Amateur radio operators who engage in satellite communications by now are very familiar with needing to compensate for Doppler frequency shifts. Author D. Ripani writes in this May 1958 issue of Radio & TV News magazine how he was caught off guard by the need to compensate for relative motion between the satellite and his fixed receiver. He needed to continually readjust while tracking the Explorer 1 satellite (launched February 1, 1958). Nowadays, many (probably most) Hams use software to automatically track and tune transceivers based on readily available ephemeris data published on orbital paths. Due to elliptical* orbits that vary in altitude above the Earth's surface, the Doppler shift is not a constant for any satellite.
Mentioned is the calculated Doppler shift of ± 2,900 Hz based on Explorer's orbital speed of about 18,000 mph. The included screenshot is from my RF Cafe Calculator Workbook (free download) Doppler Shift calculator, which agrees with Mr. Ripani's estimate.
I do need to take exception with the author's claim that the velocity of propagation of the signals, in both his train whistle sound and radio signal examples, changes depending on relative closing and opening velocities of two entities. In fact the velocity of the sound/radio wave does not change regardless of the relative speeds of the train or satellite and the listener; that is why the apparent frequency changes. Both the speed of light and the speed of sound are constant in a given medium**.
* A circular orbit is elliptical with an eccentricity of 0; a straight line is an ellipse with an eccentricity of 1.
* For supersonic sound waves, the compressed portion of the wavefront at the front of the object move faster than Mach 1. However, this is not so for light sources. Recall the unofficial Einsteinian Commandment regarding special relativity: "Thou shalt not add thine own speed directly to the speed of thine fellow traveler."
Receiving "Explorer's" Radio Signals
By D. Ripani, W9JAQ
Some puzzling aspects concerning signals from our first earth satellite are cleared up here.
The reception of 108.00 mc. and 108.03 mc. radio signals from Explorer I, and future satellites operating in the v.h.f. band, clearly demonstrate two interesting phenomena that may prove puzzling at first.
The first is the "Doppler Effect." Recalling high school physics, "Doppler Effect" was usually illustrated by imagining an observer standing at a railroad crossing and a train rushes by with its whistle blowing. As the train approaches this observer, the whistle's pitch sounds higher in frequency and as the train recedes the pitch becomes lower. While the train is directly abreast of the observer, the whistle's true pitch is heard. Obviously, the whistle has not changed its pitch. What has changed, though, is the velocity of propagation. As the train approached the observer the relative velocity of propagation, in relation to the observer increased and, consequently, the whistle's pitch rose in frequency. As the train sped away, the velocity of propagation decreased and the apparent frequency dropped. While the train was abreast of the observer, the relative velocity of propagation did not change and the tone heard was the true sound of the train whistle.
Like so many others, the author relegated "Doppler Effect" to some obscure corner of the brain and forgot it, that is, until the first time he listened for the Explorer on 108.03 mc. - and couldn't hear it. Using a low-noise, crystal-controlled converter feeding a Collins 75A4, set for 800-cycle bandpass, nothing was heard until the receiver was tuned about 2 kc. higher in frequency. At 108.032 the signal was heard just above the noise level. And when it had finally faded out about 9 minutes later, it was transmitting on , about 108.028 mc.; a total shift of approximately 4000 cycles. Dusting off the old physics books revealed a formula for calculating Doppler shift as applicable to sound waves, but with minor alterations, it is suitable for determining frequency shift.
± ƒs = VF/984
± ƒs = plus and minus maximum frequency shift.
V = speed of the satellite in feet per second.
F = satellite frequency in megacycles.
With the Explorer's velocity of about 18,000 m.p.h., or 26,400 feet per second and a frequency of 108.03 mc., the value is approximately ± 2900 cycles.
This total shift of almost 6 kc. holds true for a satellite passing directly overhead but in most cases the satellite will pass at some distant point thereby lowering somewhat the total frequency shift. Here in Wisconsin, at a point nearly one thousand miles away, the maximum shift proved to be about 3200 cycles. A quick substitution of Sputnik's frequency of 20 mc. in the formula (same approx. speed as Explorer) gives an answer of ± 500 cycles - which explains why most listeners did not notice the Doppler shift on Sputnik's signal. On the other hand the Doppler shift can be a real problem in space communications unless automatic frequency control devices are incorporated in the receivers - as jets, using single-sideband communications have already discovered. In fact, as an interesting sidelight, a few minutes with the formula will reveal some pertinent as well as troublesome future communications problems that may need solving when super-speed spaceships take off. Using a speed of 90,000 m.p.h. and a frequency of 200 mc., this Doppler shift can amount to 50 mc.!
The other interesting observation involves the orbiting time. Explorer's time of complete orbit was given as almost 115 minutes, yet our clocked intervals came to 121 minutes. This proved puzzling until it was recalled that although the Explorer requires only 115 minutes to return to the same spot in space, the earth beneath it has in the meantime moved almost 2000 miles further east and for "line of sight" reception of Explorer's signal, the satellite had to continue for an additional ninth of an hour, about 6 minutes, to get in radio range.