What's the observed wavelength for a red hydrogen line (rest wavelength equals 656nm) coming from a star moving at 30,000 km per s (3x104 km per s) Away from the Earth?
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Let's do this using both the non relativistic and relativistic version of the Doppler shift equation
delta L/L = v/c where L is the wavelength and delta L is change in L
since the motion is away from earth, the line is redshifted to longer wavelengths
delta L/656nm = 3x10^4km/s / 3x10^5km/s
delta L/656 nm = 0.1
delta L = 65.6 nm or L observed = 656nm + 65.6 nm = 71.6nm
this speed is 1/10 the speed of light, so we should also consider the relativistic equation for Doppler shift
delta L/L = (Sqrt[1+v/c]/Sqrt[1-v/c]) - 1
v/c=0.1, so this becomes
delta L/L = Sqrt[1.1/0.9] -1 = 0.1055
or delta L = 0.1055*656nm = 69.23nm and L observed = 725.2nm
delta L/L = v/c where L is the wavelength and delta L is change in L
since the motion is away from earth, the line is redshifted to longer wavelengths
delta L/656nm = 3x10^4km/s / 3x10^5km/s
delta L/656 nm = 0.1
delta L = 65.6 nm or L observed = 656nm + 65.6 nm = 71.6nm
this speed is 1/10 the speed of light, so we should also consider the relativistic equation for Doppler shift
delta L/L = (Sqrt[1+v/c]/Sqrt[1-v/c]) - 1
v/c=0.1, so this becomes
delta L/L = Sqrt[1.1/0.9] -1 = 0.1055
or delta L = 0.1055*656nm = 69.23nm and L observed = 725.2nm