# Measure of the height of a mountain of the Moon.

## What do you need?

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

## Exercise.

Estimate the height of a mountain of the moon.

## Working out

#### What do we Know?

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.

#### What do we have to find out?

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

#### Work out.

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

- With the program SalsaJ open the photo of the previus step.
- In the photo, the blue circles show the mountains that you can study.
- 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.
- 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.
- We Know the radius of the moon, because we Know the diameter of the Moon.
- What is the length of the mountain shadow (the segment AM).
- 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.

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.