Photons have relativistic mass. While the photon itself doesn’t have mass in the conventional sense, it does have energy, and remember that E=mc^2; energy is mass and mass is energy. This means that a photon has a kind of ‘virtual’ mass. A photon can push on something like a solar sail by hitting the sail and imparting momentum, causing the reflected photon to have less momentum, and therefore less mass/energy (a longer wavelength).
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