Problem 11. If a source emitting light at wavelength Xem is moving away from you at speed v the you observe its wavelength at Aob according to the following equation for Doppler shift in special relativity (with 3=v/c) dob Xem 1. Using Eq. (5.2), show that the redshift z when ve can be written as z = 8 +0 (3²) Here we have neglected all powers of 3 higher than 2. Find dz/dß at 3 = 0. 2. Find 0(3²) term in Eq. (5.3) 3. Calculate z if a galaxy is receding at 3000 km/s? (5.2) (5.3)

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Problem 11. If a source emitting light at wavelength Xem is moving away from you at speed u the you observe
its wavelength at Aob according to the following equation for Doppler shift in special relativity (with 3 =v/c)
Aob
Xem
1. Using Eq. (5.2), show that the redshift 2 when u < c can be written as
z = 3+0 (8²)
(5.2)
(5.3)
Here we have neglected all powers of 3 higher than 2. Find dz/d3 at 3 = 0.
2. Find O(3²) term in Eq. (5.3)
3. Calculate z if a galaxy is receding at 3000 km/s?
4. If the galaxy emits light with frequency 500 THz, what is the frequency at which this light is observed?
Transcribed Image Text:Problem 11. If a source emitting light at wavelength Xem is moving away from you at speed u the you observe its wavelength at Aob according to the following equation for Doppler shift in special relativity (with 3 =v/c) Aob Xem 1. Using Eq. (5.2), show that the redshift 2 when u < c can be written as z = 3+0 (8²) (5.2) (5.3) Here we have neglected all powers of 3 higher than 2. Find dz/d3 at 3 = 0. 2. Find O(3²) term in Eq. (5.3) 3. Calculate z if a galaxy is receding at 3000 km/s? 4. If the galaxy emits light with frequency 500 THz, what is the frequency at which this light is observed?
Expert Solution
Step 1

Given the doppler shift formula as:

λobλem=1+β1-βredshift, zz=1+β1-β-1  =1+β-1-β1-β   =1+β1/2-1-β1/21-β1/2 Using the Binomial expansion formula, 1+xp=1+px+pp-1x22!+.....x<1, here β=x=vc<1

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