Question

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 19 the distance of Mercury from our sun, and it takes the planet only 3.09 days to make one orbit (assumed to be circular). What is the mass of the star? Express your answer (a)in kilograms and (b)as a multiple of our sun's mass.

Answer 1

  I'll tell you how to do it but you must crunch the numbers. 

Use Kepler's 3rd Law 

T^2 = k R^3 

where k = 4(pi)^2/ GM 
G =gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2 
M = mass of this new planet 
pi = 3.14159265 
T =3.09 days = 266976 seconds 
R = (579,000,000km)/9 = 64333333.3 km 

a) 
Solve Kepler's 3rd Law for M. Your answer will be in kg 


b) 
mass of the sun = 1.98892 × 10^30 kilograms 
Form the ratio 
M(planet)/M(sun)