Measuring the size of the Solar System – Parallax

By guest blogger Peter Bond

Edmond Halley’s method, which involved observations of a transit made from widely spaced places, was based on the principle of parallax. This uses the fact that objects appear to shift position against a fixed background if they are observed from two different places. The further the object, the smaller the parallax shift.

This principle can be shown by holding one finger in front of your face. Look at it with the left eye, then with the right eye. You will notice that the finger seems to shift position, even though it has not been physically moved.

If you move the finger further from your face and carry out the same experiment, you will notice that the amount of parallax shift is smaller. If the distance between your eyes is known, and the angle from each eye to the finger is measured, it is possible to use simple trigonometry to calculate the distance of the finger.

For the transit of Venus, observers on the Earth are separated by thousands of kilometres, so they will see the disc of Venus at slightly different locations on the Sun’s disc. By making observations from two widely spaced points on the Earth’s surface, and timing the start and end of the transit accurately at each place, you can work out the solar parallax, the apparent difference in the position of the Sun from those two locations.

By measuring the angular shift between the apparent locations of Venus across the Sun, and taking into account the baseline distance between the two observing sites, you can calculate the distance to Venus by using triangulation.

In practice, however, this is an extremely difficult measurement to make because the disc of Venus is so small (1/60 of a degree) and the parallax angles are very difficult to measure directly (1/120 of a degree). This is why astronomers use each entire path of Venus (the ‘chord’) across the Sun’s disc as a better way of determining the parallax angle.

An explanation of the calculation method used by Halley can be found here.

For your own transit of Venus parallax calculator, click here.

Today, distances in the Solar System are calculated with great precision through very different means, such as ground-based radar and time delays in radio signals from spacecraft.

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