Table 1: Definitions of variables.
$A_{\rm V}$ Ring particle bolometric Bond albedo
$A_{\rm S}$ Saturn bolometric Bond albedo =0.342
B Earth elevation above the ring plane
B' Solar elevation above the ring plane
$C_{\rm H}$ Specific heat ( ${\rm J~kg^{-1}~K^{-1}}$)
C(B', $\tau $) Particle fractional lit area
C(B$\tau $) Particle fractional visible area
$D_{\rm AU}$ Sun-Saturn distance in astronomical units
$\epsilon_{\rm ir}$ Infrared emissivity of ring particles, $\epsilon_{\rm ir}=1$
F1 Direct sunlight
F2 Sunlight reflected by Saturn
F3 Thermal radiation from Saturn
F4 Sunlight scattered by nearby particles
$\Gamma $ Thermal inertia ( ${\rm J ~m^{-2}~ K^{-1} ~s^{-1/2}}$)
K Thermal conductivity ( ${\rm W~m^{-1}~K^{-1}}$)
$\mu$ sin(B)
$\Omega_{\rm P}$ Solid angle of the lit planet hemisphere
$\Omega^{'}_{\rm P}$ Solid angle of the planet hemisphere
$\Omega_R$ Solid angle subtended by all nearby particles
p Porosity of the particle regolith
z Depth in particle
$\rho_0, \rho$ Volume density of the regolith ( $\rho_0=918$ ${\rm kg~m^{-3}}$)
$S,~\sigma $ Solar constant =1370 ${\rm W~m^{-2}}$, Stefan constant
$\tau $ Ring optical depth
${T_{\rm B}}$ Ring brightness temperature
$T_{\rm S}$ Particle surface temperature
$T_{\rm P}$ Saturn planet effective temperature, $T_{\rm P}=95$ K
$\omega$ Particle mean motion

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