Motie "Light Sail"

In article <M9LfhAAAw7E$EwWN@econym.demon.co.uk>,
Mike Williams <mike DeleteThis @econym.demon.co.uk> wrote:

> Wasn't it Michael Ash who wrote:
> >In article <pRZWKAAKV3E$Ewwe@econym.demon.co.uk>,
> > Mike Williams <mike DeleteThis @econym.demon.co.uk> wrote:
> >> Wasn't it pervect who wrote:
> >>>If the light sail is stationary, light pressure exerts a force on the
> >>>light sail - but the force does no work. work=force*distance
> >>>(power=force*velocity), and the sail isn't moving, so the applied
> >>>force is doing no work and generates no power.
> >>
> >> Doesn't that end up with you getting into something like a "Zeno's
> >> paradox" situation? If the force does no work, then it doesn't start the
> >> sail moving, so light pressure can never move a stationary sail.
> >
> >Like Zeno's Paradox, this "problem" is easily resolved through the
> >appropriate application of calculus.
>
> I don't think so. Can you apply calculus to a single photon?

You can apply calculus to *anything*.

> If the energy of the photon doesn't change (see earlier in the thread,
> not quoted here) then the energy of the sail doesn't change, and it
> doesn't move.

KE = .5mv^2

dKE/dv = mv

When your velocity is zero, your change in energy for some small change
in velocity is zero.

What really happens, of course, is that a single photon hits the sail
and starts it moving by a very very small amount. In the process, the
photon gets reflected at a very slightly longer wavelength, transferring
a very very tiny bit of energy to the sail. The reason the photon's
energy is for all intents and purposes the same is because the sail's
energy is also for all intents and purposes unchanged. But as you can
see above, nearly unchanged energy does *not* translate to nearly
unchanged momentum.

> I also reckon that you get a rather odd effect if the energy imparted to
> the sail comes from the Doppler shift on the photons due to the sail
> moving. The faster the sail moves, the greater is the Doppler shift, and
> so each photon loses a greater amount of energy to the sail. A constant
> photon flux which causes a sail to accelerate would impart an
> acceleration that would be directly proportional to the speed already
> achieved, whereas one would intuitively guess that a constant flux would
> impart constant acceleration.

A constant flux does impart constant acceleration. I don't know where
you're getting this stuff about greater acceleration with greater speed.
The photons lose more energy to the sail, sure, but it also *takes* more
energy to make the sail gain the same amount of velocity at higher
speeds, KE being proportional to v^2 and all that.
 >> Stay informed about: Motie "Light Sail" 

"Mike Williams" <mike RemoveThis @econym.demon.co.uk> wrote in message
news:M9LfhAAAw7E$EwWN@econym.demon.co.uk...

> I also reckon that you get a rather odd effect if the energy imparted to
> the sail comes from the Doppler shift on the photons due to the sail
> moving. The faster the sail moves, the greater is the Doppler shift, and
> so each photon loses a greater amount of energy to the sail. A constant
> photon flux which causes a sail to accelerate would impart an
> acceleration that would be directly proportional to the speed already
> achieved, whereas one would intuitively guess that a constant flux would
> impart constant acceleration.

Not really. As others have remarked, a constant photon flux with a constant
frequency yields a constant acceleration, and the easiest way is to compute
this acceleration is to use the conservation of momentum.

The rate at which momentum is transfered will be N times the momentum
transfer per photon, where N is the photon flux (number per unit time), and
the momentum transfer per photon is 2h/wavelength.

It's easy to see that if N and the photon wavelength are constant, the rate
at which momentum is transfered will also be constant.

If the object is moving relativistically, neither the photon flux N nor the
momentum per photon will be constant as the velocity increases. In fact,
they'll both change by the same factor, the doppler shift factor, which is
sqrt(1-beta/1+beta) (for objects moving away), where beta is the normalized
velocity v/c. There's a fairly neat way of looking at this which makes it
easy to get this result, but I won't get into it unless there is some
interest.

In any event, for a relativistically moving body, the total rate of transfer
of momentum will be reduced by a factor (1-beta)/(1+beta) due to the
combination of doppler shift and reduced photon flux.
 >> Stay informed about: Motie "Light Sail" 

Mike Williams wrote:

> I also reckon that you get a rather odd effect if the energy imparted to
> the sail comes from the Doppler shift on the photons due to the sail
> moving. The faster the sail moves, the greater is the Doppler shift, and
> so each photon loses a greater amount of energy to the sail.

Think about it from the standpoint of the sail - the light hitting
it is also red-shifted as its velocity relative to the star increases.
In other words, as the sails speed relative to the star increases,
lower-energy photons hit it. Does that help?

--
Brian Davis
 >> Stay informed about: Motie "Light Sail" 

John David Galt wrote:

 > Des Kavanagh wrote:
  >> In the Light Sail, a photon strikes a mirror, at optimum
  >> efficiency at normal incidence (not that that matters, but for
  >> simplicity) and is reflected. Photon does not change
  >> frequency, no energy loss.
  >>
  >> How can the Sail gain kinetic energy?
 >
 > The photon's energy of motion is a vector quantity. Reflection
 > imparts velocity to the sail equal to the difference between
 > the photon's old
 > and new kinetic-energy vectors. The fact that they are the
 > same size does not mean that the (vector) difference between
 > them is zero.

Sorry. Energy is a scalar. Kinetic enegry, for example, is
m(V.V)/2 (scalar times vector inner product divided by scalar
yields scalar). You are right for momentum, however.

The change in energy of the light sail is reflected (haha) in the
change in frequency of the photon (a decrease for speeding up a
sail moving away, and an increase for slowing down a sail coming
in to the light source.)
--
Edward Cherlin, Simputer Evangelist
Encore Technologies (S) Pte. Ltd.
Computers for all of us
<a style='text-decoration: underline;' href="http://www.simputerland.com," target="_blank">http://www.simputerland.com,</a> <a style='text-decoration: underline;' href="http://cherlin.blogspot.com" target="_blank">http://cherlin.blogspot.com</a><!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Motie "Light Sail" 

Edward Cherlin wrote:
 >
 > John David Galt wrote:
 >
  > > Des Kavanagh wrote:
   > >> In the Light Sail, a photon strikes a mirror, at optimum
   > >> efficiency at normal incidence (not that that matters, but for
   > >> simplicity) and is reflected. Photon does not change
   > >> frequency, no energy loss.
   > >>
   > >> How can the Sail gain kinetic energy?
  > >
  > > The photon's energy of motion is a vector quantity. Reflection
  > > imparts velocity to the sail equal to the difference between
  > > the photon's old
  > > and new kinetic-energy vectors. The fact that they are the
  > > same size does not mean that the (vector) difference between
  > > them is zero.
 >
 > Sorry. Energy is a scalar. Kinetic enegry, for example, is
 > m(V.V)/2 (scalar times vector inner product divided by scalar
 > yields scalar). You are right for momentum, however.
 >
 > The change in energy of the light sail is reflected (haha) in the
 > change in frequency of the photon (a decrease for speeding up a
 > sail moving away, and an increase for slowing down a sail coming
 > in to the light source.)
 > --
 > Edward Cherlin, Simputer Evangelist
 > Encore Technologies (S) Pte. Ltd.
 > Computers for all of us
<font color=purple> > <a style='text-decoration: underline;' href="http://www.simputerland.com," target="_blank">http://www.simputerland.com,</a> <a style='text-decoration: underline;' href="http://cherlin.blogspot.com</font" target="_blank">http://cherlin.blogspot.com</font</a>>

Despite all that I have read, both here and sci.physics et al,
I have a fundamental problem understanding how a Light Sail
can impart energy.

To reduce it to simplicity, hence eliminating Doppler shift
and/or relativistic considerations:

Consider a stationary Light Sail. A photon impinges on it
and is reflected. The phot presumably is reflected at
180 at C, no frequency change hence no energy loss.
How can the Sail gain energy?<!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Motie "Light Sail" 

On my first read of this thread- I thought the idea was ludicrous. But
having read the article- there could be some merit... ah well- if Gold is
correct (and bravo to him) it's okay with me. I've always thought light
sails were dull. I want nuclear propulsion and I want it now!

Still, the concept has been around for decades (centuries?)- it's amazing no
one ever brought this up before. Not impossible- just amazing!

Paul M


"Des Kavanagh" <"deskavanagh-AT("@)earthlink-DOT(.)net> wrote in message
news:E1VOa.91646$Io.7938014@newsread2.prod.itd.earthlink.net...
 > A recent article in New Scientist suggests that Light Sails
 > cannot be used to propel spacecraft. The argument is made that
 > such a system would contravene the First Law of Thermodynamics
 > and would constitute a perpetual motion machine of the first kind.
<font color=purple> > <a style='text-decoration: underline;' href="http://www.newscientist.com/news/news.jsp?id=ns99993895</font" target="_blank">http://www.newscientist.com/news/news.jsp?id=ns99993895</font</a>>
 > A more detailed explanation from the original proponent of the theory:
<font color=purple> > <a style='text-decoration: underline;' href="http://www.arxiv.org/html/physics/0306050</font" target="_blank">http://www.arxiv.org/html/physics/0306050</font</a>>
 >
 > NASA are currently developing Light Sail propelled vehicles.<!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Motie "Light Sail" 

On the third hand (sorry)- Gold says the Mirror gets hot very quickly...

Surely, something could be done with the heat?


PaulM





"Des Kavanagh" <"deskavanagh-AT("@)earthlink-DOT(.)net> wrote in message
news:E1VOa.91646$Io.7938014@newsread2.prod.itd.earthlink.net...
 > A recent article in New Scientist suggests that Light Sails
 > cannot be used to propel spacecraft. The argument is made that
 > such a system would contravene the First Law of Thermodynamics
 > and would constitute a perpetual motion machine of the first kind.
<font color=purple> > <a style='text-decoration: underline;' href="http://www.newscientist.com/news/news.jsp?id=ns99993895</font" target="_blank">http://www.newscientist.com/news/news.jsp?id=ns99993895</font</a>>
 > A more detailed explanation from the original proponent of the theory:
<font color=purple> > <a style='text-decoration: underline;' href="http://www.arxiv.org/html/physics/0306050</font" target="_blank">http://www.arxiv.org/html/physics/0306050</font</a>>
 >
 > NASA are currently developing Light Sail propelled vehicles.<!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Motie "Light Sail" 

Des Kavanagh <"deskavanagh-AT("@)earthlink-dot(.)net> wrote:
> Consider a stationary Light Sail. A photon impinges on it
> and is reflected. The phot presumably is reflected at
> 180 at C, no frequency change hence no energy loss.
> How can the Sail gain energy?

There are actually THREE possibilities for the photon (as NO mirror
has a 100% reflectivity):
1) the photon as reflectivity without loosing energy and/or impulse.
If you work out the formulas that will mean that the MASS of the
lightsail (and attached ship) will be INFINITE large (the so called
"immovable object"). The lightsail won't move and will not gain
energy then.
2) much MORE likely, when the mass of the lightsail (etc) is large but
NOT infinitely so: some impulse will be transferred from the photon
TO the lightsail (as the mass still is MUCH then the relativistic
mass of the photon, it will only be a very small amount).
Now the photon DID loose energy, so the reflected photon will have a
lower frequency (energy of a photon is directly proportional to its
frequency). This will happen to MOST of the photons.
3) as the mirror is NOT 100% reflective, some photons will be ABSORBED
by the lightsail, imparting all of their energy and impulse TO it.
Due to this the sail will "heat up" too, and the excessive warmth
will be radiated away by emission of (new) photons of a much LOWER
frequency (and thus energy), mostly within the infrared frequency band.

In both cases, 2 and 3, the lightsail WILL gain energy and impulse (motion).
So it will start moving (away from the light emitting source, that is:
the sun/star it was standing still in respect OF).

Of course there is no such thing as an object standing still ABSOLUTELY,
it will always be moving compared to other objects (than the one you based
your frame of reference on).
--
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** Eef Hartman, Delft University of Technology, dept. EWI/TWA **
** e-mail: E.J.M.Hartman DeleteThis @math.tudelft.nl, fax: +31-15-278 7295 **
** snail-mail: P.O. Box 5031, 2600 GA Delft, The Netherlands **
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 >> Stay informed about: Motie "Light Sail" 

On Wed, 09 Jul 2003 22:25:06 -0700, Hop David
<hopspage RemoveThis @tabletoptelephone.com> wrote:

>
>
> Erik Max Francis wrote:
>> GrapeApe wrote:
>>
>>
>>> Intuition lies, but mine tells me that such a solar sail would never
>>> even get
>>> the first puff of solar wind within them. I may side with the New
>>> Scientist
>>> until there is a working prototype.
>
> The New Scientist article used the spinning of a Crookes Radiometer as
> evidence of Gold's claim. The devices down here aren't really in a
> vacuum. The thin air on the dark side expands from heat and pushes the
> radiometer. I'm told if the device were opened to the vacuum of outer
> space light pressure would dominate and the wheel would spin the other
> way.
>
> Henry Spencer has cited the example of Radarsat 1, which has a sun-
> synchronous orbit. Continuous sunlight pushes it's solar arrays and radar
> antenna towards the earth. 2/3 of its station keeping fuel needs to be
> used to counteract this push, an effect its designers hadn't expected. I
> believe acceleration due to light pressure is already well supported with
> empirical evidence.

The solution is simple: Just slow it down in its orbit just enough so
that the pull of the sun's gravity will balance the push of the
sunlight!
 >> Stay informed about: Motie "Light Sail" 

Tim Bruening wrote:

> The solution is simple: Just slow it down in its orbit just enough so
> that the pull of the sun's gravity will balance the push of the
> sunlight!

Congratulations, you're now replying to posts that are four-and-a-half
years old instead of seven.

--
Erik Max Francis && max.RemoveThis@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
A man that studieth revenge keeps his own wounds green.
-- Francis Bacon
 >> Stay informed about: Motie "Light Sail" 

Erik Max Francis wrote:

> Tim Bruening wrote:
>
> > The solution is simple: Just slow it down in its orbit just enough so
> > that the pull of the sun's gravity will balance the push of the
> > sunlight!
>
> Congratulations, you're now replying to posts that are four-and-a-half
> years old instead of seven.

I tried to enter the Larry Niven group on my own computer, rather then via
Google, but could only get about 200 posts from 2003.
 >> Stay informed about: Motie "Light Sail"