lew@ihlpa.UUCP (Lew Mammel, Jr.) (03/06/85)
I just spent an inordinate amount of time digging through my "archive" ( a box ) of netnews hardcopy and finally found my article of Oct 1983 on the relativistic lightsail problem. Quoting myself: We can calculate the momentum of the reflected photons in the following way. First, calculate the momentum of the incident photons in the sail frame. Second, reverse the sign of the momentum (reflection from sail which is stationary in this frame.) Third, calculate the momentum of the reflected photons in the rest frame. If p is the initial momentum, these steps yield: 1) gamma*(1-beta)*p /* redshift */ 2) -gamma*(1-beta)*p /* reflect */ 3) -gamma^2*(1-beta)^2*p /* red shift again */ ... this gives delta(v) = 2*p/(1+beta) [end of quote] I went on to evaluate the equation of motion. I found that the time scale of the problem was given by T = (m*c^2) / (2*I * p*c) m = mass of ship p = momentum of photon I = photons per second striking sail ... that is, the rest energy of the ship divided by twice the impinging power. A beam of 1 megawatt/meter2 and a sail of 1 gram/meter2 gives T = 1e8 sec, or about 3 years. My solution gave this table of times required to reach the given speeds: v/c t/T .5 1.065 .9 15.316 .95 43.048 .99 474.26 .999 14917.6 Lew Mammel, Jr. ihnp4!ihlpa!lew
gjk@talcott.UUCP (Greg Kuperberg) (03/08/85)
It is indeed the case that when light bounces off of a moving mirror/light sail it red shifts. This can be interpreted as follows: Because the light accelerates the craft with a light sail, it transfers some of its energy to the ship. The red shift is precisely this loss of energy. And finally, photons, shmotons---it works just as well with Maxwell's equations. In fact, special relativity predates photons by a decade or two. --- Greg Kuperberg harvard!talcott!gjk "2*x^5-10*x+5=0 is not solvable by radicals." -Evariste Galois.