Light sail SPS; Sun-Earth L1 (was Correcting my own math -- CORRECTED)

Hi Ian,
On 05.02.2012 02:41, Ian Woollard wrote:
> On 4 February 2012 22:20, Frank > > wrote:
>
> > How would a power sattellite stop that phenomenon?
> > After all, a power sattellite is nothing else as a solar sail
> > spacecraft, it get's at least half the thrust from solar light pressure
> > as a solar sail spacecraft, but it just hasn't the provisions to handle
> > this forces by solar sailing.
> >
>
> Yes, but your analysis doesn't go far enough. Lightsails actually work by
> deliberately tipping themselves to the incident light to give an
> acceleration vector along the orbital trajectory, otherwise nothing much
> happens.

Sounds reasonable.
>
> So the answer to the question is that it doesn't matter. Over the course of
> a year, the geosat directly faces the sun at all times, and the sun ends up
> having pushed on all sides of the GEO sats orbit around the Earth. The push
> deranges the orbit... it will be elliptical... a bit.. at all times..
> because of this, but after a year, it's back where it started, the push has
> cancelled.
>
> So it's only second order effects that matter, because to first order it
> doesn't do anything at all.

Still, for a sat which might have a solar cell area of about 50 - 70
sqm., the east/west station keeping is already perturbed through the SRP
and those secondary effects are already accounted for on regular sats.

I understand, that for station keeping in an geostationary orbit
the fuel needed for this east/west station keeping is much less, than
the north/south control.

But is it still much less for a square km sized power sat with a solar
cell area of say 8000000 (eight million) square metres?
Thats quite a few orders of magnitude of SRP-forces more as on
communication sats, but a reasonable figure for a power sat.

I remember Keith Henson writing that engineers calculated tons of fuel
needed to operate a power sat.

And station keeping is not the only action where fuel is needed.
Attitude control and pointing would also need some fuel and that could
be saved with solar sailing too.

>
> If you still don't believe me, consider that the simple lightsail push
> effect goes as inverse square law on distance from the sun, but so does
> gravity, and it's in the same direction; and I hope you're not claiming
> that the Sun's gravity catastrophically destabilises geosats???

No, catastrophically not, but what matters are costs,
if the secondary effects you mentioned would demand already half of the
sattelite mass in fuel comsumption for 15 years of a comsat lifetime and
we consider that this fuel has to get delivered to the power sat in GEO,
fuel consumption should get some closer look.
Especially if the SRP force, which already initiates fuel consumption,
grows orders of magnitude compared to a comsat.

The power sats are simply not refuelled. A power sat, which supposedly
should have a much longer lifetime would have to be refuelled with fuel
transported to GEO, which is much more expensive than delivered to LEO.

Best wishes

Frank