The spectrum of a star is used to measure its radial velocity with respect to the Sun, the component of the star's velocity vector that is pa rallel to a vector connecting the star's centre to the centre of the Sun. The measurement relies on the Doppler effect, in which rad iation is shiftedin frequency when the source is moving towards or away from the observer. When a star emitting electromagnetic radiation of frequency v moves with a speed s relative to an observer, the observer detects radiation of f requency vreceding, = vf or vapproaching = v/f, where f = {(1 - s/c)/(1 + s/c)}1/2 and c is the speed of light. (a) Three lines in the spectrum ofatomic iron of the star HDE 271 182, which belongs to the Large Magellanic Cloud, occur at 438.882 nm, 441.000 nm, and 442.020 nm. The same lines occur at 438.392 nm, 440.510 nm, and 441.510 nm in the spectrum of an Earthbound ironarc. Determine whether HDE 271 182 is receding from or approaching the Earth and estimate the sta r's radial speed with respect to the Earth. (b) What addit iona l information would you need to calculate the rad ial ve locity of HDE 271 182 with respect to the Sun?

The spectrum of a star is used to measure its radial velocity with respect to the Sun, the component of the star's velocity vector that is pa rallel to a vector connecting the star's centre to the centre of the Sun. The measurement relies on the Doppler effect, in which rad iation is shiftedin frequency when the source is moving towards or away from the observer. When a star emitting electromagnetic radiation of frequency v moves with a speed s relative to an observer, the observer detects radiation of f requency vreceding, = vf or vapproaching = v/f, where f = {(1 - s/c)/(1 + s/c)}1/2 and c is the speed of light. (a) Three lines in the spectrum ofatomic iron of the star HDE 271 182, which belongs to the Large Magellanic Cloud, occur at 438.882 nm, 441.000 nm, and 442.020 nm. The same lines occur at 438.392 nm, 440.510 nm, and 441.510 nm in the spectrum of an Earthbound ironarc. Determine whether HDE 271 182 is receding from or approaching the Earth and estimate the sta r's radial speed with respect to the Earth. (b) What addit iona l information would you need to calculate the rad ial ve locity of HDE 271 182 with respect to the Sun?