A pulsar is a collapsed, rotating star that sends out a narrow beam of radiation

Question

A pulsar is a collapsed, rotating star that sends out a narrow beam of radiation, like the light from a lighthouse. With each revolution, we see a brief, intense pulse of radiation from the pulsar. Suppose a pulsar is receding directly away from Earth with a speed of 0.810c, and the starship Endeavor is sent out toward the pulsar with a speed of 0.950c relative to Earth. If an observer on Earth finds that 152 pulses are emitted by the pulsar every second, at what rate does an observer on the Endeavor see pulses emitted?

Explanation / Answer

The important data here are the apparent pulse rate as seen on Earth, and the Endeavor's speed relative to Earth. If Endeavor is going toward the pulsar, the frequency it sees isn't affected by whether it's putting Earth behind it or approaching Earth. Thus the situation is identical to approaching an Earth transmitting pulses at 154/s, and we can ignore the pulsar's speed relative to Earth. So, using the Lorentz transform, we have beta = v/c = 0.96 f1/f0 = sqrt((1+beta)/(1-beta)) = 7 Freq. observed on Endeavor = 7 * 154 = 1078 pulses/s See the ref. for an explanation.

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