Mass is generally defined as “at rest”. Photons can’t be “at rest” because they’re always moving at the speed of light, so mass doesn’t even make sense as a concept for photons.
So with Newton, light has no momentum because he defined momentum as mass times velocity. But photons DO have momentum even if talking about their mass doesn’t make sense. For light with all the cool Einstein relativity stuff, a photon’s momentum is Planck’s constant divided by wavelength of the photon (higher energy, shorter wavelength photons have more momentum). So that means light can also transfer that momentum to things that DO have mass, like a solar sail, just like if you were to smash particles with mass into a solar sail.
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