Transit of Venus

Finding the distance of a remote object (1)
Finding the distance of a remote object (2)
Finding the distance of the Sun from the Earth

How do you find out how far the Earth is from the Sun?

How do you suppose astronomers found out the distance between the Earth and the Sun? It's not something you can measure, after all. The activity described here should give you an idea about what they do.

Finding the distance to a remote object (1)

Start by putting a ball (big enough to see clearly) about 30m away from you (outside, in a large hall, or similar). This is represented by the purple disc in the diagram on the right. Two people should then stand in positions A and B, as indicated on the diagram, preferably somewhere you can find a straight line between the two points (as on a football pitch, for instance). Put two metre rules on the ground at A and B (as shown by the short lines at A and B) so that they are at right angles to the straight line between A and B.

Now measure the angles marked in blue. The ball should be centrally placed between the two observers, so that these two angles are equal, so move either the ball or the positions of A and B until the angles are the same. Record these angles. Now measure the distance, d, between A and B. You should be able to use these observations, together with trigonometric results, to find the distance R.

Repeat this for different positions of A and B, different positions of the ball, and different angles. What happens if the angles at A and B are not the same?

Finding the distance to a remote object (2)

When astronomers use transits to find the distance of the Earth from the Sun, they actually measure time, and use this to find the parallax angle. In this next activity, you can use observations of time to find distance.

This activity needs somone who can walk so that their speed remains constant (not too fast or too slow). To help them walk in a steady rhythm, you could have other students singing or they could listen to music on a Walkman. Start by getting them to walk a measured distance, say 30m, and time then. It would be a good idea to do this several times, then take the average of the times.

Now, use the distance you measured and the time you observed to calculate an estimate for their average speed. How accurate do you think this estimate is? Can you get some idea of the least and greatest values that would be reasonable?

Then send this person somewhere further away (but not so far you lose sight of them!). Get them to walk along between two trees or a line on your field or similar, and measure the time they take. Use the speed you have already calculated together with the time they took to calculate the distance they walked. Do this several times for different distances. Again, can you calculate what the least and greatest sensible distances are - that is, get an idea of the error involved in your estimations.

Finally, if you can measure how far away they actually were in some way, you will be able to find out how accurate your estimates were.

Finding the distance of the Sun from the Earth

Astronomers measure the angle shown in red in the diagram above, which they call parallax, to find the distance of the Sun from the Earth (the astronomical unit, or au). As you can see, you need a planet in transit across the Sun to do this. The diagram on the right shows the general idea. The maths of how astronomers calculate the actual distance is quite difficult. If you want to have a look at how it is done, there are various websites which you could have a look at:

http://www.vt-2004.org/Background/Infol2/EIS-G4.html
http://skolor.nacka.se/samskolan/eaae/summerschools/TOV0.html
http://www.imcce.fr/vt2004/en/fiches/fiche_n05_08_eng.html

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