1. The problem statement, all variables and given/known data A distant observer is at rest relative to a spherical mass and at a distance where the effects of gravity are negligible. The distant observer sends a photon radially towards the mass. At the distant observer, the photon's frequency is f. What is the momentum relative to the distant observer of the photon when it is distance r from the mass? Assume that r > the radius of the mass. 2. Relevant equations h = planck's constant f = frequency of the photon at some distance from the mass relative to the distant observer's frame of reference fobs = frequency of the photon at the distant observer's position relative to the distant observer v = velocity of the photon at some distance from the mass relative to the distant observer's frame of reference l = wavelength of the photon relative to the distant observer's frame of reference r = radial distance from the mass to the photon c = the speed of light in free space p = momentum of the photon relative to the distant observer's frame of reference Rs = Schwarzschild radius of the point mass = 2GM/c2 where G = gravitational constant and M = mass of the spherical mass. 3. The attempt at a solution Here are two attempts with two different answers. They make assumptions which may not be correct. Attempt 1 When the distant observer sends out the photon, it has a momentum of -hfobs/c. If the photon were to hit the mass and its energy totally absorbed by the mass and converted into kinetic energy, then the momentum of the mass would be -hfobs/c due to conservation of momentum. Thus the momentum of the photon relative to the distant observer would be -hfobs/c just prior to the collision, and it would be -hfobs/c at all times regardless of its distance r to the radial mass. Attempt 2 p = -h/l l = v/f v = c(1-Rs/r) - from the Schwarzschild metric f = fobs therefore p = -hfobs/c(1-Rs/r) The reason that f(r) = fobs is that an observer at r will see a blueshifted photon (f'(r) = blueshifted(fobs) ) but their clock is slower so they'll see more cycles per their second. The distant observer will see fewer cycles per their second so that the frequency at r relative to the distant observer = f = redshifted(f') = redshifted(blueshifted(fobs)) = fobs.