Lab 2

Time is of the Essence

Introduction

The mainstay of world communications is the satellite-based telecommunications system. Although the average person can function without an understanding of the workings of a communications satellite system, it is a fascinating and growing technology that should be more widely understood. Inherent to this system is a time delay between sending and receiving messages. On-camera professionals benefit from understanding that this time delay exists. Technicians must compensate for this delay. Exact timing becomes important for establishing a programming schedule; this includes selling commercial time, or scheduling interviews between two or more individuals in different cities. To deal with questions of transmission delays requires an understanding of how a communications satellite system works.

The technology problem in this lab, directed toward questions of transmission time, deals with a range of issues concerning satellite communication systems. As you address the problem, you will be expected to use the scientific method which involves five steps – problem, question, hypothesis, test, decision. The scientific method will support and guide your thinking process as you work on the lab.

Technology Problem

Communication from one location on earth to another often makes use of satellites. Since signals do not travel instantaneously, there is a time delay between when they are sent and received. The technology problem is to calculate the time delays between various pairs of cities. You will first determine transmission delays for a simplified version of the problem where it is assumed that the earth is flat and the satellite remains in a fixed position above Chicago. After solving this idealized version of the problem, you will calculate time delays for a more realistic situation – the earth is spherical and the satellite is in a geostationary orbit above the equator. However, before starting to solve this problem, you will need to develop a strong knowledge base about satellites, communication satellites, orbits, coordinate systems, signal transmission rates, etc. This will lead you to do extensive research activities.

Bibliotechnology Research

In accordance with the first two steps of the scientific method (problem, question), you should pose and answer questions that will help you to develop a better understanding of telecommunications problems. You should investigate the basics of communication satellites before tackling the problem of transmission delays.

This leads to bibliotechnology research. A variety of web sites are available for this purpose. Key words or phrases that will help you find pertinent information on the web include: communications satellite, telecommunications, how satellites work, and satellite motion. The following are some areas of research that will support your work on this lab.

Areas of Research

• History of communications satellites
• Types of orbit (selection of different types yields different solutions)
• Kepler's Laws of Planetary Motion
• Newton's Law of Gravitation
• How are telecommunications signals transmitted?
  (Speed of light and accuracy in milliseconds or three decimal places)
• Satellite Placement
• Satellite Cost
• Speed of Light and Speed of Sound
• Height of satellites
• Latitude and longitude

You also need to locate sources that provide information about distances between cities.

Mathematics Tools

You will need to select mathematics tools that you can use to describe and solve the technology problem. Some mathematics tools that you should find helpful include:

• Pythagorean Theorem
• Distance = rate * time
• Right triangle trigonometry
• Methods for solving equations
• Dimensional analysis
• Concepts and methods involving precision and accuracy
• Spherical coordinates

Write a paper that includes a brief history of communications satellites and an in-depth explanation of satellite orbits. Be sure to cite your sources. Create a glossary of terms that are used in communications satellite technology. If you find any tables, diagrams or charts that are useful, include them also.

After writing the background paper on satellites, you should have a basic understanding of communications satellites and satellite orbits. You will be ready to address the problem of time delay between broadcasts at two different sites.

Model Development

Part A
Simplified Version of Problem – Satellite over Chicago

The following problem is a simplified version of the actual situation. This version does not take into consideration the curvature of the earth, and it also places a satellite in a geostationary orbit over Chicago, which is not possible.

The Los Angeles Dodgers and the Chicago Cubs are playing a Major League Baseball Playoff game in Dodger Stadium in Los Angeles. The game is scheduled to start in Los Angeles at 1 pm. Since it is a playoff game, it is televised throughout the United States. The network that is televising the game is headquartered in New York City. This is where the broadcast is controlled, where national commercials originate, and where the national commentators originate their messages. A satellite is located approximately one-third of the way across the country, in geostationary orbit above Chicago. (From your research, you should have discovered that it is impossible to place a satellite in geostationary orbit above Chicago.) This means that although the game is played in Los Angeles, the television signal is sent to the satellite directly above Chicago, and forwarded to New York. After it is received in New York, it is routed to various points, including a return to the satellite above Chicago. From the satellite it is then sent down to the local distribution point.

This process generates many questions:

Based on your research, what is a reasonable height for the satellite?

How far does the signal travel from the stadium in Los Angeles to the distribution site in Chicago?

At normal transmission rates how long does it take to get there? (i.e. What is the time delay for this transmission?)

What is the angle of elevation from Los Angeles where the signal originates to the satellite over Chicago? What is the angle of depression from the satellite to New York City?

Estimation is a useful tool in problem solving. Estimate what you think would be the distance from New York City to Chicago and from Chicago to Los Angeles via the satellite. Also estimate what you think is a realistic amount of time for a signal to travel the distances discussed (the time delay).

Develop and write down a plan that you can use to address this problem. Make a scale model of the communications situation. This can be done on paper, with a 3-D model or computer generated.

This is a good place to apply the third and fourth steps of the scientific method – to formulate and test a hypothesis about the effect of satellite placement on signal delay. You can think of the model you developed as a hypothesis about the situation. Test your hypothesis (model) by writing a program for your graphing calculator or computer that computes the distance and time given any two cities and one satellite. Write the program or series of programs so that given the distance between any two cities and the height of the satellite, the programs will output the distance the signal travels, the time it takes, the angle of elevation from one city to the satellite, and the angle of depression from the satellite to the second city.

Test your program

• Select 5 pairs of cities in the United States, including your own city. With the satellite over Chicago, use your program to calculate the distance the signal travels, the time it takes, and the angles of elevation and depression for each pair. Record your results.
• Select 5 different pairs of cities in the Western Hemisphere. With the satellite over Chicago, use your program to calculate the distance the signal travels, the time it takes, the angle of elevation, and the angle of depression for each pair. Record your results.

Part B
Realistic Version of Problem – Satellite Over the Equator

Change the position of the main satellite. You should have discovered in your research that the satellites in the main satellite communication network are in geostationary orbit over the equator. Determine an appropriate location for a satellite over the equator to transmit signals from locations in the United States to locations south of the equator.

• Select 5 different pairs of cities in the Western Hemisphere. In each pair one city is north of the equator; the other south of the equator. With the satellite over the equator, write a program to calculate the distance the signal travels, the time it takes, and the angles of elevation and depression for each pair. Record your results.

The solution of this problem requires use of longitude, latitude, and spherical coordinates.

Model Portfolio

As part of the solution to the technology problem, you will need to create a model portfolio. The model portfolio should contain a thorough description of the technology problem and its identifying characteristics. It should also include your paper on the history and orbits of communication satellites. You need to explain the mathematics, technology, and science you use to solve the problem. In addition, you need to include the mathematical and/or physical models you create. It is important that you keep a careful record of all of your work. The model portfolio should be complete enough so that someone else could follow your work step by step. The model portfolio will be very helpful when you present your thesis defense.

Thesis Defense

The thesis is the core of your model portfolio. The thesis defense involves presenting your model portfolio to an audience. The presentation will include:

1. a thesis statement regarding your conclusions pertaining to the placement of the satellite;
2. a scale model of the basic problem;
3. the mathematical solution to the problem including all calculations;
4. the basic algorithm for a graphing calculator or computer program(s) to calculate the distance, time, angle of elevation; and angle of depression; and
5. background research on satellites.