RE: starship-design: Massively Distributed Computing for SETI

```> From owner-starship-design@lists.uoregon.edu Sun Mar 18 15:54:38 2001
> From: "L. Parker" <lparker@cacaphony.net>
>
> > Given the relative positions of the stars haven't moved visibly
> > in thousands of years.  We can aim a fixed vector.
> > The only problem is earth orbit around the sun.  If beam array
> > isn't a ring around the sun, I.E. if its around a
> > point in orbit, the ship would have to follow the beam
> > in a helical course around a direct vector from the sun,
> > toward the target star.
> >
> > No serious math needed, or really possible. We can't aim
> > the beam because we can't know where the ship is to aim it at.
>
> Actually, there is more to it than that.
>
>
> "Moved visibly" is not the same thing as haven't moved. All stars are in
> motion, they follow their own orbits about the center of the galaxy as I am
> sure you know. Our sun is in one such orbit, any target star is going to be
> in another orbit traveling at a different velocity.
>
> We cannot simply aim the beam at the star, the star will not be there when
> the beam arrives. We must aim the beam at where the star will be when the
> beam gets there. This is a non-trivial task considering that all distances
> to stars are currently _estimated_.
>
> Then you must add for the motion of the beam array in its orbit about Sol.
> As was stated by Kelly this induces a helical component, and if we are in
> orbit about Earth or some other planet, it induces another helical
> component. Although it is possible for the ship to correct its course for
> helical movement of the beam source, this involves tacking the sails to
> maintain a steady course on a continuous basis and involves an element of
> risk if we lose the beam entirely and it doesn't solve the other problem.
>
> That is actually the easiest problem to solve. The second problem involves
> Doppler drift. As the ship gains velocity, it begins to experience Doppler
> drift or "red shift". Unfortunately, the sail is composed of a material
> designed to reflect a particular wavelength of radiation. It may also
> reflect other wavelengths, but not with the same efficiency. Therefore the
> beam transmitter must be capable of tuning the output across a range of
> frequencies to keep the energy received by the sail at a constant
> frequency.
>
> This means we must know the exact speed, course and distance
> of the sail at all times, constantly update the targeting data
> for the sail, the beam source, and the sail's destination,
> all in four dimensions, one of which has at least one harmonic
> component if not two to compute a continually changing
> target solution and frequency solution for the beam.
>
> Any way we approach this, the solution is going to be compute
> intensive, and it involves many of the same types of calculations
> being done by the SETI team, which was why I found the article
> so interesting.
>
Add to that the consequences of even small aim errors
on interstellar distances. I would like to remind you
of the "deviation tble" I have sent to the list
some five years ago... Here it goes:

------------------------------------
>From zkulpa Thu Oct 24 16:49:07 1996
From: zkulpa (Zenon Kulpa)
To: starship-design@lists.uoregon.edu

Note that the table gives deviation at target due to
the change of ORIENTATION of the beaming device,
the sensitivity to change of its POSITION is, fortunately, far smaller.
Actually the sensitivity factor for position change equals 1 (one) -
how much the platform moves sideways, so much does the beam at target
(after some years...).
However, if the platform moves along the Sun-centered orbit,
its velocity is of the order of tens of kilometers a second
(see another table below), hence it must compensate
for its change of position with appropriate change of orientation,
and the latter must be VERY accurate (as the deviation table shows).
Moreover, the change of orientation must change very accurately
with the distance to the target ship. The latter, I am afraid,
is hard to know exactly in real time at long distances
(e.g., the acceleration/speed will vary due to many factors,
among others the accuracy of aiming the beam [and hence the
thrust], the distribution of unknown masses along the way
[e.g., invisible gas clouds or stray brown dwarf nearby...]).

==================================================================
The beaming platform must orbit the Sun, thus:

a) It will move quite fast, depending on the distance
from the Sun, e.g:

Distance
Orbit   from Sun  Velocity  Remarks
of      [mln km]    [km/s]
----------------------------------------------------------------
Mercury      60        50   good place for solar-powered lasers
Earth       150        30   near home...
Jupiter     800        13   lots of local resources & moons to mine
Pluto      6000         5   rather too far...

b) So, it must constantly change its aim if it is not going
to miss the target by hundreds of kilometers every 10 sec or so...
And by how much it must change the aim?
I have compiled the table below, where:

"Size" is the "principal" dimension of the laser/maser gun component
(e.g., the length of the laser "tube", or the diameter
of the deflecting mirror, or microvawe antenna dish);
"Tilt" is the amount by which one end/edge of the gun component
moves relative to the opposite one (in milimeters);
"Angle" is the tilt angle (in radians) corresponding to this tilt;
"Distance" is the distance to the target (in light years),
and the table entries contain the "Sweep" (in kilometers),
i.e. approximate distance by which the beam moves sideways
at the target distance:

We have:

Sweep/Distance = Tilt/Size

I.e. (for small angles):

Angle = Tilt/Size

For simplicity, in the table I have rounded the light year
to 10^13 km (instead of more exact 9.4543*10^12 km).

Size   Tilt   Angle  |             Distance to target [ly]
[km]   [mm]   [rad]  |          1              5              10
----------------------+------------------------------------------------
0.1    0.1   10^-6  |    10 000 000     50 000 000     100 000 000 km
1     10^-5  |   100 000 000    500 000 000   1 000 000 000 km
10     10^-4  | 1 000 000 000  5 000 000 000  10 000 000 000 km
----------------------+------------------------------------------------
1      0.1   10^-7  |     1 000 000      5 000 000      10 000 000 km
1     10^-6  |    10 000 000     50 000 000     100 000 000 km
10     10^-5  |   100 000 000    500 000 000   1 000 000 000 km
----------------------+------------------------------------------------
10      0.1   10^-8  |       100 000        500 000       1 000 000 km
1     10^-7  |     1 000 000      5 000 000      10 000 000 km
10     10^-6  |    10 000 000     50 000 000     100 000 000 km
----------------------+------------------------------------------------
100      0.1   10^-9  |        10 000         50 000         100 000 km
1     10^-8  |       100 000        500 000       1 000 000 km
10     10^-7  |     1 000 000      5 000 000      10 000 000 km
-----------------------------------------------------------------------
[Note: for mirrors you must MULTIPLY the result by 2]

E.g., a 100-kilometer diameter microvawe dish
tilted by only 1 mm (1/25th of an inch) at the edge, sweeps the beam
at 1 ly distance by 100 000 (one HUNDRED thousand) kilometers!
(i.e., almost one-third of the Earth-Moon distance)

I am afraid that such deflections are easily obtainable
by heat distortions of the structure or gravitational perturbation
from an asteroid flying some million kilometers away...

==================================================================

-- Zenon Kulpa
```