An interstellar spaceship is leaving earth at a speed of, Ask an Expert

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An interstellar spaceship is leaving Earth at a speed of %u03B2 = 0.548 for a deep space expedition. The captain tunes the onboard microwave radio transmitter to f0 = 2.01 GHz to send his reports back to Earth.

a) To which frequency should we tune our receivers on Earth to have the best reception?

b) 112 years later the mission is completed, the spaceship turns around and returns to Earth with the same speed. To which frequency should our grandchildren tune their radios to receive the captain's reports?

c) What is the arithmetic mean of the down-shifted and the up-shifted frequencies?

d) What is the geometric mean of the down-shifted and the up-shifted frequency?

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