Can I build an instrument to measure the size of the Sun and of the Moon? (Intermediate)

How would I go about measuring how wide (in degrees) the disk of the moon appears? Can I use the fact that we are able to divide the celestial sphere in 360degrees? I was thinking of setting up 2 strings to line up with either side of the full moon, then measuring the time (t) it takes for one side of the moon to reach the other string. Using the ratio x/360deg = t/24 h, I would be able to calculate the apparent diameter of the moon (x).

Your idea on how to measure the size of the Moon is interesting, but you will have to be very careful to make accurate measurements. In the formula you gave, you should do x/360=t/(24h50min) because the Moon takes longer than 24h to come back to the same spot in the sky. Second, I don't see why you need two strings. Wouldn't one be enough? you just measure the time between each side of the Moon crosses it. The most problematic thing I can see is that if the Moon goes slightly on a diagonal path you will not get a good measurement. The best time to do your experiment would therefore be when the Moon is at its highest point in the sky, so it goes fairly straight (at midnight when there is a full Moon would be the best time).

If you want to compare the results from your experiment to something else, I tell you how to build a very simple instrument that will enable you to measure the diameter of both the Moon and the Sun. You will need a box, a ruler, some aluminum foil, and a needle. The device you are going to build is the same as you would use to look at a solar eclipse. Since I cannot draw things to explain you how to do it, have a look at this web page which explains it clearly.

If you build long enough of a box, you will be able to measure the diameter of the image of the Sun (or of the full Moon), which we will call d, and you will also know l, the length of your box. From that, you can get the actual diameter by doing: D=L*d/l where L is the distance to the object: L=150 000 000 km for the Sun, L=384 000km for the Moon. If you want, you can calculate the angular diameter, theta, by doing: theta=(d*180)/(l*Pi). You should get about 1/2 degree for both the Sun and the Moon.

If this doesn't work well for the Moon, I can think of another way of doing it. Tape a coin in your window, and tape one end of a string just on the side of the coin. Then looking with one eye, and holding the string just on the edge of your eye, walk back from your window until the coin exactly blocks the full Moon. Now l will be the length of the string between the coin and your eye at that point, and d the diameter of the coin. You can use the fomulas above to calculate the diameter of the Moon.

This website also presents another (slightly more complex) method of measuring the same thing.