A distant star is traveling directly toward Earth with a speed of 32790 km/s. Wh

Question

A distant star is traveling directly toward Earth with a speed of 32790 km/s. When the wavelengths in this star's spectrum are measured on Earth, are they greater or less than the wavelengths we would find if the star were at rest relative to us?

The measured wavelengths are greater than what they would be if the star were at rest relative to us?
The measured wavelengths are less than what they would be if the star were at rest relative to us?

By what fraction are the wavelengths in this star's spectrum shifted?

Explanation / Answer

use doppler effect for light
f > frequecy
f(observed) = f(source) [(c+v)/(c-v)]^1/2 ------------- (1)

Here v is the relative velocity of source and observer and v is considered positive when the source is approaching. in wavelength terms
= c/f
flip (1), multiply by (c - speed of light)
(observed) = (source) [(c - v)/(c + v)]^1/2
when v=0, at rest, > (observed) = (source) >>>

(observed) = (source) [(c - v)/(c + v)]^1/2
v = 32790*1000, c = 3*10^8
(observed) = (source) [265160000/32790000]^1/2
(observed) = (source) [26516/32790]^1/2
(observed) = (source) [0.8992]
-------------------------------
fraction wavelength shifted=/= [(observed) - (source)]/ (source)
/= [0.8992 - 1](source) / (source)
/= - 0.1007
shows observed one is less than what would be observed when at rest

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