Have you ever looked up at the night sky? Probably yes, but have you ever seen a satellite whizzing by? I have seen a lot of satellites and I am always amazed at just how fast they are. But just how fast are they? You could try and figure out how fast they are going by looking it up on the internet, but that would be too easy right? We like a good challenge and so we set out to try and figure out how fast they are going by looking at the doppler shift we can observe. If you have never done anything with an SDR (Software Defined Radio) this is a good starting project and it will show you what those great little devices are capable of.

Supplies

A computer
Any SDR with a reasonable frequency range]
An antenna tuned to the frequency you are trying to measure
Orbitron (a computer program

Step 1: Finding Your Satellite

If you have a favorite satellite, you could try and measure it's signal, but I have only tested the NOAA weather satellites. They have the advantage of having a signal in the 130 MHz range, so almost all SDR will be able to pick them up. Also, they are in sun-synchronous orbits, so they will reach everyone in the world. If you have chosen your satellite, you should download the program called 'Orbitron'. It is free software that enables you to see when your satellite will pass and at what angle it will pass.

Step 2: Making the Antenna

We need a right hand circularly polarized antenna tuned to 137 MHz to be able to receive the signal. I will use a simple V-dipole, but you can use any other design you like.

Step 3: What SDR to Use?

I will use the rtl-sdr v3 usb dongle. they work great for this kind of work and you can also use them to listen to airplanes talking to ground control and so many other things.

Step 4: Finishing the Hardware

We connect the antenna to the SDR (using coax-cable) and plug it in our computer. Fire up SDR# and tune in to a frequency of a known radio station. If you hear a clear signal, you did everything right. If not, check all of the connections.

Step 5: Now the Fun Begins!

Open up Orbitron and look for a pass when the satellite is almost vertical above you. We want the satellite to be as high in the sky as possible to get more accurate results. Because the world is a sphere ( at least the majority of the population thinks so), and our calculations will later assume a flat earth, we need it to pass as close to overhead as possible. If it is a really low pass, the calculations will think the satellite is going really slow because of the curvature of the earth and the relative motion between us and the satellite. Also open up SDR# and tune to the frequency of the satellite. In SDR# you have an option to record the signal. When you see the signal, start recording it. In the image you can see an example of a signal from a NOAA weather satellite.

Step 6: Processing the Information

With our recorded signal, we are now ready to calculate the relative speed between us and the satellite. I used Excel to do the calculations, but you can choose any program you like. This is a bit theoretical, but even I can understand it so everyone should also be able to understand it.

In the first column we write the time. We take the beginning of the recording as being 0.
In the second column, we write what elevation the satellite was at that time. Remember we can see the elevation in Orbitron. You can look back in time to see what the elevation was. Write this in radians, because Excel uses this for it's calculations. You can use the command RAD() to make it automatically convert degrees in Radians.
In the third column we write the observed frequency. Make sre this is as accurate as possible, because this will be what determines the accuracy in the end. We make sure we convert the MHz to Hz, because the formula will use this
.The fourth column contains the constant frequency of the satellite. While we see it as a changing frequency, the satellite sends out a fixed frequency. You can look this up on the internet, there are many good websites that contain this info. Make sure this is also in Hertz.
The next column contains the speed of light c (299 792 492 m/s).
Now for the sixth column we will be measuring the relative speed using the formula : E2*(1-(D2/C2)). If we translate this to the units we get : c*(1- (f(satellite) / f(observed) ). If you only want to know the relative speed, this is it! Now if you want to find the absolute speed, we need some other formulas.
This one is pretty simple =F2/COS(B2). We divide the relative speed by the elevation, and so we can calculate the absolute speed.
The other colums are optional and I used them to prove a point, but I wont cover them here.