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distance to the Moon [try it]


How far is the Moon? You don’t have to look up the answer in a book. You can measure it yourself, and quite easily at that. You will need an accomplice however.

For this, you will need some way to record the precise location of the Moon in the sky relative to the stars in the constellation it is in, and one of your team will need to travel to far distances. If you have a digital camera, or have some way of measuring angles from the horizon and from the zenith, you can use the principle of parallax to measure the distance.

See the figures embedded here. They are representations of what one would see from Delhi and Bangalore, early on 2011-mar-19 (a Full Moon day, and in fact one where perigee is the smallest all year), at the same instant. You can see the Moon as a white blob at the right edge near the middle, in the constellation Leo. At middle of the left edge is Saturn. Now, notice where the Moon is relative to the stars. It appears to be displaced slightly northwards when seen from Bangalore. This is because of parallax. Can you get an estimate of the distance to the Moon from these two figures?

These figures were made using XEphem, but rather than resort to software, you should physically take pictures of the Moon in the sky at the same time from two widely separated points, align them using the background stars, and measure how much the Moon has been displaced between the two pictures.

The width of the Moon is about half a degree. It looks as though the Moon has moved about half of that between these two images. Delhi is about 1750 km from Bangalore. What do you get for the distance to the Moon?

How good is your estimate? What can you do to improve it?

What is the uncertainty in your estimate?

Can you also measure the distance to Saturn from the same images?