Hot Jupiters. In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star HD 179949 (hence the term “hot Jupiter”). The orbit was just the distance of Mercury from our sun, and it takes the planet only 3.09 days to make one orbit (assumed to be circular). (a) What is the mass of the star? Express your answer in kilograms and as a multiple of our sun’s mass. (b) How fast (in km/s) is this planet moving?

Solution 28E Introduction We have to first calculate the mass of the star. Then we have to find out the speed of the planet hot jupiter. Step 1 The distance from the sun to jupiter is a = 5.88 × 10 m 11 j Hence the distance from the star HD 179949 to hot jupiter is a = a /9 = 6.53 × 10 m 10 hj j Now orbital time period of hot jupiter is T = 3.09 day = 2.67 × 10 s5 hj Now the orbital time period is given by 2a 3/2 T = Gm s 4 a 3 m = s GT 2 Now putting the values of the planet hot jupiter we have 4 (5.88×1011m)3 33 m s 11 2 2 5 = 2.31 × 10 kg (6.67×10 N.m /kg )(2.67×10 s) 33 Hence the mass of the planet is 2.31 × 10 kg .