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Radio signals toward Earth

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Imagine that a civilization in another planetary system is sending a radio signal toward Earth. As our planet moves in its orbit around the Sun, the wavelength of the signal we receive will change due to the Doppler effect. This give SETI scientists a way to distinguish stray signals of terrestrial origin (which will not show this kind of wavelength change) from intrerstellar signals.

(a). Use the average orbital speed of the Earth as 29.79 (km/s) to calculate the speed of the Earth in its orbit. For simplicity, assume the orbit is circular.

(b). If the alien civilization is transmitting at a frequency of 3000 MHz, what wavelength (in meters) would we receive if the Earth were moving neither toward nor away from their planet?

(c) The maximum Doppler shift occurs if the Earth's orbital motion takes it directly toward or directly away from the alien planet. How large is that maximum wavelength shift? Express your answer both in meters and as a percentage of the unshifted wavelength you found in (b).

(d) Discuss why it is important that SETI radio receivers be able to measure frequency and wavelength to very high precision.

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