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From: lew@ihlpa.UUCP (Lew Mammel, Jr.)
Newsgroups: net.space,net.physics
Subject: reflection of photons from a lightsail
Message-ID: <141@ihlpa.UUCP>
Date: Wed, 6-Mar-85 00:50:24 EST
Article-I.D.: ihlpa.141
Posted: Wed Mar  6 00:50:24 1985
Date-Received: Thu, 7-Mar-85 03:49:59 EST
Distribution: net
Organization: AT&T Bell Laboratories
Lines: 41
Xref: watmath net.space:3670 net.physics:2205

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