Space probes communicate with controllers on Earth using radio waves. Suppose a

Question

Space probes communicate with controllers on Earth using radio waves. Suppose a probe has a radiotransmitter that operates at a frequency of 202.0 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 2.405E+4 Hz higher 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.)

Explanation / Answer

f' = observed frequency = 2.405 x 104 Hz

f = actual frequency = 202 x 106 Hz

c = speed of wave = 3 x 108 m/s

v = relative velocity

using the formula

f' = f (1 - (v/c) )

2.405 x 104 = (202 x 106) (1 - (v/(3 x 108)))

v = 2.99 x 108

towards earth

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