Satgen 201    Doppler Part 2     by GM4IHJ                   30th Jan 93
BID of this message is SGEN201  . Please use it if you retransmit this msg

If a satellite coming towards us is transmitting a radio signal,  the
signal heard by us is higher in frequency than the actual transmitted
signal.You can think of this as the satellite partially catching up on its
own signal and thereby compressing it , shortening its wavelength and
hence raising its frequency. In a similar manner a retreating satellite is
heard by us at a frequency lower than the one which it is transmitting,
having apparently pulled ahead of its signal thereby stretching it ,
increasing its wavelength and thereby lowering its frequency. The higher
the velocity of the satellite relative to our station , the greater this
doppler shift of frequency. Only when a satellite has no motion relative
to our station, ie at the closest point of approach where it has stopped
approaching us, but has not yet started to move away from us. Only then
when relative velocity is zero, do we get the exact transmitted frequency
with no doppler shift up. or down. How can we calculate the expected
doppler shift of the satellite signal, so that we will know exactly where
to tune ? Most amateur radio tracking software predicts the slant range
between the satellite and the ground station. So if the Keplerian elements
are predicting satellite position every two minutes ,we can get satellite
velocity relative to our station from two consecutive readings of slant
range 2 minutes apart. Eg 1212ut slantR 2236 kms : 1214ut slantR 1876 kms
Mean sat velocity at 1213ut = 360 kms / 120 seconds = 3 kms/sec
Please note that this method gives us velocity at the mid point of these
two readings. Not all software points this out.
Another problem encountered with doppler calculations, must be dealt with
before leaving velocity calculations and going on to calculate doppler
shift. This is a problem which occurs when people try to calculate maximum
doppler shift from, maximum satellite velocity. As one radio amateur put
it :- RS at 1000 km altitude does an orbit in 105 minutes : One orbit = PI
x 2 x (1000 + 6378 ) kms = 46360 kms: Sat speed = 7.36 kms/sec
Why therefore he says . "Does my software never calculate a speed above
6.36 kms/sec". In fact , his software is right and he is making the
mistake of assuming that the satellite is coming directly at him. It never
can. The satellite never points directly at your station . It can only
point at a spot 1000 kms above your station, when nearing closest approach
on an overhead pass . When the satellite is on your horizon coming
directly towards the spot above your station, its track pointing is
tangential to the earth's surface at the horizon. So a satellite such as
RS12 at 1000 kms altitude which sees the horizon 30 degrees around the
earth from it sub sat point, appears from your station to have a horizon
approach velocity of NOT 7.36 km/sec but one of 7.36 x Cosine 30 degrees =
6.36 km/sec. You are said to view the satellite from an angle of 30
degrees on its bow . Hence the decreased relative velocity. You never see
it from directly ahead or astern . So maximum relative velocity depends on
satellite height which is why as you will see , the higher the satellite
the lower the maximum relative velocity and therefore the smaller the
overall doppler shift. More on the actual doppler calculation and
measurement in future satgens. Remember Doppler may not seem to be
important , but it is the only thing you can use to find out what the
satellite is doing. There simple are no other clues unless the satellite
is signalling meaningful telemetry messages describing its state and its
environment. 73 de GM4IHJ @ GB7SAN