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\caption[Notation Standard for \textit{Planetary Ring Systems} (\today)]{Notation Standard for \textit{Planetary Ring Systems} \\ \\ Draft \today \\ \\ The following variables have changed since the draft of October~23: $B$, $B_\odot$, $D_2$, $D_3$, $D_e$, $I/F$, $N_2$, $N_3$, $Q$, $Q_\mathrm{ext}$, $Q_\mathrm{T}$, $R$, $W$, $W_e$, $s$, $\alpha$, $\kappa$, $\mu$, $\mu_0$, $\nu$, $\dot{\Omega}$, $\varpi_0$, $\dot{\varpi}$, $\tau_\mathrm{LOS}$, $\tau_\perp$ } \\

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$B$ & elevation angle (angle of observer above rings):  $B = | 90^\circ - \theta_e |$ \\
$B_\odot$ & solar elevation angle (angle of Sun above rings):  $B_\odot = | 90^\circ - \theta_i |$ \\
$D_2$ & area filling factor (fraction of ring surface area occupied by particles) \\
$D_3$ & volume filling factor (fraction of total volume occupied by particles) \\
$D_e$ & equivalent depth (see Glossary) \\
$E$ & Orbital energy \\
$F_D$ & azimuthal drag force \\
$F_G$ & central gravitational force from planet, $GM_Pm/a^2$ \\
$F_I$ & inertially fixed force \\
$F_m$ & gravitational force from a moon \\
$F_N$ & component of perturbing force normal to orbit plane \\
$F_r$ & radial component of perturbing force (cylindrical coordinates) \\
$F_R$ & radial component of perturbing force (spherical coordinates)\\
$F_z$ & vertical component of perturbing force \\
$F_\lambda$ & azimuthal component of perturbing force \\
$F_\Theta $ & tangential component of perturbing force (in orbit plane) \\
$G$ & gravitational constant  \\
$H$ & ring vertical thickness \\
$I$ & orbital inclination \\
$I/F$ & reflectivity (see Glossary) \\
$I_m$ & moon's inclination  \\
$J_2$ & planetary oblateness parameter \\
$\vec{L}$ & orbital angular momentum \\
$M_P$ &  planet mass \\
$M_m$ & moon mass  \\
$N_2$ & surface number density of ring particles \\
$N_3$ & volume number density of ring particles \\
$Q$ & tidal quality factor \\
$Q_\mathrm{ext}$ & photometric extinction coefficient \\
$Q_\mathrm{T}$ & Toomre's $Q$ \\
$R$ & physical radius of an object \\
%$T$ & ring transmission coefficient \\
$U$ & gravitational potential \\
$V_r$ & average radial velocity of ring particles  \\
$V_z$ & average vertical velocity of ring particles \\
$V_\lambda$ & average azimuthal velocity of ring particles \\
$W$ & radial width \\
$W_e$ & equivalent width (see Glossary) \\
$a$ & orbital semi-major axis  \\
$a_m$ & moon's orbital semi-major axis \\
$c$ & root-mean-square ($rms$) velocity dispersion \\
$c_z$ & vertical $rms$ velocity dispersion \\
$e$ & orbital eccentricity \\
$e_f$ & forced eccentricity \\
$e_l$ & free eccentricity \\
$e_m$ & moon's eccentricity \\  
$f$ & true anomaly  \\
$h$ & $e\cos(\varpi-\lambda_0)$ \\
$k$ & $e\sin(\varpi-\lambda_0)$ \\
$k_r$ & radial wavenumber \\
$m$ & ring particle mass \\
$n$ & orbital mean motion \\
$n_P$ & pattern speed \\
$r_H$ & Hill radius \\
$r_R$ & Roche limit \\
$\vec{r}$ & particle's position vector \\
$r$ & radial distance from planet's spin axis \\
$s$  & ring particle radius (in context of a size distribution) \\
$u_r$ & random radial velocity of ring particles \\
$u_z$ & random vertical velocity of ring particles \\
$u_\lambda$ & random azimuthal velocity of ring particles \\
$\vec{v}$ & particle's velocity vector \\
$v_r$ & radial velocity of ring particles \\
$v_z$ & vertical velocity of ring particles \\
$v_\lambda$ & azimuthal velocity of ring particles \\
$x$ & cartesian approximation of radial coordinate \\
$y$ & cartesian approximation of  azimuthal coordinate \\ 
$z$ & vertical displacement above ring-plane \\
$\alpha$ & phase angle \\
$\epsilon$ & coefficient of restitution \\
$\kappa$ & radial (epicyclic) frequency \\
$\lambda$ & inertial longitude  \\
$\lambda_0$ & reference longitude  \\
$\lambda_T$ & Toomre critical wavelength  \\
$\mu$ & $\sin B$ \\
$\mu_0$ & $\sin B_\odot$ \\
$\nu$ & vertical frequency \\
$\nu_{\rm eff}$ & effective kinematic shear viscosity \\
$\Omega$ & longitude of ascending node \\
$\Omega_m$ & moon's longitude of ascending node \\
$\dot{\Omega}$ & nodal regression rate \\
$\dot{\Omega}_0$ & free nodal regression rate \\
$\omega$ & argument of pericenter \\
$\omega_c$ & collision frequency  \\
$\varpi$ & longitude of pericenter \\
$\varpi_0$ & single-scattering albedo \\
$\varpi_m$ & moon's longitude of pericenter \\
$\dot{\varpi}$ & apsidal precession rate \\
$\dot{\varpi}_0$ & free apsidal precession rate \\
$\varphi_{CR}$ & resonant argument of a corotation resonance \\
$\varphi_{LR}$ & resonant argument of a Lindblad resonance \\
$\varphi_{VR}$ & resonant argument of a vertical resonance \\
$\rho$ & ring particle mass density \\
$\rho_{\rm crit}$ & Roche critical density \\ 
$\rho_P$ & planet mass density \\
$\Sigma$ & ring surface mass density \\
$\tau$ & ring optical depth \\
$\tau_D$ & dynamical optical depth \\
$\tau_\mathrm{LOS}$ & line-of-sight optical depth \\
$\tau_\perp$ & normal optical depth \\
$\theta_e$ & emission angle (angle of target-observer vector from north pole) \\
$\theta_i$ & incidence angle (angle of target-Sun vector from north pole) \\
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