A hot Neptune with orbits a star of mass with period (about days) on an eccentric…

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 hot Neptune with mpsin⁡i=0.050 MJm_p\sin i = 0.050\,M_J orbits a star of mass M∗=0.80 M⊙M_* = 0.80\,M_\odot with period P=0.020 yrP = 0.020\,\mathrm{yr} (about 7.37.3 days) on an eccentric orbit with e=0.30e = 0.30. Using 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 KK, and state whether this amplitude would be detectable against a stellar activity noise floor of 1 m s−11\,\mathrm{m\,s^{-1}}.

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