Determining the Speed of Recession of the Galaxy Hydra

Classical Mechanics Level 5

The light emitted by a galaxy contains a continuous distribution of wavelengths because the galaxy is composed of millions of stars and other thermal emitters. However, some narrow gaps occur in the continuous spectrum where the radiation has been strongly absorbed by cooler gases in the galaxy. In particular, a cloud of ionized calcium atoms produces very strong absorption at 394 nm 394 \text{ nm} for a galaxy at rest with respect to the Earth. For the galaxy Hydra, which is 200 million ly away, this absorption is shifted to 475 nm 475 \text{ nm} . How fast is Hydra moving away from the Earth?

  • Speed of light is 299792458 m/s 299792458 \text{ m/s} .
  • Round your answer to the nearest integer.
  • Give your answer in m / s m/s unit.
Image credit: Wikipedia .


The answer is 55406280.

Farhabi Mojib by Farhabi Mojib , 23, Bangladesh

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1 solution

Relativistic Doppler Effect:

475 n m 394 n m = c + v c − v \frac{475 nm}{394 nm} = \sqrt{\frac{c+v}{c-v}}

v = 55406280 m / s v = 55406280 m/s

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