# Labs from Chicago, Fall 1993 : Satellite Footprints.

Dr. Jim Sweitzer
Labs written for the CARA Space Explorers, Fall 1993

This is meant to be handed out to the students.

## Introduction

In this short investigation your group will discuss and learn about what a satellite "footprint" is and how to determine its size. The footprint of a satellite is very important in communications because it tells us which and when we can communicate with or through a satellite.

Work in your groups to answer the following questions. The completed work sheets are due at the end of this class period.

## 1. How light travels

Discuss among yourselves what you know and/or think about light.

a. Describe briefly what you think light is.

b. How does your group think light travels, in straight lines or in curved lines?

c. If you think it travels in straight lines, list two or more facts that support your claim.

d. If you think light travels in curved lines, describe what you would see if you were at a corner and a friend were around the corner. (See the picture below.) You should also draw how the light might travel. Write your description of what happens in words to the right of the picture.

Although we haven't proven it yet, radio waves are a type of light, just like the light that is illuminating this room. We can't see radio waves with our eyes, but our radio receivers can. We can't make radio waves with a light bulb, but our radio transmitters can. All you need to know now is that the radio waves we will be talking about move the same way light moves.

## 2. How far can you see?

a. What's the farthest anyone in your group has seen? (Forget about the stars, let's just think now about seeing things on the Earth.) Were you up high or low on the ground? Can you recall how far you saw?

b. Suppose the Earth were a perfectly flat disk of radius 6,378 km and you were standing on a mountain top right at the center. How far could you see? Draw your line of site on the following picture. (Hint: The horizontal line, which is just the surface of the Earth goes on to a distance of 6,378 km.) Neglect the fact that the atmosphere would dim your view. (See picture below.) If you turned in each direction, how much of this flat Earth's surface could you see?

c. But the Earth isn't flat. The following picture is a cross-section of the Earth with an exaggerated mountain. Imagine someone is at the top of the mountain, but too small to see in this picture. Draw how far a person could see in each direction along the Earth's surface. How much of the Earth's total surface area do you think they could see? Estimate the fraction of its area. (Be careful with this one, the Earth is a sphere.)

## 3. How far can satellites "see?"

Now, your group should figure out how far you could see if you were riding with a satellite and looking towards the Earth. Use the following diagram and draw the greatest distance each satellite can see for the altitudes I have given below. You will need to use a ruler and bend it slightly to measure along the curve of the Earth. On this diagram the scale is 1mm = 80 km. Fill in the right column of the table with your answers. If you have time, sketch a plot of the relationship between satellite altitude and how far it can see along the surface of the Earth.

## 4. Who can "see" a satellite?

a. Using the map on the following page, draw four circles showing how far each of the satellites listed on the previous page can "see." It's very important to note that this is also the only region on Earth that can "see" or communicate with the satellite when it is over that part of the Earth. This circle is called the footprint of the satellite. Assume each satellite is located right above the North Pole. The scale on this map is 10 mm = 1,223 km. Then, fill in the following table with a simple yes or no in each box answering whether the satellite can be seen from this location or not.
```                                       Locations
Satellite at   Chicago   Top of Alaska   Iceland   Scotland
North Pole
-------------------------------------------------------------
1. Shuttle

2. Iridium

3. Globalstar

4. Ellipso

```
b. As a satellite orbits the Earth what happens to its footprint?