Question

Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. The electromagnetic radiation we receive from this hydrogen gas has a Doppler-shifted wavelength of 1995 nm when it reaches earth. From experiments done on earth, we know the source wavelength is 1875 nm. What is the speed of the gas relative to earth

Answer 1

Therefore the speed of the gas relative to earth is μ = 0.06195c.

What is Doppler Shifting?

If a body producing radiation has a non-zero radial velocity in relation to an observer, the emission's wavelength will change depending on whether the body is moving closer to or farther away from the observer. The Doppler shift refers to this shift in the measured wavelength or frequency.

λobs = λs√(1 + μ/c)/(1 - μ/c)

λobs = Observed wavelength

λs = Wavelength of the source

c = Speed of light in vacuum

μ = Relative velocity of the source to the observer

Therefore replacing in the previous equation we have,

1995 = 1875√(1 + μ/c)/(1 - μ/c)

√(1 + μ/c)/(1 - μ/c) = 1.064

(1 + μ/c)/(1 - μ/c) = 1.064²

(1 + μ/c) = 1.064² × (1 - μ/c)

Solving for μ ,

(1 + μ/c)= 1.064² - 1.064² × μ/c

μ/c + 1.064² × μ/c =  1.064² - 1

2.132μ/c = 0.132

μ/c = 0.132/2.132

μ = 0.06195c

to learn more about doppler shifting go to - brainly.com/question/23841569

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