The $P_1$ and $P_2$ approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere

The spherical harmonics method in the $P_1$ and $P_2$ approximations is used to analyze radiative heat transfer for a space vehicle entering a planet's atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle's flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of $-5^\circ$.