One way astrophysicists have identified “extrasolar” planets orbiting distant stars is by observing redshifts or blueshifts in the star’s spectrum due to the fact that the star and planet each revolve around their common center of mass. (See Scientifi c American, August 2010, 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 speed of the star revolving around the system’s center of mass. (b) Assume that Earth is in the planet’s orbital plane, so that at one point in its orbit the star is moving directly toward Earth, and at the opposite point it moves directly away from Earth. How much is 550-nm light redshifted and blueshifted at those two extreme points?
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