PatrickHenry says: "The mass of the photon (whatever that is) won't change, nor it's speed (in vacuuo). So I don't see any changes in momentum. Only changes in wavelength seem likely..."
At first blush, the problem seems even more troublesome than that. You see, the photon has no mass, so when we say that momentum is p = m*v (momentum equals mass times velocity), it would first appear that, since the photon has no mass, neither can it have any momentum whatsoever!
And worse, since energy is e = m*v2 = m*c2 it would also appear that (without mass), neither can the photon can have any energy. (Of course, anyone who has ever sat in the sunlight, intuitively knows better than that.)
However, with just a little mathematical slight of hand...
Einstein showed us that the energy of a quanta of light (a photon) can also be determined from e = h*f (Planck's constant times frequency). The fact that energy could equal both h*f as well as m*v2, makes sense if you reduce both of those terms to their fundamental dimensions (units of mass, length, time) and see that they are both m*l2/t2, which are the fundamental dimensions of energy.
Since momentum equals m*v and energy equals m*v2, all we need do to arrive at momentum is to divide energy by velocity, p = m*v = m*v2/v. Therefore, since we know that e = h*f, the equation for momentum would become p = h*f/v = h*f/c.
Rearranged in terms of frequency (to see if we have any red shift), the equation becomes f = p*c/h. Since variables c and h are constants, the equation says that the only way for frequency to change is for momentum to change. And since wavelength is inversely proportionate to frequency, L = c/f, when frequency lowers (red shift), the wavelength must lengthen.
--Boot Hill