### Question

How are solar sails possible? If photons have no mass, how can they push on something?

Asked by: Peeps

### Answer

Indeed, photons have no mass. However, they DO have energy and momentum. It turns out
that energy and momentum are the requirements that make a solar sail work, not mass.

If we think about a slow massive particle, like a bowling ball, we can help to make sense
of this. If the bowling ball is not moving, then it can't make anything move. And a heavy
bowling ball can make something move more than a light bowling ball (if we assume both
bowling balls are moving with the same speed). To summarize, how much something moves (how
much momentum is transferred) depends linearly on both the bowling balls' mass and speed.
Momentum (for slow moving massive objects) is defined as p = m*v (p is the momentum, m is
the mass, and v is the velocity).

This momentum is what gets transferred when wind hits a normal sail. But photons have
momentum without having mass! This is how they can push things around, they transfer
momentum. For a photon, E = h*f = mc^{2} so, p = hf/c. In this case, p is once again momentum, h is Planck's
constant (6.62 x 10^{-34} Joule*seconds), and f is the frequency of the photon.
This is how a solar sail works. Photons transfer some of their momentum to the sail,
thereby propelling it along very much like a sailboat in the ocean.

Answered by: Andreas Birkedal-Hansen, M.A., Physics Grad Student, UC Berkeley