A Saturn-like planet with orbits a star of mass on a circular orbit ( ) with period

PHYSICS · Subjective · Fermi University Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems · Celestial mechanics and planetary systems

Stars from the Inside, Ch Planetary systems: formation estimates, transits and the atmospheres of other worlds

Problem

A Saturn-like planet with mpsin⁡i=0.30 MJm_p\sin i = 0.30\,M_J orbits a star of mass M∗=1.0 M⊙M_* = 1.0\,M_\odot on a circular orbit (e=0e=0) with period P=8.0 yrP = 8.0\,\mathrm{yr}. Using the practical-units formula K=28.4 m s−1(mpsin⁡iMJ)(Pyr)−1/3(M∗M⊙)−2/3(1−e2)−1/2,K = 28.4\,\mathrm{m\,s^{-1}}\left(\frac{m_p\sin i}{M_J}\right)\left(\frac{P}{\mathrm{yr}}\right)^{-1/3}\left(\frac{M_*}{M_\odot}\right)^{-2/3}(1-e^2)^{-1/2}, find the star's radial-velocity semi-amplitude KK.

Browse the problem library