Wavelengths of light from a distant galaxy are found to be 0.5% longer than the corresponding wavelengths measured in a terrestrial laboratory. At what speed is the galaxy receding?

Question

Wavelengths of light from a distant galaxy are found to be 0.5% longer than the corresponding wavelengths measured in a terrestrial laboratory.  At what speed is the galaxy receding?

Asher Cohen · Accepted Answer

Speed at Which the Galaxy is moving = 1492.537313432836 km /sec

Red-Shift = (#Lambda_"L"# - #Lambda_"O"#)/ #Lambda_"O"# In this case, #Lambda_"O"# is the Observed Wavelength. #Lambda_"L"# is the Wavelength measured in a Laboratory. The wavelength that was observed is now 0.5% longer than the wavelength that was measured in a lab. #Lambda_"O"# = 0.005 * #Lambda_"L"# + #Lambda_"L"# Red_shift = (#Lambda_"L"# - (0.005 * #Lambda_"L"# + #Lambda_"L"#))/ (0.005 * #Lambda_"L"# + #Lambda_"L"#) Red_shift = (#Lambda_"L"# - 0.005#Lambda_"L"# - #Lambda_"L"#))/ ((1.005#Lambda_"L"#)) Shift_red = -0.004975 Redshift * Lightspeed equals speed. 0.004975 * 300000 km/sec is the speed. The galaxy is moving at a speed of 1492.537313432836 km/sec.

Ariana Acosta · Answer

undefined If the wavelengths are 0.5% longer, the redshift (z) is 0.005, and you can calculate the velocity using the redshift formula, which is velocity = z * speed of light.