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1. Astronomers on Earth observe a feature at 442 nm in the spectrum of a distant quasar. However, it is known that this feature corresponds to 581 nm in the rest frame of the quasar. Calculate the speed of the quasar. Enter your answer as a fraction of the speed of light, positive if the quasar is approaching, negative if it's receding.
I used
It was easier for me to think about this in terms of frequency than wavelength, so I converted the wavelengths into frequency by using
c = speed of light
L = lambda, wavelength
f = frequency
u = speed of source
c/L = f
So 3e8/442e-9 = 6.79e14
3e8/581e-9 = 5.16e14
So the observed frequency is 6.79e14 Hz and the actual frequency is 5.16e14 Hz.
fobs=(1-u/c)femitted
6.79e14 = (1-u/c)(5.16e14)
1.316 = 1-u/c
.316=-u/c
-.316c=u
Now, this isn't right. I'm using (1-u/c) versus (1+u/c) because the relative speed of the object is negative if they're approaching, and the wavelength is getting blueshifted, so they're moving towards each other. However, that produces a negative answer, and the question states to enter a positive answer if they're moving towards each other.
Anyone see any mistakes in my work?
Thanks a lot in advance~
Homework Equations
I used
The Attempt at a Solution
It was easier for me to think about this in terms of frequency than wavelength, so I converted the wavelengths into frequency by using
c = speed of light
L = lambda, wavelength
f = frequency
u = speed of source
c/L = f
So 3e8/442e-9 = 6.79e14
3e8/581e-9 = 5.16e14
So the observed frequency is 6.79e14 Hz and the actual frequency is 5.16e14 Hz.
fobs=(1-u/c)femitted
6.79e14 = (1-u/c)(5.16e14)
1.316 = 1-u/c
.316=-u/c
-.316c=u
Now, this isn't right. I'm using (1-u/c) versus (1+u/c) because the relative speed of the object is negative if they're approaching, and the wavelength is getting blueshifted, so they're moving towards each other. However, that produces a negative answer, and the question states to enter a positive answer if they're moving towards each other.
Anyone see any mistakes in my work?
Thanks a lot in advance~