# Labs from Chicago, Fall 1993 : Doppler Effect and Satellites.

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

This is meant to be handed out to the students.

## Doppler Introduction

Last summer you might recall (or maybe you won't because you weren't here) that you did a lab on the Doppler effect. This is just a fancy name for the fact that when ever something that is putting out waves moves relative to something else, then the frequency of the waves "heard" by someone else changes. Doppler, himself, tested this effect by putting a trumpet player on a railroad car. When the car was stationary you heard a pure note, let's say it was a "c". When the car, with the trumpeter, was moving towards Doppler, then he heard a higher note, a "d". And when the car moved away, he heard a note lower than "c", a "b".

Maybe you have heard an El train here in Chicago when it is going to pass up your stop. (This always seems to happen to me when the temperature outside is below zero!) The engineer blows the whistle. He hears just one, unchanging, pure tone. You, on the platform hear the note change. First, it is higher when the train approaches, then it quickly lowers as the train passes and heads away from you. What's happening is that the frequency of the wave is changing, like in the diagram above. Don't forget that higher frequency means higher notes and a lower frequency means a lower note.

There's a formula for this effect. It reads like this:

[Frequency Shift]/[Frequency] = [Speed of Source]/[Speed of Sound]

## Satellites and the Doppler Effect for Light

Satellites don't have horns, but they do have telemetry beacons. Last week we listened to the beacon for the RS 12 satellite. The content of the beacon's message was in Morse Code. We won't worry about that for now. You might recall, that we had to constantly change the frequency that the radio was set at to keep the note we heard sounding the same. The radio has a way of adjusting the frequency you hear depending on where you set the dial. With Morse Code the radio wants to produce a particular sound frequency (that is, a tone) that we can hear. Then, we kept this tone constant by varying the receiver's radio frequency all during the pass.

This may seem a little confusing, but the only thing we need to remember is that the radio dial measures the actual radio frequency received when the tone is the loudest. The satellite gives off radio waves, so the above equation must be modified for light waves. Let's also go to using symbols. Here they are:

• D= Frequency Shift ( in KHz(*)) In this case, this will be the maximum total frequency shift you heard
• F= Frequency of Satellite Beacon at rest (in KHz)
• V= Speed of the Satellite ( in kilometers per second) In this case, this will be the maximum speed change of the satellite.
• C= Speed of Light (in kilometers per second)
(*)Footnote:KHz is the symbol for frequency units. It stands for Kilo Hertz. Kilo means a thousand and Hertz means one cycle per second. The audio frequency we heard when the radio was beeping was 0.8 KHz or 800 cycles per second. The satellite's beacon is in the tens of thousands of KHz and is due to radio waves.

D/F = V/C

## Measuring the Speed of Light

We can actually turn around what we know about the Doppler effect and using radio data on the satellite to measure the speed of light. The reason we can do this is because the radio is very accurate and the satellites move very fast.

Here's the data for a pass. It shows the time and the actual observed frequency (the beacon is is 29,408 KHz = F in the above equation).

```Wednesday, December 15, 1993     ------  Orbit #14347  ------
Local      Doppler(KHz)

3:38:00 PM    29,408.618
3:39:00 PM    29,408.614
3:40:00 PM    29,408.606
3:41:00 PM    29,408.591
3:42:00 PM    29,408.563
3:43:00 PM    29,408.514
3:44:00 PM    29,408.424
3:45:00 PM    29,408.264
3:46:00 PM    29,408.24
3:47:00 PM    29,407.776
3:48:00 PM    29,407.601
3:49:00 PM    29,407.501
3:50:00 PM    29,407.446
3:51:00 PM    29,407.416
3:52:00 PM    29,407.398
3:53:00 PM    29,407.389
3:54:00 PM    29,407.384
```
Plot these Doppler shifts versus time in the plot on the next page. (Hint! You probably should do some rounding on the numbers above.)

[Graph paper doens't work in hypertext.]

From the data, what is the maximum frequency shift?

_________________________________KHz. (=D)

Recalling that the F= 29,408 KHz, then what must D/F be?

________________________________

Doppler tell us that this last number is just the difference in the satellite's speed divided by the speed of light.

We already figured out the satellite's speed last week. We figured it in Km/hour. Here we need it in Km/sec -- it is 7.4 Km/s. If we could see the satellite coming straight at us and straight away from us, this would mean that the total difference in speed of the satellite during the pass would be 2X 7.4 Km/s or 14.8 Km/s. In reality, the satellite moves at a slight angle to us when we first see it. This introduces a slight factor from trigonometry (which we won't get into). This number is 0.87. So, the V in the equation above is now 14.8 km/s x 0.87 = 12.9 km/s. This is the speed difference during the entire satellite pass. It is the V in the Doppler equation.

Now, using the space below, plug the last number as well as the ratio of frequencies you found above into the Doppler Equation. What value do you get for the speed of light?