Two transiting planets orbiting the same star have periods and

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

Two transiting planets orbiting the same star have periods

P_1 = 12.0\,\mathrm{d}

and

P_2 = 18.5\,\mathrm{d}

, close to the

3{:}2

mean-motion resonance (

j=3

). The transit-timing super-period is

P_{\rm TTV} = \frac{1}{\left|\dfrac{j}{P_2} - \dfrac{j-1}{P_1}\right|}.

Find

P_{\rm TTV}

in days, and explain in one sentence how the amplitude of the timing variations (not the super-period itself) is used to weigh the perturbing planet.

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