Planets Beyond the Solar System. On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. What is the mass of HD 68988? Express your answer in kilograms and in terms of our sun’s mass. (Consult Appendix F.)

Solution 29E Introduction We have to calculate the mass of the planet HD 68988. Then we have to compare the ratio between star HD 68988 and sun. Step 1 The orbital period is given by 2a3/2 T = Gm s 6 9 Here m issthe mass of the star and a = 10.5 × 10 km = 10.5 × 10 m, and the orbital period 5 T = 6.3 day = 5.44 × 10 s. So the mass of the star is given by 4 a3 4 (10.5×10 m)3 30 m s 2 = 11 2 2 5 2 = 2.31 × 10 kg GT (6.67×10 N.m /kg )(5.44×10 s) Hence the mass of the star HD 68988 is 2.31 × 10 kg . 30