Question

Some observations reported on an astronomical object (quasar 3C-9) suggest that, when it emitted the light that has just reached the earth, it was moving away from the earth at a speed of about (4/5),c (a) One of the lines identified in its spectrum has a wavelength of about 1200 A when emitted from a stationary source. At what wavelength must this line have appeared on the observed spectrum of the quasar? (Note: 1 Å= 10-10 m and c = 3 × 108 m/s.) (b) Quasars emit energy at such a huge rate that astronomers believe they must burn out in a relatively short time. If the lifetime of 3C-9 were assumed to be 106 years as measured in its own rest frame, over what total span of earth time would radiation from it be received at the earth? (Assume that its velocity relative to the earth remains constant.)

Answer 1

Given that some observations on a reported on an astronomical object suggest that when it emitted the light that has just reached the earth. The observed wave length is (Relativistic case) lambda = lambda_0 squareroot 1 + v/c/1 - v/c = (1200 A^0) middot squareroot 1 + 4/5/1 - 4/5 = (1200 A^0) squareroot 1.8/0.2 = (1200 A^0) squareroot 9 (1200 A^0) (3) = 3600 A^0 \r\n The time (concept of time diaction) is t = t_0 /squareroot 1 - v^2 /c^2 = 10^6 years/squareroot 1 - (4/5)^2 = 10^6 years /squareroot 1 - (0.64) = 10^6 years /0.6 = 16.67 times 10^5 years t = 16.67 times 10^5 years