Terry Blanton wrote:
From: Harry Veeder>
In reality the wavelength (and consequently momentum) of the reflected photon
is slightly less than the wavelength ( momentum ) of the incoming photon.
That should say "slightly longer" instead of "slightly less"!
But, but, but, that means the sail should be black not reflective, right?
No. If it's reflective, it absorbs all the incoming momentum. For each
photon with momentum "p", a black sail absorbs momentum of "p".
But if it bounces the photons off, a reflective sail picks up momentum
of (almost!) 2*p from each photon. So it absorbs _twice_ the incoming
momentum. (Cool, huh? COP=2, maybe?) Until the sail is moving at
appreciable velocity away from the sun, the wavelength shift of the
reflected photon is negligible, and in fact even after it's moving
quickly it still gets twice the bang from each photon if it reflects
them rather than absorbing them.
You can view this as ordinary mechanics, and treat the photons like
little billiard balls. The same thing happens with a ball: If it
bounces off something, it transfers twice the momentum as it does if it
sticks. In the case of a ball, it's easy to understand, though. For
consider a rubber ball hitting a wall:
The ball rushes at a wall. It touches the wall, but of course it
doesn't stop _instantly_.
Instead, the ball compresses, which takes finite time; as it's
compressing, the surface of the ball touching the wall pushes on the wall.
Then, IF it bounces off, it expands again, and pushes itself away; as
it's expanding, it's still pushing on the wall.
IF, instead, the ball squishes and doesn't bounce back, but just sticks
to the wall in a little flattened pancake, then the second half of the
interaction -- the "push off" part -- doesn't happen, and the wall
doesn't gain the extra impulse. So, hitting and sticking only pushes on
the wall for about half the time hitting and bouncing off pushes on it
for, and so it transfers about half the momentum.
And one other thing: If it's a mirror, you can angle it in order to
steer the ship. The thrust is always perpendicular to the mirror's
surface. If it's plain black, you can't do that -- the thrust is always
parallel to the paths of the incoming photons.
