Lunar and Solar Diameters

On this page we give a summary of how you, applying your own Astronomy On Line data, may be able to measure the diameter of Sun and Moon.

Let us take a look at our Pinhole Camera. Any such camera or the equivalent mirror method works on the geometrical principle of scaled triangles:

Click on image to see larger version (28 K).

As you may see on the very first drawing above, the large shaded triangle is equivalent to the small triangle. This gives us the following mathematical relations:

During the 1996 October eclipse students from class 6A in Gymnasium beim Augarten, Vienna (Austria) did send these data:

"Mirror and Screen Method (distance mirror screen: 27,2 m) Width during the maximum: 25 cm. We hope our measurements will help you with your work to determine the distance and the size of the Moon"

Let us assume that during the August 1999 eclipse we will obtain results similar to what this group did back in October 1996.

During the August 1999 Eclipse the lunar distance will officially be 373 200 km.
Entering these values in the equation above you get:

This means a lunar diameter of: 3430 km to be compared with the official value: 3476 km.

Exercise 1:

Enter your own eclipse data, maybe including your own lunar distance and find your value for the lunar diameter.

Exercise 2:

Assuming we know the distance to the Sun as 1 AU = 149,600,000 km, now apply the same theory as above to find the physical diameter of the Sun!
Compare your value with the official value: 1,392,000 km. Show that the diameter of the Sun is nearly 100 times larger than the Earth.

Exercise 3:

An accurate measurement of the apparent solar diameter can be achieved as follows:
Mark the western (leading) edge of the Sun and time how long it takes before the other edge (the following eastern edge) passes this mark.

Knowing that the Sun roughly moves 360 degrees in 24 hours (15 degrees in 1 hour) you can calculate the apparent size of the Sun.

By repeating this timing several times an accurate value with no more than 1% deviation with a Pinhole Camera is possible!

You can improve your result if you correct for the solar declination (on August 11 at 12 h UT: +15,3 degrees).

Exercise 4

Applying some high school math (click for details) you convert the size of the projected solar image into a measure of the angular solar extension. Do this and compare with the official results given in the 2D Math Chapter.