Yes. If you need ultimate proof, consider not just the
Doppler effect, but the Compton effect. Electrons are
perfect mirrors and have no temperature. But thermodynamics
is upheld anyway when they scatter photons.


"Geoffrey A. Landis" wrote in
message
om...
Despite a recent article in New Scientist, a solar sail
does not break
the laws of physics.

In an article in New Scientist recently, maverick
astronomer Thomas
Gold cast doubt about solar sails:
"Thomas Gold from Cornell University in New York says the
proponents
of solar sailing have forgotten about thermodynamics, the
branch of
physics governing heat transfer. Solar sails are designed
to be
perfect mirrors, meaning that they reflect all the photons
that strike
them. Gold argues that when photons are reflected by a
perfect mirror,
they do not suffer a drop in temperature. "

Unfortunately, Gold has apparently forgotten to account
for a
well-known physical effect: the Doppler shift.

It's worth saying that the photon pressure on a spacecraft
is not
theoretical; its effect on spacecraft is measurable, and
it has been
observed and measured to great precision routinely in
space. Photon
pressure-- the solar sail effect-- has already been used
for an
operational space mission; it was for spacecraft attitude
control on
the Pioneer Venus-Mercury mission.

The Crookes radiometer does not operate on photon
pressure, and the
explanation for how it operates has been known for over a
century.

The energy transfer to a solar sail can be accounted for
from the
Doppler shift of reflected photons; even when the
reflectivity is
100%, a photon looses energy when reflecting from a moving
sail. This
effect exactly corresponds to the energy increase of the
sail. No
sophisticated physics is needed to analyze this effect, it
is a
problem suitable for a homework assignment for a college
undergraduate.

When the sail is moving, then the reflected photons are
Doppler
shifted, and leave the sail with lower energy than they
arrived. This
loss of energy exactly equals the energy imparted to the
sail, a fact
which can be trivially verified by using Newton's laws,
the Doppler
formula, and the Einstein equation for photon momentum
p=E/c

If the sail is not moving, there is no Doppler shift.
However, note
that since energy is proportional to momentum squared, the
derivative
of energy with respect to momentum is zero for a
non-moving sail.
Thus, when the sail is stationary, it can reflect photons
with perfect
efficiency and still gain momentum at no energy cost.

For completeness, note that if the sail is moving *toward*
the light
source, then the phtons are Doppler shifted to *higher*
energy by the
reflection. This implies that the sail must lose energy--
which is
correct; when the sail moves toward the light source, it
slows down.

--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis