Measure of the height of a mountain of the Moon.

1. Paper and pen.
2. The program Salsa J (you can download this program in this page: http://www.houspain.com/gttp/salsaj) for the image proccesing.
3. Knowledge of:

Similar triangles

Estimate the height of a mountain of the moon.

In this exercise we only Know the diameter of the moon: 3476 Km. The piece of infomation that we don´t Know, we will find out by using the program SalsaJ for the image processing.

The objective of this exercise is to Know the height of mountains of the moon by usingMathematics.

You will can solve this exercise if you do the following steps:

1. You can download the following photograph if you click on them.
   
                        Monte Pico                                       Monte Piton
2. With the program SalsaJ open the photo of the previus step.
3. In the photo, the blue circles show the mountains that you can study.
4. We have to write the scale of the photo in the program SalsaJ, for this we only need to Know the diameter of the moon. 3476 Km.
5. What is the distance from the terminador to the mountain shadow (segment TB)? Terminador is the line that differentiate the illuminate zone of the not illuminate zone of the moon.
6. We Know the radius of the moon, because we Know the diameter of the Moon.
7. What is the length of the mountain shadow (the segment AM).
8. Calculate the height of the mountain. You remember the following points:

• The segment because the curvature is negligible, owing to the mountain height is lesser than the radius of the moon.
• The mountain is near of the terminador to reject the curvature the segment TB is a straight line.

• How we get the following figure?

BM = mountain height (we want calculate it)
OB = radius of the moon (We Know it)
AM = length of the shadow of the moon (we know it)
TB = distance of the mountain to the terminador.

• You can check your solves of this exercise, you look for the mountain height in internet.