A transiting planet is found on a circular orbit with period

PHYSICS · Multi-part · 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

P = 3.00\,\mathrm{d}

. Fitting the light curve gives the scaled semi-major axis

a/R_* = 9.0

, where

a

is the orbital radius and

R_*

is the stellar radius. The planet's mass is negligible compared with the star's,

m_p \ll M_*

. ((a)) Starting from Kepler's third law and the definition of mean density, derive an expression for the mean stellar density

\rho_*

that uses only

a/R_*

and

P

, with no separate appearance of

M_*

R_*

. ((b)) Evaluate

\rho_*

for the numbers above, using

G = 6.674\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}

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