# II.5 Lunar Craters

Astronomy On Line students - in a first, joint project of its kind - have evaluated the distance to the Moon.

Their result: 412 000 km, was very close to the real value: 390406 km.

On this page - we give a summary of how we - applying Astronomy On Line Data - are able to measure one more important factor - the Lunar diameter.

Let us take a look at our Black Box Camera. Any such camera - or the equivalent mirror method - will work on the geometrical principle of scaled triangles :

Figure 1. Click on image to see larger version (JPG, 28k).

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

Figure 2.

During the eclipse - the lunar angular diameter (0.26 Deg) was nearly alike the solar angular diameter (0.27 Deg).

These pictures were taken by Astronomy On Line students close to the Full Moon, two weeks later:

Figure 3.

They applied in both cases the same instruments - a second-hand 500 mm tele photo lens - mounted in front of a CCD camera. This mosaic makes it reasonable for us to assume that both the sun and the moon had approximately same angular diameters.

Several groups have applied box cameras - or the equivalent mirror method.

Quoting from one of the reports - send by the students from class 6A in Gymnasium beim Augarten group in Vienna (Austria):

.......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....

Entering these values in the equation above you get:

Figure 4.

This means a Lunar Diameter of : 3800 km - to be compared with the official value : 3476 km. - only 9 percent off !!!

Congratulations to the students in 6A !

Exercise 1:

Enter your own eclipse measurement "w" values - or enter the data from other groups.

Exercise 2:

Assuming we know the distance to the Sun as 1 AE = 149,600,000 km - now apply the same theory as above to find the physical diameter of the Sun !

Compare with official values : 1392000 km. Show that the diameter of the Sun is nearly 100 times bigger than that of the Earth.

Exercise 3:

Repeat the blackbox camera measurements - or the similar mirror method on a sunny day. Use your own data to perform exercise 2.

### Measure the Size of a Lunar Crater

The triangle method applied above also works on even more sophisticated instruments, like e.g. CCD equipped telescopes.

The picture below shows a Lunar Crater - called Copernicus. These photos were taken by Astronomy On Line students - working with a CCD equipped 16-inch Schmidt telescope. This instrument had an effective length of f = 2.5 metres.

In order to proceed - you need to know the size of our picture.

CCD cameras are small - similar to the tiny negatives you may apply in modern pocket cameras.

In our case - the vertical dimension of our "negative" is 6,5 mm.

Figure 5. Click on image to see larger version (JPG, 19k).

Show that the Copernicus crater (situated in the lower half of the image) has a dimension on our "negative" equal to only a fraction of this : 0.57 mm.

No need to tell you that the real crater is of course much bigger than 0.57 mm...

Again - we apply our distance - and the triangle derived formula from above and get :

Figure 6.

Apply your pocket calculator - and show the diameter of this crater is nearly 100 km !

Exercise 4

Identify the craters below on a Lunar Map. Estimate the diameters.

Figure 7.

Exercise 5

Photograph the Moon craters yourself. There are several methods - the most easy is simply to focus your camera to infinity - and hold or mount it behind the eyepiece of your telescope. If everything is correctly lined up - and in focus - you may within a number of tries get very nice pictures ! Reports and images are welcome !

### Where do these Craters come from ?

Figure 8. Click on image to see larger version (JPG, 21k).

Until about 1920-1930 - these Moon craters were WRONGLY believed to be of volcanic origin.

Investigating moonlike Earth craters like the Canyon Diabolo in Arizona (USA) scientists found evidence of huge energy and pressure - conditions far above what was seen in volcanic craters. Examples are known from Canada - where 80 meters of rock had been melted like if it was made of butter. The source of these Moon and Earth craters had to be impact by meteorites or comets.

Today about 150 IMPACT craters are known worldwide - more are to be discovered - but on planet Earth these geological structures sooner or later wear down due to our planets rain, frost and wind.

In start of the 1990s a Petrol Mining Company found evidence of a huge impact crater below the Yucatan peninsula.

The age of this 300 km wide crater is precisely 65 million years - coincident with the extinction of e.g. the dinosaurs.