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Doppler Shifts

9006-011

 

9006-011a


For an object moving towards the receiver, the Doppler shift is given by:

 
       v
dfd = ---.f
       c
 

where:

v = line-of-sight velocity (3 x 104 m/s),
f = optical frequency (4.57 x 1014 Hz),
c = velocity of light (3 x 108 m/s).
 

Using the values given in parentheses, the motion of the Earth around the Sun at a velocity v = 30 km/s can produce optical Doppler shifts at 656 nm as high as:

 

fd = 46 GHz

 

Because of these very large Doppler shifts it must be possible to offset the frequency of the local oscillator laser by about this amount in order to bring the beat (I.F.) frequency down into the low GHz region.

 

9006-011b


Doppler shifts due to stellar and planetary motions are 3 x 105 as large for the visible optical link than for the microwave link, so we will need the ability to track the chirping beacon frequency, due to motions at both ends of the link.

Since the line-of-sight velocity will vary as a planet rotates or orbits its star, the Doppler shift undergoes a chirp. The maximum chirp or change in frequency of the Doppler shift of an object following a circular path is given by:

 
       2wr
dfd' = ---.f
        c
 

where:

w = angular velocity (7.27 x 10-5 rad/s),
r = radius of planet or orbit (6.371 x 106 m).

 


9006-011c


The maximum chirp introduced by the rotating Earth for a telescope mounted at the equator is given by substituting the values in parentheses into the previous equation:

 

fd' = 51 kHz/s

 

The chirp due to the motion of the Earth around the sun is obtained by setting = 1.99 x 10-7 rad/s and r = 1 A.U. = 1.496 x 1011 m:

 

fd' = 9 kHz/s

 

Thus, for a terrestrial mounted transmitting or receiving telescope, the main chirp effect is due to the rotation of the planet. Since we are generally assuming that both ends of the link are outside planetary atmospheres, these Doppler shift and their associated chirps may be very different, depending on the orbital period about the planet, or star. Due to motions at both ends of the link, Doppler shifts could be twice as large as indicated here. Alternatively, they may be very low if the aliens de-chirp their signals to cancel the induced chirp.

 

The Columbus Optical SETI Observatory
Copyright (c), 1990

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