An aircraft is in steady level flight at \(M_{\infty}=0.55\) with \(T_{\infty}=273^{\circ} \mathrm{K}\) and \(p_{\infty}=10,000 \mathrm{~N} / \mathrm{m}^{2}\). Performance data for the aircraft's airfoil measured under incompressible conditions indicate that the lift coefficient is 0.2 at the angle of attack associated with level flight. Estimate the aircraft's weight if the aerodynamic reference area is \(15 \mathrm{~m}^{2}\).