problem_5 - AST 822: Electromagnetic Radiation Problem Set...

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AST 822: Electromagnetic Radiation Problem Set 5: due Wednesday, November 9 1) An observer in the inertial frame of reference K sees a particle moving in the xy plane, with velocity u x = u cos θ and u y = u sin θ . The inertial frame of reference K 0 is moving relative to the frame K at a velocity v = βc along the x axis. In the K 0 frame, the particle’s velocity is u 0 x = u 0 cos θ 0 and u 0 y = u 0 sin θ 0 . a) If the particle being viewed is a photon, what are sin θ and cos θ in terms of θ 0 and β ? b) What is the aberration angle Δ θ θ 0 - θ in the limit β ¿ 1? c) If the Earth is moving on a circular orbit with a velocity v = 30 km s - 1 , what is the maximum aberration you expect in the position of stars over the course of a year? (This eFect is the “aberration of starlight”, ±rst measured by James Bradley in AD 1728.) 2 a) In an inertial frame K 0 , a neutron is at rest, and thus has a lifetime t 10 3 s. In an inertial frame K , the neutron is highly relativistic, and has an energy
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problem_5 - AST 822: Electromagnetic Radiation Problem Set...

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