Orbit B

```>>David gave me these numbers
>>Pluto's mean orbital velocity is 4.74 km/sec.
>>Earth's mean orbital velocity is 29.79 km/sec.
>>
>>Are these right?  They seem backwards.
>
>I'ld agree.   It seems odthat you'ld accelerate out from the inner system
>to a slower velocity.  I suppose you might be losing the dif to potential
>energy changes.

Comparing energy is an excelent way here: The further away from the Sun, the
less kinetic energy is needed to overcome the ever more decreasing
gravitational energy from the Sun.

And if you like formulas, Brian :)

centrifugal acceleration: v^2/r
gravitational acceleration: G M/r^2

For a stable orbit both need to be equal: v^2/r=G M/r^2 --> v^2=G M/r
So while intuition may leave you in the dark, formulas make reality (sort of).

>But I suppose it isn't critical for our discusion.  Assumeing a beam
>diameter 40 times the dimeter of earth.  4.76Km/s will still have you cross
>the beam in 31 hours.

Yes, but theoretically you could build the beam-array much farther away from
the Sun. I guess the only limit is where the gravitational acceleration of
the Sun becomes less than that of nearer bodies or less than the
acceleration caused by the beaming itself.
Besides that, you assume the array is moving perpendicular to its beaming
direction. Since the array is slowly moving in a circle it could start
beaming at a time where it's own motion is in about the same direction as as
the direction of the beam. This way the perpendicular movement is much less.

>>Don't we already have computers that could be programed to reasonably figure
>>this aiming problem out?
>
>They could given current accurate info.  But given that the info has to
>travel at the spped of light, it would be months out of date by the time
>the mirror systems got it.  Given that the actuall rates will varry back
>and forth a bit durring the interveaning time (given random flexing of the
>sail, and random variations of the beam), and we can't predict what these
>variations will be.  The aiming calculations will be precise calculations
>bases on very bad information.  I.E. computer generated guesses.  Even
>assuming not one unexpected thing ever happens on the ship or mirror.  If
>you guess wrong even once.  You're aiming the beam into empty space and the
>ship is racing away from where you think it is.
>
>Just to complicate things.  The mirror is moring at a high fraction of the
>speed of light.  So relatavistic distortion will distort the beam, mirror,
>and apparent space.

All this is irrelevant, computers could calculate the path far in advance.
Besides that, the Asimov could follow the beam (up to certain limits).

```