Re: Engineering Newsletter

[Steve VanDevender <stevev@efn.org>]

KellySt@aol.com writes:
 > The papers I've seen on on solar sails seem to disagree with
 > you.  RThey propose angling the sial to alter the thrust
 > vector.  Which would be impossible if the momenum transfer was
 > always in the direction of the photons origional vector.

You don't seem to have read what I wrote, so I'll repeat it below.

 > >> A reflected photon transfers momentum to a reflector normal to
 > >> the reflecting surface.

This in no way contradicts your understanding.  If you tilt a
sail, you get a sideways thrust on the sail.  The momentum
transfer is in the direction against the normal (the
perpendicular to the surface) of the sail.

However, absorbing a photon is different.  In this case
conservation of momentum requires that all of the photon's
momentum and energy be transferred into the absorbing object.
What I was objecting to earlier was Kevin's bald assertion that
an absorbed photon adds momentum only relative to the normal of
the absorbing surface, apparently because he did not properly
analyze the behavior of reflection.

You can think of reflection as a two-step process: absorption and
re-emission.  Momentum is transferred equally (as required by
conservation of momentum) in each step.  Kevin's mistake seemed
to be in his calculation of the quantity of momentum transferred
in each step, based on the total momentum transferred between the
time before absorption and after re-emission.

When a photon is absorbed, all of its energy is transferred into
the absorber, and all of its momentum (not just some, as Kevin
thought).  If the photon was absorbed by a reflector, then it is
instantly re-emitted, and the emitted photon has the same
magnitude of energy and momentum as the original, but the
momentum is in a different direction, and the reflector gets a
new momentum component to compensate.  The vector sum of the
photon momenta before and after the reflection is the negative of
the momentum transferred to the reflector, but the momentum
transfer in each stage is not just half of this resultant vector.
For an instant, the reflector speeds up the same way it would if
it was never planning to re-emit the photon; an instant later it
is accelerated in the direction opposite the emitted photon.

 > Come to think of it all solar sailing would be impossible,
 > since the purpose is alway to add or subtract velocity
 > perpendicular to the solar light vector.  Also it would be
 > rather strange given thatthe photon has changed its course and
 > mometum vector to one crossing the ship and beam vectors.
 > Since its new course has an added lateral vector, there must
 > have been a coresponding lateral vector componenect in the
 > reflection of the sail.

Light sailing would be useless if you couldn't get velocity
components in other directions, say to put yourself in an orbit.
Fortunately light sails don't work the way you think they do.
In fact, your statement here contradicts your statement above --
either tilted light sails produce sideways thrust or they don't.

To get velocity away from the star in the direction of light
emitted from the star, aim your light sail to reflect light
directly back at the star.  To get velocity towards the star,
turn your light sail sideways or furl it completely, and let the
star's gravity accelerate you.  There isn't a way to use the sail
to accelerate yourself towards the star any faster than the
star's gravity would accelerate you, though.  Tilt the sail, and
you get an additional velocity component perpendicular to the
light emitted from the star.  You are right, even though you
don't want to believe yourself.

 > I have a lot of problem bying the idea that the light bouncing
 > off a sail doesn't lose energy proportional to the kinetic or
 > heat energy gain of the ship.  Th power has to be coming from
 > somewhere.

If the sail is reflective to the incident photon, then the photon
doesn't lose energy as a result of reflection.  The ship changes
velocity because the photon changes direction.  That's where the
"power" comes from.

If you don't buy conservation of momentum and energy, you won't
get very far in physics.

Here's an interesting thought experiment that I don't remember
posting to the Starship Design forum, but that some of you may
have seen since I do remember mailing it to somebody.

You have two optically flat perfectly reflective mirrors
(purchased from the same physics supply store where you get
frictionless surfaces and other gedankenexperiment supplies).
You also have a very powerful laser capable of emitting a short
but extremely bright laser pulse, with sufficient momentum that
the pulse can accelerate these mirrors measurably.

Set up the two mirrors parallel to each other and facing each
other, such that light can reflect between the mirrors
indefinitely.  Place the laser between them, and have it emit a
light pulse aimed to reflect between the two mirrors; remove the
laser immediately so that the light does not strike it but
instead reflects between the two mirrors.

What happens to the mirrors?  What happens to the light pulse?
An answer describing the limit state of the mirrors and light
pulse is acceptable; you don't have to perform a step-by-step
analysis of each reflection.