In the redshift of radiation from a distant galaxy, certain radiation, known to have a wavelength of 434 nm when observed in the laboratory, has a wavelength of 462 nm. (a) What is the radial speed of the galaxy relative to Earth? (b) Is the galaxy approaching or receding from Earth?
(a) The radial speed of the galaxy is 0.062c or .
(b) The observed wavelength is longer than the proper wavelength; hence, the galaxy is receding from us.
In astronomy applications, the velocities of galaxies are estimated using Doppler shifts. Doppler shift is the difference between the observed and proper wavelength of light. The wavelength measured in the rest frame of the source is called proper wavelength . And the detected wavelength is related to the proper wavelength as
Where, is the speed parameter.
Inserting the given values in the above equations
Hence the radial velocity of the galaxy is 0.062c or .
If the observed wavelength is longer than the proper wavelength, it implies that the galaxy is moving away from us and is said to be red-shifted.
If the observed wavelength is shorter than the proper wavelength, it implies that the galaxy is moving toward us and is said to be blue-shifted.
Here, the observed wavelength is longer than the proper wavelength; hence, the galaxy is receding from us.
An armada of spaceships that is 1.00 ly long (as measured in its rest frame) moves with speed 0.800c relative to a ground station in frame S.A messenger travels from the rear of the armada to the front with a speed of 0.950c relative to S. How long does the trip take as measured (a) in the rest frame of the messenger, (b) in the rest frame of the armada, and (c) by an observer in the ground frame S?
Figure 37-21 shows one of four star cruisers that are in a race. As each cruiser passes the starting line, a shuttle craft leaves the cruiser and races toward the finish line. You, judging the race, are stationary relative to the starting and finish lines. The speeds vc of the cruisers relative to you and the speeds of the shuttle craft relative to their respective starships are, in that order, (1) 0.70c, 0.40c; (2) 0.40c, 0.70c; (3) 0.20c, 0.90c; (4) 0.50c, 0.60c. (a) Rank the shuttle craft according to their speeds relative to you, greatest first. (b) Rank the shuttle craft according to the distances their pilots measure from the starting line to the finish line, greatest first. (c) Each starship sends a signal to its shuttle craft at a certain frequency f0 as measured on board the starship. Rank the shuttle craft according to the frequencies they detect, greatest first.
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