Mass of Star Using Celestial Mechanics

AI Thread Summary
A newly discovered planet, HD 168443b, orbits the G6 IV star HD 168443, which is located 37.9 parsecs from Earth. The planet has a mass of 8.01 Jupiter masses and was identified using the radial velocity method due to the star's motion. Key orbital parameters include a period of 58.1 days, a semimajor axis of 0.29 AU, and an eccentricity of 0.530. Calculating the star's mass involves applying Kepler's laws, and the barycentre's position relative to the star is also a point of discussion. The assumption of negligible planetary mass is questioned based on the calculated mass ratio.
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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 Lsun 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.
 
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Try find an equation that relates the information you are given with the unknown G*Mstar. Hint: you need to use the orbital period.
 
Yeah I got parts a-d..But now I'm stuck on part e...
 
The barycentre in this case simply is the centre of mass of the planet and the star.
 

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