Expert: Courtney Seligman - 1/29/2010

Question
QUESTION: How much mass would a photon effectively have at 99.995% the speed of light. How about an electon. If nothing resembling mass makes sense I could use electron/volts.

ANSWER: Photons have no mass, and only move at the speed of light; so the first part of your question has no answer.

For an electron moving at the specified speed, the "mass" would be 100 times its rest mass. However, Einstein felt that this number should not be considered a mass, but simply an increase in the apparent inertia, or resistance to a change in motion, of the body. In other words, he felt that the mass should be considered a constant,even though the effort required to change the motion increased, in this case by 100 times, relative to the effort required to change the motion at low speeds.

---------- FOLLOW-UP ----------

QUESTION: I should have been able to figure out the first part of my question, but the use of "light sails" implies that photons have some kind of mass. Is it the energy inherent in a photons wavelength thatprovides the mass like push?

Answer
Photons have energy, corresponding to their wavelength -- the longer the wavelength, the less the energy -- and momentum, corresponding to their energy (the higher their energy, the greater their momentum). When they reflect off the sails, their momentum in one direction is changed into momentum in another direction. Their change in momentum (due to the change in direction) is transferred to the sails, pushing them (more or less) in the direction the light was heading.

To understand this, you might look up the term "impulse". This is the force acting on an object, multiplied by the length of time the force acts. When a bat hits a ball, a large force is applied for a short time. In the case of light and solar sails, a small force is applied for a long time; but if the time is long enough, the small force can produce just as big an impulse. So if you think of the rain of photons on the sails as a lot of very small bats (or balls), they can eventually produce just as much of an impulse as a big force would, in a shorter period of time.

To understand this mathematically (in general terms, rather than point by point), we combine Newton's Force Law, and Law of Action and Reaction. If both equations are multiplied by the time the force acts, the Force Law becomes "the impulse acting on an object equals its change of momentum", and the Law of Action and Reaction becomes "the impulse acting on one object is equal and opposite to the impulse acting on the other object", and/or "the change in momentum of one object is equal and opposite to the change of momentum of the other object".

In other words, as the light bounces off the sails, it is pushed (more or less toward the Sun) by the sails, and the sails are pushed (more or less away from the Sun) by the light. The momentum change of the light is transferred to the sails, in an equal and opposite manner. Just as with ocean sails, "tacking" can be used to move against the wind, or in this case, toward the Sun; but usually, solar sailing is envisioned as a way to move away from the Sun, so tacking is only used to control the exact direction of that movement.