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 0.800c, and the starship Endeavor is sent out toward the pulsar with a speed of 0.960c relative to Earth.

Part A

If an observer on Earth finds that 151 pulses are emitted by the pulsar every second, at what rate does an observer on the Endeavor see pulses emitted?

Explanation / Answer

Use the Gamma factor for each relative reference frame:

Gamma = 1/[sqrt(1 - (v2/c2))] where v is the relative velocity of an object with respect to the reference frame, and c is the speed of light in a vacuum (299 792 458 m/s).

Gamma for Earth relative to the Pulsar is 1.66667
Gamma for Earth relative to Endeavor is 3.57143

Based on the Earth-centered reference frame:
Gamma for Endeavor relative to the Pulsar is 1.90476

As the Gamma factor is dimensionally compatible with time, we can calculate the Endeavor's observation of the Pulsars period:

151 * 1.90476 = 287.6187 pulses per second

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