A spherical spacecraft of radius $R$ is constructed from two thin hemispherical shells joined along a flat seam. The leading hemisphere has mass $m$, and the trailing hemisphere has mass $2m$. At a certain instant, the spacecraft is moving at speed $v$ through a region of deep space filled with stationary dust of uniform mass density $\rho$. The velocity of the spacecraft is perpendicular to the seam. The dust particles collide perfectly inelastically with the spacecraft. Assuming the mass of the accumulated dust is currently negligible compared to $m$, what is the compressive force between the two hemispheres?