js2j@mhuxt.UUCP (sonntag) (03/13/85)
I disagreed rather strongly with Mike Augeri's analysis of lightsail
acceleration, so I was moved to analyze the problem myself. Unfortunately,
I did the problem in both the lightsail frame of reference and in a rest
frame of reference (rest wrt. the light source). Unfortunately, I got
different results. Either I made a mistake I can't find, or relativity
somehow dictates that I *should* get different results. Anyway, here are
the results. Maybe some physics whiz can point out the problem.
We have a light source. For simplicity, a laser which produces light
of wavelength l. The laser is aimed at the sail, which is moving away with
velocity v. The sail is oriented so that the beam of light strikes per-
pendicularly to the sail. Like this:
--------- |
| laser } ~~> ~~> |
--------- | <- sail
In the lightsail's frame of reference:
initial photon momentum: h/l', where h is planck's constant.
final " " : -h/l'
momentum transferred: 2h/l', where l'=l/(1-v/c). (c is speed of light)
momentum transferred: 2h(1-v/c)/l
In the laser's frame of reference:
initial photon momentum: h/l
final photon momentum: h/l'
Wait! I just realized that observers on the sail and on the laser should
see different wavelengths for the photon after reflection. In fact, the
observer on the laser should see the reflected photon redshifted by even more
than the sail-rider saw. So, to continue:
final photon momentum: h/l'', where l''=l/(1-v/c)^2
momentum transferred: 2h(1-v/c)/l + (h/l)(v/c)^2
Well, this is better than I did the first time. You see that the
results are the same except for the (v/c)^2 term. I suspect that this
difference has something to do with special relativity. (Either that,
or I've *still* got it wrong.) Can anyone clarify?
--
Jeff Sonntag
ihnp4!mhuxt!js2j
"That little red hen said to that little red rooster:
You don't come 'round no more, like you used to." - Taj Mahal