One way astrophysicists have identifi ed extrasolarplanets orbiting distant stars is by

Chapter 2, Problem 105

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One way astrophysicists have identifi ed extrasolarplanets orbiting distant stars is by observing redshiftsor blueshifts in the stars spectrum due to the fact that the star and planet each revolve around their commoncenter of mass. (See Scientifi c American, August2010, p. 41.) Consider a star the size of our sun (mass 1.99 1030 kg), with a planet the size of Jupiter(1.90 1027 kg) in a circular orbit of radius 7.79 1011 m and a period of 11.9 years. (a) Find the speedof the star revolving around the systems center ofmass. (b) Assume that Earth is in the planets orbitalplane, so that at one point in its orbit the star is movingdirectly toward Earth, and at the opposite point itmoves directly away from Earth. How much is 550-nmlight redshifted and blueshifted at those two extremepoints?

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