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 0.960crelative 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

Use the Gamma factor for each relative reference frame:

Gamma = 1/[sqrt(1 - (v^2/c^2))] 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 1.70

Gamma for Earth relative to Endeavor is 3.57

Based on the Earth-centered reference frame:

Gamma for Endeavor relative to the Pulsar is 3.57-1.70 = 1.87

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

152 * 1.87 = 284.45 pulses per second

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