Question

Question :Suppose that you'd like to find out if adistant star is moving relative to the earth. The star is much toofar away to detect any change in its brightness as itmoves towardor away from the earth. Instead we can use the Doppler effect todetermine its relative speed. For this problem we are going to lookat the spectrallines from hydrogen, specifically the one with awavelength of 656.46 nm.(A)Suppose that you measure the light ofa star between 640 and 680 nm and you get a very strong peak around650 nm. What can you say about the star's motion?moving (away from earth-towardearth-not moving relative to the earth-movingtangent to the direction of the earth)(B)What is $V_star$ , the speed at which the star is movingrelative to theearth?Express youranswer as a fraction of the speed of light to twosignificant figures.(C)Suppose that youmeasured a peak at 680 nm instead. What is the relative speed $V_star$ of the star to the earth in this case?Express youranswer as a fraction of the speed of light totwo significant figures.(D)The hydrogen atoms in astar are also moving at high velocity because of the random motionscaused by their high temperature. As a result, each atom isDopplershifted a little bit differently, leading to a finite width of eachspectral line, such as the 656.46-nm line we were just discussing.For a starlike our sun, this leads to a finite width of thespectral lines of roughly . If our instruments can only resolve tothisaccuracy, what is the lowest speed ,greater than 0,that we can measure a star to bemoving?Express youranswer in kilometers per second to two significantfigures.

Answer 1

(a)As we know that if the observed wavelenth is less than theoriginal wavelength then the object is moving towards theearth.(b)By using the formula where Δλ = 40 nm.λ₀= 656.46 nm.(c)By using the formula where Δλ = 40 nm.λ₀= 680nm.(d)By using the formula where Δλ = 0.040 nm.λ₀= 656.46 nm.answer is 18.28 km/s.