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# Doppler Shifts

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

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```       v
dfd = ---.f
c```
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### 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).
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### 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:

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```       2wr
dfd' = ---.f
c```
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### where:

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

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### 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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