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The disk self-gravity alters both the planet's angular velocity 
and the disk's rotation profile 
as:
is the planet's orbital radius, 
denotes the Keplerian angular velocity, and:
is defined as 
as 
as
and the disk's rotation profile as:
![\Omega_p = \left[ \Omega_K^2(r_p) - \frac{g_r(r_p)}{r_p} \right]^{1/2},](local/cache-vignettes/L179xH61/bc680b55dc627befa49b77bbae6d4683-7a032.png "\Omega_p = \left[ \Omega_K^2(r_p) - \frac{g_r(r_p)}{r_p} \right]^{1/2},")
is the planet's orbital radius, denotes the Keplerian angular velocity, and:
![\Omega(r) = \left[ \Omega_K^2(r) \left\{ 1 - (1+\sigma-2f)h^2r^{2f} \right\} - \frac{g_r(r)}{r} \right]^{1/2},](local/cache-vignettes/L339xH61/e250965a3d6ad3266de633f38cdd415e-5f93a.png "\Omega(r) = \left[ \Omega_K^2(r) \left\{ 1 - (1+\sigma-2f)h^2r^{2f} \right\} - \frac{g_r(r)}{r} \right]^{1/2},")
is defined as ASPECTRATIO, as FLARINGINDEX and as SIGMASLOPE. When the disk self-gravity is taken into account, the initialization of the planet's angular velocity is done by function init_planetarysys_withSG in sgsysinit.c, while that of the fluid elements is done by function init_azimutalvelocity_withSG in sgvelinit.c.
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