The problem is that I'm doing what seems to be perfectly reasonable algebra but I'm getting a result that makes no sense. Let's say a photon travels from the left and hits a stationary solar sail which is perpendicular to the light. There is perfect reflection and a change in momenta for both objects. For momentum we have: p_iphoton + p_iSS = p_fphoton + p_fSS => h/c*nu1 + m*(0)^2 = h/c*nu2 + mv h/c*(nu1-nu2) = mv energy: KE_iphoton + KE_iSS = KE_fphoton + KE_fSS h*nu1 + 0 = h*nu2 + mv^2 h*(nu1-nu2) = mv^2 = c*mv => v = c (KE_iphoton is the photon's initial kinetic energy, p_iphoton is its initial momentum, KE_fphoton is the final KE, etc.; h = planck's constant, c = speed of light, m = mass of solar sail, v = final velocity of solar sail, nu1 = initial frequency of photon, nu2 = final frequency of photon.) Obviously, the final speed of the solar sail isn't the speed of light. What did I do wrong?