--- In spacesettlers@yahoogroups.com, Al Globus wrote:
> I do not think the spacing between sats needs to be nearly as large as proposed. I don't know where the numbers came from, perhaps comsats.

The 109x diameter spacing I cited is the maximum length of the umbra:
http://en.wikipedia.org/wiki/Umbra

"The umbra (Latin for "shadow") is the innermost & darkest part of the shadow, where the light source is completely blocked by the occluding body. An observer in the umbra experiences a total eclipse."

The length of the umbra changes as the distance of the earth to the sun changes. The closer the earth is to the sun, the shorter the umbra. The farther the earth is from the sun, the longer the umbra -- up to a maximum of 109X the diameter of a circular occluding object (at an Earth-Sun distance of about 94.5 million miles, which occurs in current times in June every year).

Therefore, the larger the SPS, the larger the umbral length. A 2 km diameter SPS casts a 218 km umbra. A 20 km diameter SPS casts a 2,180 km umbra.

Also, as I mentioned before, the spacing would actually have to be *larger* than 109x the diameters, because of the orbit-compressing effect of solar light pressure on the SPS units. Instead of being circular about the earth, the SPS orbits will have to be farther from the earth on the sun side, and closer to the earth on the night side. The sps units will also be speeding up and slowing down, as well, because of this solar light pressure.

This light-pressure problem was mentioned by Keith Henson almost three years ago, by the way. See his posts on light pressure, here:

+++---+++
In GEO the earth is the object being orbited around and the light
pressure is not radial from the earth.

Consider a very light sail in GEO. If it is anything but edge on to
the sun, it would be blown out of GEO and away from the earth like
dandelion fluff.

Heavy objects are accelerated one way and then 6 months later the
other way. Light power sats pick up nearly 1000 m/sec velocity over 3
months compared to orbital velocity of 1500 m/sec.
+++---+++

...and here:

+++---+++
Seriously, this is a huge problem with some of the designs companies
are currently considering putting up. They are talking extremely
large amounts of money to service the power sats with replacement
reaction mass for station keeping, mainly against solar light
pressure.

If you or any of the solar sail people know how to solve it this
problem, it would be of huge interest.
+++---+++

...and here:

+++---+++
PS, for station keeping reasons, you want a power satellite to be as
efficient as possible (to reduce the area). And the more mass the
better. Lots of mass averages the light pressure acceleration over a
year. Really light power sats require many tons every year of station
keeping reaction mass to prevent light pressure from blowing them away
like dandelion fluff.
+++---+++

...and here (the original light-pressure message from Keith Henson):

+++---+++
Countering light pressure on powe satellites.

Unfortunately these tricks do not eliminate the cost of fuel to offset
light pressure.

This is a serious problem on very lightweight power sats (0.4kg/kW or
less) where light causes accelerations in the 1/10,000 m/sec^2 range.
Unless opposed, this acceleration builds up ~8 m/sec/day, ~1km/sec
over 120 days. Orbital velocity at GEO is ~3km/sec. It is easy to
see uncorrected light pressure would cause a serious orbital
disturbance. A satellite in the 4kg/kW range only builds up ~100m/sec
over the same time and can to some extent average out the light
pressure over a year (galactic east half the year, galactic west the
other half).

While modeling this situation it occurred to me that an active gravity
gradient control might be able to offset light pressure.

At 1 AU the radiation pressure is around 4.6 micro newtons per square
meter, 9.2 micro newtons per square meter reflected.

That's 4.6 to 9.2 newtons per square km. (See attached spreadsheet)
+++---+++

On Feb 3, 2012, at 7:45 PM, hitssquad wrote:

>
> --- In spacesettlers@yahoogroups.com, Al Globus wrote:
> > I do not think the spacing between sats needs to be nearly as
> large as proposed. I don't know where the numbers came from, perhaps
> comsats.
>
> The 109x diameter spacing I cited is the maximum length of the umbra:
> http://en.wikipedia.org/wiki/Umbra
>
> "The umbra (Latin for "shadow") is the innermost & darkest part of
> the shadow, where the light source is completely blocked by the
> occluding body. An observer in the umbra experiences a total eclipse."
>
Are you concerned that the sats will eclipse each other during certain
parts of the orbit at the equinoxes? Seems there should be a way
around that.

>
> This light-pressure problem was mentioned by Keith Henson almost
> three years ago, by the way. See his posts on light pressure, here:
>
> +++---+++
> In GEO the earth is the object being orbited around and the light
> pressure is not radial from the earth.
>
> Consider a very light sail in GEO. If it is anything but edge on to
> the sun, it would be blown out of GEO and away from the earth like
> dandelion fluff.
>
I've runs sims on that. Most of the acceleration cancels out over a
24 hour period, but not quite all. At 100 g/m^2 after a year you have
unacceptable movement so some station keeping is needed. However,
it's not all that bad. Just an engineering problem to solve.

To be specific:

-- The force along the orbital direction cancels out in 24 hours

-- The force normal to the orbital plane cancels out in 24 hours

-- The only component that doesn't cancel is normal to the Sun, but
due to orbital mechanics this mostly affects the eccentricity -- which
you can live with. You might even be able to use it to avoid the
shadowing problem above.

You just need to be clever, and not give up at the first little
problem that rolls along.

On Feb 3, 2012, at 7:45 PM, hitssquad wrote:

> The 109x diameter spacing I cited is the maximum length of the umbra:
> http://en.wikipedia.org/wiki/Umbra
>
> "The umbra (Latin for "shadow") is the innermost & darkest part of
> the shadow, where the light source is completely blocked by the
> occluding body. An observer in the umbra experiences a total eclipse."
>
> The length of the umbra changes as the distance of the earth to the
> sun changes. The closer the earth is to the sun, the shorter the
> umbra. The farther the earth is from the sun, the longer the umbra
> -- up to a maximum of 109X the diameter of a circular occluding
> object (at an Earth-Sun distance of about 94.5 million miles, which
> occurs in current times in June every year).
>
> Therefore, the larger the SPS, the larger the umbral length. A 2 km
> diameter SPS casts a 218 km umbra. A 20 km diameter SPS casts a
> 2,180 km umbra.

Wait a minute. The plane of GEO is inclined 22+ degrees to the
ecliptic. So how is it that SSPs eclipse each other even at the
equinoxes?