The Relativistic Lighthouse · AI Generator #GEN-362E8732

Physics

Problem

A neutron star rotates with period

T = 1.0\;\text{s}

and emits a narrow beam of radio waves from a hotspot on its surface. The hotspot is located at distance

R = 10\;\text{km}

from the rotation axis. An astronomer on Earth observes this pulsar and notices that the received radio frequency varies periodically as the neutron star rotates. When the hotspot is moving directly toward Earth, the observed frequency is

f_{\text{high}} = 1420.8\;\text{MHz}

. When the hotspot is moving directly away from Earth, the observed frequency is

f_{\text{low}} = 1419.2\;\text{MHz}

. (a) What is the speed

v

of the hotspot as it orbits around the neutron star's rotation axis? (b) What is the rest frequency

f_0

of the radio waves emitted by the neutron star?

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