= Stellar quadrupole disturbing function
{title2=$\mathcal R_\star=GM_\star r^2P_2(\cos\psi)/a_p^3$}
For a particle far inside a planet's stellar orbit, the planet-centred <disturbing function> is $GM_\star/|\boldsymbol r_\star-\boldsymbol r|-GM_\star\boldsymbol r\cdot\boldsymbol r_\star/r_\star^3$. Expanding the first term cancels its dipole against the <indirect disturbing function>. Dropping the spatially constant monopole leaves $GM_\star r^2(3\cos^2\psi-1)/(2r_\star^3)$, where $\psi$ is the angle between the two offset vectors. The omitted instantaneous terms are $O(GM_\star r^3/r_\star^4)$. The gradient of the retained expression is the leading differential stellar tidal acceleration.
Back to article page
