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Solar sailing DOESN"T break laws of physics'



 
 
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  #33  
Old July 6th 03, 08:45 PM
Henry Spencer
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Default Solar sailing DOESN"T break laws of physics'

In article ,
Alex Terrell wrote:
Momentum = mass * velocity
If mass = 0 and velocity = 3E8, then momentum = 0
Please tell me what I'm missing?


In a relativistic world, things moving at the speed of light follow
different rules.

Momentum is not m*v; rather, it is m*v/sqrt(1-v^2/c^2), which reduces to
approximately m*v when vc.

As is easy to see, for m=0 and v=c, momentum is 0/0, i.e. indeterminate.
Which is not surprising, since photons of different energies carry
different amounts of momentum. Photon momentum is, in fact, E/c, where
E is the energy.
--
MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer
first ground-station pass 1651, all nominal! |
  #34  
Old July 6th 03, 09:10 PM
Allen Thomson
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Default Solar sailing DOESN"T break laws of physics'

(John Ordover) wrote

Someone correct me if I'm wrong, but in general an analogy to solar
sailing would be to move a terrestrial sailboat by hitting the sail
with a whole lot of high-speed ping-pong balls.

Light is massless but not energy-less, natch, so it winds up having a
similar effect on objects to the ping-pong balls. Just as some of the
momementum of the ping-pong balls would be transfered to the sails,
some of the energy of the light is transfered to the sail. Just as
the ping-pong balls would therefore lose some energy, the photons in
the light lose some energy, but light does that all the time.

So what's the problem?


It's probably better/easier to think of the sail as flat and rigid,
like a sheet of plywood. But that said, the ping-pong ball analogy
is an excellent one and captures most of what's going on with solar
sails in the reflective case (the balls bounce off). A useful addition
is to consider the case in which the balls are sticky and stay on the
sail, corresponding to absorption (assume that the balls are extremely
light so the added mass is negligible). Real solar sails are a
combination of reflective and absorptive -- some balls bounce, some
stick.

The difference is important, because reflection allows the sail to
tack against the photon wind by canting itself, whereas the
absorptive case only produces a thrust in the direction of the wind.
A sail that can tack can add or subtract orbital angular momentum wrt
the sun and spiral between planets; one that can't tack can't do that.
  #35  
Old July 6th 03, 09:16 PM
George William Herbert
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Default Solar sailing DOESN"T break laws of physics'

Alex Terrell wrote:
If photons have mass, and if they travel at c, how come they don't
have infinite mass? Since they don't have infinite mass, they can have
no mass, and therefore no momentum.


You were doing fine until that last part. How do you conclude that no
mass means no momentum?


Please don't misintepret me. I do "believe" in solar sails. I'm just
trying to figure out how it works, because, in the normal world:

Momentum = mass * velocity

If mass = 0 and velocity = 3E8, then momentum = 0

Please tell me what I'm missing?


Photons have momentum inversely proportional to
their wavelength, independent of their rest
mass (which is zero).

P = h / lambda

This is also equal to their energy divided by the
speed of light:

P = E / c

See for example pp 1109 in Halliday and Resnick 2nd ed.


-george william herbert


  #36  
Old July 6th 03, 09:51 PM
Gregory L. Hansen
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Default Solar sailing DOESN"T break laws of physics'

In article ,
Alex Terrell wrote:
(Gregory L. Hansen) wrote in message
...
If photons have mass, and if they travel at c, how come they don't
have infinite mass? Since they don't have infinite mass, they can have
no mass, and therefore no momentum.


You were doing fine until that last part. How do you conclude that no
mass means no momentum?


Please don't misintepret me. I do "believe" in solar sails. I'm just
trying to figure out how it works, because, in the normal world:

Momentum = mass * velocity

If mass = 0 and velocity = 3E8, then momentum = 0

Please tell me what I'm missing?


Momentum isn't always mass * velocity. We find out what the real world is
like by running experiments, and light has momentum but no detectable
mass. It has energy, though, and mass itself is related to rest energy by
m=E/c^2.

--
"Is that plutonium on your gums?"
"Shut up and kiss me!"
-- Marge and Homer Simpson

  #39  
Old July 6th 03, 11:35 PM
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Default Solar sailing DOESN"T break laws of physics'

In article , (Alan Anderson) writes:
(Alex Terrell) wrote:

If photons have mass, and if they travel at c, how come they don't
have infinite mass? Since they don't have infinite mass, they can have
no mass, and therefore no momentum.

You were doing fine until that last part. How do you conclude that no
mass means no momentum?


Please don't misintepret me. I do "believe" in solar sails. I'm just
trying to figure out how it works, because, in the normal world:

Momentum = mass * velocity

If mass = 0 and velocity = 3E8, then momentum = 0

Please tell me what I'm missing?


You're missing the difference between "the normal world" and "Newtonian
physics", that's all. The relativistic formula for momentum has an extra
factor which increases as velocity approaches c, becoming infinite when
v=c, making that formula inapplicable to photons. What is zero times
infinity?

Before you even start getting to relativistic physics, the point
missed by many is that even in classical physics momentum *is not*
defined as mv (yes, there is quite a lot of physics beyond high school
physics). Momentum is defined as a gradient of the Lagrangian (yes, I
know this doesn't mean much to whoever didn't study it but, as I said,
there is lots of physics beyond high school physics). In the
particular case of a classical massive particle, this *evaluates* to
mv but that's a result, not a definition. For other entities you get
different result. Thus, even within classical physics electromagnetic
waves carry momentum even though they're massless.

Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"
  #40  
Old July 7th 03, 01:43 AM
Edward Green
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Default Solar sailing DOESN"T break laws of physics'

"Steve Harris" wrote in message ...

If there's no change in photon energy to first order, then
obviously that's a breaking of Carnot's law to first order,
since Carnot requires an decrease in photon temperature
(photon energy) for work to be extracted.


True, I snipped context and all, but I love the way "to first order"
sometimes takes on a meaning all of its own -- as if it meant
something without even specifying "with respect to X".

Carnot requires
two thermal baths of different temperatures for kinetic
energy to be gained.


Which are present when a solar sail is working.

But it's okay, because in any inertial frame where work is
being done on the sail, you see two populations of photons
(those coming and those leaving), and these two DO have two
different temperatures. That's it.


Ok. Start with a heat bath at temperature T. Extract a wee bit of
energy from it to do some useful work. Wind up with a heat bath at
temperature T - dt. Viola! Two different temperature heat baths! Ok
by thermo! :-)

No ... if that were the out, the second law would be empty. The two
different temperature heat baths were there at the start of the
problem, _before_ we introduced the sail. The are separated in
momentum space rather than physical space.

Of course the photons don't have to be charaterized by temperatures at
all ... the sail could work with pure monochromatic radiation. Yet
even if we had a complete Stefan-Boltzman distribution of frequencies
characteristic of TK, but with the momentum vectors all pointing in
one direction, that would _not_ correspond to envelopment in a heat
bath at temperture T. If diferent regions of momentum space are
populated by photons distributed differently in energy, whether or not
according to some temperatures, that's enough to get work out of the
system. And that's why a solar sail illuminated by the distant sun on
one side and exposed to the icy cold inky blackness space on the
other, can work.

So saying, the great Shaman snapped closed his dearhide covered book
of tales, and shooed the little braves off to bed to dream -- to dream
of the illiminatable black crow winging forever in blackness on sooty
wings while the coyote of the abyss howled his ceaseless song of
unnerving beauty and infinite sadness and the rosy sun-squaw is tucked
in her bed, waiting for a dawn that may never come.

And darkness descended on the world. Amen.
 




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