|
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
Espresso Engineering 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
where:
± 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.
Posted August 30, 2022
|
