Extrasolar planets and planetary systems

10.1. The radial velocity method of exoplanet detection uses the fact that a star-planet pair orbit around a common center of gravity, called the barycenter. The text states that it is possible to measure a star’s motion as little as 3 m s-1.

(a) How far from the center of the Sun is the center of mass of the Sun-Jupiter system? Is this greater or smaller than the radius of the Sun? (2 pts)

(b) What is the velocity of the Sun about the Sun-Jupiter barycenter? Would the Sun’s wobble due to Jupiter be detectable (i.e is v > 3 m s-1)? (2 pts)

10.2. A red dwarf star of mass 0.2 Msun is orbited by a planet that transits once every 20 days.

(a) Using Newton’s version of Kepler’s 3rd law, P^2=(4π^2/GM)a^3, what is the semi-major axis for the orbit of the planet, in AU? (1 pts)

(b) Assuming the orbit is circular, you can use the circumference of the circle of radius a and the period from part (a) to get the velocity of the planet. What is the velocity in m s-1? (1 pts)

(c) Assuming also that the orbit is seen exactly edge on, what is the duration, in seconds, of the dip in the light curve, if the star has a radius of 0.4 Rsun, and the size of the planet can be neglected? (2 pts)

(d) The dip in the light curve is seen to take 10 minutes to reach its low point (ignore stellar limb darkening). What is the radius of the planet. Express the radius in km, and again in Jupiter radii. (2 pts)

Sample Solution