Discovering a Planet On April 26, 1997, astronomers announced the discovery of a new plane...

Discovering a Planet On April 26, 1997, astronomers announced the discovery of a new planet orbiting the star Rho Coronae Borealis (Sky and Telescope, July 1997). The astronomers deduced the existence of the planet by measuring the change in line−of−sight velocity of the star over a period of ten months. The measurements appear to fall along a sine wave as shown in the accompanying figure.

a. What are the period, amplitude, and equation for the sine wave?

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b. How many Earth days does it take for the planet to orbit Rho Coronae Borealis?

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c. Use the equation to estimate the change in line-of-sight velocity on day 36.

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d. On day 36 do you think that the planet is between the earth and Rho or that Rho is between the earth and the planet?