Gravitational drag on a point mass in hypersonic motion through a gaseous medium

We explore a ballistic orbit model to infer the gravitational drag force on an accreting point mass M, such as a black hole, moving at a hypersonic velocity v₀ through a gaseous environment of density ρ₀. The streamlines blend in the flow past the body and transfer momentum to it. The total drag force acting on the body, including the non-linear contribution of those streamlines with small impact parameter that bend significantly and pass through a shock, can be calculated by imposing conservation of momentum. In this fully analytic approach, the ambiguity in the definition of the lower cut-off distance r_min in calculations of the effect of dynamical friction is removed. It turns out that ?. Using spherical surfaces of control of different sizes, we carry out a successful comparison between the predicted drag force and the one obtained from a high-resolution, axisymmetric, isothermal flow simulation. We demonstrate that ballistic models are reasonably successful in accounting for both the accretion rate and the gravitational drag.