and objective lens and you will have to refer to an optics text book for the necessary formula.

2) Longer observations that are quite easy to make

If you are able to make observations throughout the transit, you will be able to plot the path of Venus and note the times of first and second contacts.

If you can observe for at least half an hour you can reconstruct the whole transit as follows. Record the exact starting and finishing times of your observations. On a scale drawing, mark a line to represent the path of Venus during your observations. Now extend this straight line until it touches the limbs (edges) of the Sun's image. This is shown in the diagram.

By simple ratios you can find the time for the total transit (for instance tA).

You then need to share your results with an observer who is located at a different latitude.

You will then have their transit time tB and so will be able to calculate the Earth-Sun distance, also known as the astronomical unit (1 au).

The great advantage of this method is that you do not need to be on the same longitude (meridian) as the other observer.

A discussion of the errors of these kind of measurements will be illuminating!

Good luck and good observing!!