Mass of Star Using Celestial Mechanics

[~Sam~]

Homework Statement

A planet of mass 8.01 MJ (MJ = Jupiter's mass is known) has been discovered orbiting the star HD 168443 . HD 168443 is an G6 IV star of L = 2.09 L_sun and T = 5300 K about 37.9 pc from the Earth in the constellation Serpens Cauda. The planet, so far known only as HD 168443b, was discovered by the radial velocity method, in which the motion of the star about the star-planet barycentre causes a cyclic Doppler shift. (The planet is too close to the star to be visible, so only the motion of the star can be found.)
The period, semimajor axis and eccentricity the orbit of HD 168443b are, respectively, 58.1 days, 0.29 AU, and 0.530. Calculate the following quantities. Because this is a planet, assume in parts a and b that its mass is negligible compared to that of the star.

a. Apastron and periastron distances (equivalent to aphelion and perihelion distances for planets orbiting the Sun.
b. Mass of the star, HD 168443, in solar masses.

c.Calculate the ratio of the planet's mass to the star's mass. Is the assumption of negligible planetary mass in parts a and b reasonable?
d. The radius of the star HD 168443, in RSun.
e. What is the maximum distance of the barycentre from the centre of HD 168443, in RSun? Is the barycentre inside or outside the star?

Homework Equations

That's what I'm trying to figure out..

The Attempt at a Solution

I got part a using Rmax=a(1-e) and Rmin=a(1+e) but I'm not sure what equation to use to find the mass of the star...I have a feeling it might involve Kepler's laws.

 

[Filip Larsen]

Try find an equation that relates the information you are given with the unknown G*M_star. Hint: you need to use the orbital period.

 

[~Sam~]

Yeah I got parts a-d..But now I'm stuck on part e...

 

[Filip Larsen]

The barycentre in this case simply is the centre of mass of the planet and the star.