Space Travel & Doppler

SPACE TRAVEL & DOPPLER

Charles Hobson BA BSc(hons) G0MDK

Many events that have occurred during the latter half of the 20th century were once considered to be in the realm of science fiction. What comes to mind are the Sputniks, Couriers, Space Stations, Apollo Moon Landings, and various Space Vehicle visits to nearly every planet in the Solar System. Even today, manned space travel to Mars is in the planning stages. It doesn’t take much imagination to realize that space travel is upon us now and will become commonplace like air travel is today. Tourists are already purchasing and getting rides on orbiting spacecraft. Presently, manned expeditions to Mars would take several years: not very attractive to tourists for obvious reasons. Never the less, travel throughout the solar system is expected to become routine in the foreseeable future. For this to happen ten-fold increases in rocket propulsion and new communication systems will be needed.

Communications equipment as we know today is quite sophisticated and is becoming more so every day. It is in this area where the Radio Amateur [1] has always taken an active role. For example, Radio Amateur have been bouncing signals off the Moon (EME), constructing revolutionary low noise microwave receivers and experimenting with the new Software Designed Radio (SDR). SDR is currently revolutionizing the radio receiver, as we know it. It can be safely said that Radio Amateurs are still the pioneers of radio communication.

This article will now focus in on Space Vehicles communicating between each other and the Earth. Specifically, attention will be given to the Doppler aspects of the signals. This is where signal frequencies shift up and down for approaching and departing Spacecraft. See figure 1. below.

1 Doppler shift is not a recent discovery. Astronomers noticed it in the 19th century while observing distant galaxies. Certain galaxies appeared reddish colour indicating their recession into deeper space at high velocities. Red light is at the lower end of the visible spectrum. For example, red has a longer wavelength (lower frequency) than blue (higher frequency). From this information, astronomers were able to calculate actual velocities of receding galaxies. The astronomical term for this is “redshift”.

Doppler radar was developed during the 1940’s. It was used for determining the approach speed of landing aircraft. Today, police use Doppler radar for measuring the speed of automobiles.

What has redshift and Doppler radar have to do with space communications? Well, because of the anticipated speeds of Spacecraft, Doppler shift has to be taken into account in the design of their transmitters and receivers. For example, the received signal on Earth from a spacecraft departing at 15kms-1 and transmitting 10GHz would be 9.9995GHz, 500kHz below the transmitted frequency. By the same token, the received signal would have shifted upward by 500kHz from the spacecraft approaching Earth at 15kms-1. Furthermore, The spaceship receiver would experience the same shift from an earthbound transmitter at 10GHz. As you can see, typical transceivers as we know them today wouldn’t do very well in this kind of scenario: Spaceships operating at various speeds in the 10’s of kms-1, would experience Doppler shifts ranging from ~ minus 1MHz to +1MHz and greater. See the following chart:

Spaceship Spaceship Earth Rcvd. Freq. Earth Rcvd. Freq. Doppler speed Xmtr. Freq. Spaceship Spaceship Shift (kms-1) (GHz) departing (GHz) returning (GHz) (kHz) 5 10 9.99983333 10.000166667 166.667 10 10 9.99966667 10.000333333 333.333 15 10 9.99950000 10.000500000 500.000 20 10 9.99933333 10.000666667 666.667 25 10 9.99916667 10.000833333 833.333 30 10 9.999.0000 10.001000000 1000.000

Note: 30kms-1 is 18.66 miles per second or 67000 miles per hour

c  v  The formula for calculating Doppler frequency is: fd  f    c 

Where: fd = signal frequency received from vehicle f = vehicle transmitting frequency v = vehicle velocity in metres per second c = 299,792,458ms-1 for extreme accuracy but 300,000,000 ms-1 ok Notes: 1. f and fd can be kHz, MHz or GHz, but both must be the same units 2. c and v can be in ms-1 or kms-1, but both also must be the same units 3. c = 300,000,000 ms-1 or 300,000kms-1. 4. v is negative for closing vehicles and positive for departing vehicles

Following is a sample calculation:

2 A space vehicle is closing at 10kms-1 and transmitting at 8000MHz. Find the received Doppler signal frequency.

300,000,000ms-1 - -10000ms-1  300,000  10 8000MHz    8000MHz Fd =  -1     300,000,000ms   300,000 

= 8000MHz x 1.00003333  8000.26667MHz

The Doppler frequency shift is 266.67kHz above 8000MHz.

Now consider spaceships equipped with 10GHz transmitters and travelling at relative speeds of up to 30kms-1. They would receive signals from each other at frequencies between 9.999GHz to 10.001GHz depending on how fast and in what direction everyone was travelling. This means that the receiver would need to look at a 2MHz bandwidth. This is exactly what “Software Designed Radio” (SDR) receivers can do. Fascinating! Can you imagine looking at a display showing a spectrum of signals from 10GHz transmitters based on their relative speeds? Beam me up Scotty!

[1] Link to a news report dated December 2005