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Maybe a bit late, but I can't keep up with you guys, 40 letters in 1.5 days!
> > 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.
>This is the paradox of orbital mechanics. To go from a faster
>smaller-radius circular orbit to a slower larger-radius circular orbit,
>you have to accelerate twice -- once to raise the apoapsis of your
>orbit, again to raise the periapsis. So, in other words, yes, your
>acceleration goes largely into raising your potential energy rather than
>increasing your speed.
This doesn't make sense, after accelerating twice you are going faster, and
at the same time you are moving in a slower orbit.
You may mean the same, but I don't follow it. I would explain it like this:
When you are accelerating outwards, you are drifting to a larger orbit, then
after having stopped to accelerate, you are still moving away from the Sun,
but at the same time gravity pulling at your back, and you are slowing down,
so at the furthest point you are moving rather slow. Then gravity will pull
you to the Sun and your velocity starts increasing, untill you are closest
to the Sun and then you are decelerating again. Hence a parabolic orbit.
Comparing stable orbits isn't really a good idea.