= Constant-area capture of stationary dust
{title2=$M^2(t)=M_0^2+2\rho AM_0v_0t$}
A body of initial <mass> $M_0$ and <speed> $v_0$ collects all stationary dust swept out by constant area $A$ in a uniform cloud of <mass density> $\rho$. Then $M=M_0+\rho Ax$ and $Mv=M_0v_0$ by <conservation of momentum>. Integration gives the displayed <mass> law, $v=M_0v_0/M$ and $x=(M-M_0)/(\rho A)$. Sticking dissipates <kinetic energy> at rate $\dot Mv^2/2$. The model assumes no external longitudinal <force> and negligible relativistic corrections.
Back to article page
