Question

Space probes communicate with controllers on Earth using radio waves. Suppose a probe has a radiotransmitter that operates at a frequency of 220.0 MHz when at rest relative to the observer. This probe is now wandering the solar system. The signal you pick up from the probe is shifted 2.275E+4 Hz lower in frequency than the rest frequency given above. How fast is the probe traveling and is it traveling towards or away from Earth? (assume it is either traveling directly towards or directly away from Earth. You must get boths answers correct at the same time.)

Answer 1

According to the given problem,

a)From the doppler equation

f' = fₒ {1 / (1+v/c)}
Received freq = f', Emitted freq = fₒ, v = velocity of source*and c = speed of radio wave = 3*10⁸ m/s (* -v if source moves towards receiver) .

fₒ/f' = (v/c)

2.275*10⁴ = 220*10⁶ [v/3*10⁸]

v = 3.10*10⁴ m/s

b) A lower received frequency is a red-shift and the velocity is +ve ,so the probe is moving away from Earth.

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