starship-design: Following the beam

[T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)]

Zenon replied:

>> The beaming station makes a "focussed" (as far as interference allows) 
>> and beams it straight forward (in the direction of Tau Ceti).
>> In this case not the velocity of the orbiting station is important, 
>> but it's acceleration (to the center of gravity), which is rather low. 
>> Low enough for the starship to compensate and change its direction.
>> 
>That is, the ship must go along the helical curve with the
>radius equal the radius of the beaming station orbit
>(assuming the plane of the orbit is perpendicular
>to the direction to Tau Ceti), or along a sinusoid
>with amplitude equal to the diameter of the orbit
>(assuming the direction to Tau Ceti lies within the plane
>of the orbit).

I would prefer a plane of orbit that is perpendicular to the direction of TC
since we would not have any moments that the Sun is in the view.

>Can somebody calculate what lateral thrust (and acceleration,
>amounting to a centrifugal force for the crew) 
>will be needed for such a trajectory ?

a=4 pi^2 r/T^2  (a=v^2/r  v=2*pi*r/T)

Where
a = Acceleration in m/s^2
r = The radius of the helix in meters
T = Time to make a complete orbit in seconds

So say we have a beaming station on Earth:

a = 4 * pi^2 * 1.5E11/(3.2E7)^2 = 6.1E-3 m/s^2

Or for the moon around the Earth:

a = 4 * pi^2 * 3.84E8/(2.3E6)^2 = 2.9E-3 m/s^2

>However, I wonder if the jiggle of the direction of the beam
>due to "directional noise" can be compensated in this way
>(may I recall: a tilt of the 100km diameter beaming antenna
>by 1/25th of an inch at the edge (i.e., a 1/100 000 000 directional error)
>gives a sweep of 100 000 km at 1 ly distance).

The only ways to avoid jiggling are to increase the sail/receiver or to make
the sender more stable.
About the stability of the laser, is a 1 millimeter jiggle not a little bit
large? In fact, if we have jiggles of that size, we have to use microwaves.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Before we go further discussing apertures/jiggles, we should first determine
what resonable limits for wavelenghts will be, when we use phased arrays.

Timothy