# Re: starship-design: Required microwave-antenna size. 100-light-year trip.

```> From: kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39)
>
> At 1:22 AM 10/24/96, DotarSojat@aol.com (Rex Finke)  wrote:
> --------
> >The range boundary between the "near" and "far" fields can be
> >defined as the distance at which the focused image spot size is
> >equal to the size of the beam-forming aperture, and at that range
> >the spot size is that given by Fraunhofer diffraction (with a
> >factor of 2 to go from radius to diameter), so--
> >     spot diameter = De = range * 2 * 1.22 * lambda/De
>
> ???  Doesn't   De = range * 2 * 1.22 * lambda/De
> Reduce to       1 = range * 2 * 1.22 * lambda
>
No. It reduces to:   De^2 = range * 2 * 1.22 * lambda     ;-))

> Questions:
> How much range deviation can you tolerate?  Since the beam is being aimed
> at a ship you can't see in real time.  You'ld have to expect it would drift
> ahead or behind the exact focus spot.  How much slack is allowed?
>
> What is the lateral deviation of the beam?  I.E. whats the power per m^2 in
> the center vs the edge of the focused spot?  The differences would distort
> the sail and alter the ships course and acceleration.
>
> As mentioned above, how precicely can we measure the possition of an object
> floating in space?  Assuming each microwave emmiter platform has laser
> ranging info to each/some of the others.  Can you get the nessisary
> possitional accuracy?  (Within a couple MM?)  Note you don't need to
> control the position that accurately, just know what it is so you can
> compensate for it.
>
Let me recall below my deviation tables, buried long ago
in the old LIT newsletter archives.
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]

I.e., 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

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