Re: EUREKA!!!!!!!!!! (ha ha ha ha ha ha) >:-)

[Kevin C Houston <hous0042@maroon.tc.umn.edu>]

On Mon, 20 Nov 1995, Steve VanDevender wrote:

> Kevin C. Houston writes:
> 
>  > On Wed, 15 Nov 1995 KellySt@aol.com wrote:
>  > 
>  > > I still have questions about momentum transfer vs power absorbsion. This
>  > > neat conversion of absorbed power and momentum bothers me.  I would think
>  > > that converting the power would use up the energy that would generate the
>  > > thrust.  Maybe I'm confused?
>  > > 
>  > 
>  > Not at all, if you reflect, you get twice the momentum that you'd get if 
>  > you absorbed.  so there is no violation of energy conservation.
> 
> This is not strictly true.  In fact, I've been quite dubious of
> Kevin's claim that his configuration of solar sails would really
> produce deceleration.  In fact, I believe that you can't use a
> static sail (that is, one permanently attached to the spacecraft)
> to decelerate, as to produce deceleration the reflected photon
> must increase in momentum to compensate for the spacecraft
> decreasing in momentum; the static sail is tied to the spacecraft
> so it cannot change its momentum separately from the spacecraft.
> The previously-mentioned "Dragonfly" sail (from Robert L.
> Forward's _Flight of the Dragonfly_) accomplishes deceleration by
> splitting the sail into a retro-reflecting portion that focuses
> energy back to the remaining portion of the sail attached to the
> spacecraft; in this case the retro-reflecting sail increases in
> momentum to compensate for the spacecraft's decrease in momentum,
> and thereby ends up carrying all of the momentum from the beamed
> power by the time the spacecraft has come to "rest".
> 
> Consider a photon with momenergy [ p, p, 0 ] (that is, energy p,
> momentum p in the x direction, no momentum in the y direction),
> incident on a mirror with initial momenergy [ m, 0, 0 ] tilted at
> an angle theta, such that when theta = 0 the mirror reflects the
> photon straight back along its original path, and positive theta
> means counterclockwise rotation of the mirror.  After reflection,
> the photon has momenergy
> 
> [ p, -p * cos(2 * theta), -p * sin(2 * theta) ],
> 
> and to conserve momenergy the mirror must then have momenergy
> 
> [ m, p * (1 + cos(2 * theta)), p * sin(2 * theta) ].  
> 
> (the total system momenergy remains [ m + p, p, 0 ]).
> 
> You'll note that the expression (1 + cos(2 * theta)) is always
> greater than or equal to 0.  In other words, the x-component of
> the mirror's momentum after reflection is always forward, or at
> best nil.  So you can steer by tilting the sail, but you can't
> slow down.
> 
> If you use multiple reflections, then you can analyze the
> behavior simply by considering the final photon momentum after
> the reflections.
> 
> In the case of a double reflection that leaves the photons
> travelling in the same direction they originally were (maybe
> parallel to their original course) then there is _no_ net change
> in spacecraft momentum.  If you change the direction of the
> photons, then you must _always_ leave them with a smaller
> x-component of momentum than they originally had, and this
> results in increased x-momentum for the spacecraft.  You may be
> able to decrease the efficiency of the sails as much as you want,
> but you will never produce deceleration with multiple-reflection
> schemes as long as the sails are attached to the spacecraft and
> therefore tied to the spacecraft's momenergy.
> 
> A really thorough treatment of multiple reflections would have to
> consider both the finite speed of light and the finite speed of
> propagation of changes in velocity through the spacecraft
> structure; for very high rates of acceleration these would be
> significant effects.
> 

I think you have not completely understood my proposal.  I am _not_ 
saying that the ship would slow down by this arrangement of sails, I'm 
only saying that the foreward momentum of the photons would be dumped 
into sideways momentum (which would then cancel out due to symetry)  the 
photons would be absorbed and converted to electricity, then used to 
power a linear accelerator.  All this rigamarole is to get around 
Timothy's valid objection that the foreward momentum of the recieved 
photons would exceed the momentum of the lineac if the antenna were not 
tilted.  I readily admit that i lack the mathmatical tools to properly 
analyze this, I was hoping that someone else could do that part.  But, 
The main point of the idea is valid, namely that by breaking up the 
sail/antenna into many conic sections, the foreward momentum of the 
absorbed photons can be dumped into the antenna's structure, and not into 
foreward acceleration of the "Asimov"