I saw this solution a while ago:
dN donates the number of photons in a certain space, f donates the occupation number, g donates the number of spin states, p donates the dimensional momentum, dt, dA, do, dE donate unit time, unit area, unit angle, and unit Energy.
dN = f * g * (d3r * d3p) / (2*pi*h)3
Since d3r = c*dt*dA, d3p = p2*dp*do
Intensity I = (E * dN) / (dt * dA * do * dE) = (c*f*g*p3)/(2*pi*h)3
Therefore, the change of the brightness of the stars when moving at velocity v is proportional to p3, which is the cubic of the doppler effect factor.