The sun (and the earth with it) are traveling at 2.00×10 4 km/s toward a star th

Question

The sun (and the earth with it) are traveling at 2.00×104 km/s toward a star that is 45.0 light years away. (A light year is the distance light travels in one year.)

If an astronomer on earth measures light of wavelength 523.4 nm from this star, what frequency would an observer at rest with respect to the star measure for the light it emits?

If an astronomer on earth measures light of wavelength 523.4 nm from this star, what wavelength would an observer at rest with respect to the star measure for the light it emits?

Explanation / Answer

Given that

The sun (and the earth with it) are traveling at 2.00×104 km/s toward a star =2.00*107m/s

We know that speed of light is (c) =3*108m/s

Then beta =v/c =2.00*107m/s/3*108m/s =0.06

a)

If an astronomer on earth measures light of wavelength from this star (lamda for the observer ) =523.4 nm =523.4*10-9m

From the doppler effect

Lamdaobserved =lamdaemittedSqrt(1-beta/1+beta)

Lamdaemitted =lamdaobserved*(1/0.94) =523.4*10-9m*(1/0.94) =556.808*10-9m =557nm

and the frequency emitted is f =c/lamdaemitted ==3*108m/s/556.808*10-9m =5.38*1014Hz

b)

The wavelength would an observer at rest with respect to the star measure for the light it emits is given by

The lamda emitted is Lamdaemitted =lamdaobserved*(1/0.94) =523.4*10-9m*(1/0.94) =556.808*10-9m =557nm

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