I would appreciate mathematically inclined SSI list members critiquing
a concept that might be called a space anchor. I came upon this
concept by accident while working on using gravity gradient to
stabilize a power sat. A ton mass radially inside or outside GEO by
63 km generates a newton of force on a tether. One inside and one
outside attached by a long bridle to the edges of a one km
transmitting antenna will provide 1000 N-m of torque to orient the
solar collectors and expends no fuel.
of the earth should keep the power sat from rotating on the tether
axis. (This axis needs to be oriented north/south. If the magnetic
field fails, there is a complicated way to use gravity gradient to
keep this axis oriented.)
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.
Thats 4.6 to 9.2 newtons per square km. (See attached spreadsheet)
A one t mass on 290k of tether provides 4.6 N force on a satellite at
GEO. (It needs to be larger because the light force is on it all
around the orbit and the correcting force applies as a sine function
twice per orbit.)
If you put the power sat in the middle of 600 km of tether with a ton
mass on each end, you could offset the light pressure when the power
sat is between the earth and the sun by reeling the tether to let the
mass on the end outside of GEO go further out--giving a net force
toward the sun to balance the light pressure. And when on the side of
the earth away from the sun, reel the string so the mass toward the
earth is further toward the earth again offsetting the light pressure.
At this length of tether it would take 1000kg of space anchor mass per
square km of power sat.
Moving the string 600 km in 24 hrs is 25 km/hr or 7 m/sec. This well
under the 200 m/sec that a one t mass would reach in 12 hours under
4.6 newtons of force so the string should not go slack.
In the large picture, this process transfers the light thrust to the
earth through gravity.
This probably needs dynamic modeling to see how far the anchor masses
would swing.
Another possibility (suggested by retired engineer Mike Ward) would be
to attach the masses to cables or long booms attached to the sunlight
collecting power surface so the messes always stayed in the direction
of the sun. I worry they would have to be stiff because at local
sunrise and sunset there is no gravity gradient force on them.
Keith Henson
PS. If this has been proposed before, please let me know so I can
give proper credit.
> [...]
>
> 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).
>
GEO is surely 1 day (the orbital period), not 1 year, isn't it?
That is, for 12 hours the satellite is moving towards the sun and light
pressure is in opposition to its orbital motion, slowing it down, while
for the next 12 hours the satellite is moving away from the sun and
light pressure is in line with orbital motion, resulting in
acceleration. I've always assumed that one could slightly reposition the
satellite in such a way that the two effects essentially canceled over
24 hours, leaving it in the same orbit it started with. Haven't actually
run the orbital numbers myself, but it sounds like something Geoffrey
Landis or somebody like that would have looked into...
That said, using tethers for orbital control of a solar power satellite
sounds like a great idea!
Arthur Smith
On Thu, Apr 16, 2009 at 6:32 AM, Arthur Smith
>> [...]
>>
>> 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).
>>
> Keith, the relevant time-period for averaging solar light pressure in
> GEO is surely 1 day (the orbital period), not 1 year, isn't it?
extreme and consider one as light as a solar sail. It just gets blown
out of orbit.
> That is, for 12 hours the satellite is moving towards the sun and light
> pressure is in opposition to its orbital motion, slowing it down, while
> for the next 12 hours the satellite is moving away from the sun and
> light pressure is in line with orbital motion, resulting in
> acceleration.
This is correct, the counter accelerations at 6 am and 6 pm average
out over a day. But the 12 noon and 12 midnight are both directed
away from the sun and screw up the orbit.
> I've always assumed that one could slightly reposition the
> satellite in such a way that the two effects essentially canceled over
> 24 hours, leaving it in the same orbit it started with. Haven't actually
> run the orbital numbers myself, but it sounds like something Geoffrey
> Landis or somebody like that would have looked into...
>
> That said, using tethers for orbital control of a solar power satellite
> sounds like a great idea!
The one thing they don't do is keep the satellite from rotating around
the tether. But there might be a way to do even that.
I am thinking of a leading and trailing tether pair where the trailing
one's CG is in a slightly higher orbital position. A cable from the
tips of the solar collectors (6 km or so below and above the orbital
plane) to the mid point of the tether would remain under tension. The
same would be true of a leading set of masses with a lower CG. This
needs numerical analysis, but if it works, it should provide a full 3
axis stabilization of a power sat with no expenditure of reaction mass
at all.
This is an alternate to using a big coil interacting with the earth's
magnetic field.
Keith
I don't think the fact that the force is pretty much constant away from
the Sun matters, because the satellite is orbiting the Earth. The
satellite is still gravitationally bound to the Earth, so the light
pressure force is in a way acting on the Earth-satellite system. Its
direct effect is an essentially constant force on the satellite; on the
other hand the satellite will also see gravitational forces from the
Moon that are not that much smaller than the light-pressure force you're
considering, which will also have a similar steady direction on a daily
basis (though rotating around once a month in the case of the Moon).
isn't obvious to me right now...
Arthur
On Thu, Apr 16, 2009 at 9:41 AM, Arthur Smith
> I don't think the fact that the force is pretty much constant away from
> the Sun matters, because the satellite is orbiting the Earth. The
> satellite is still gravitationally bound to the Earth, so the light
> pressure force is in a way acting on the Earth-satellite system. Its
> direct effect is an essentially constant force on the satellite; on the
> other hand the satellite will also see gravitational forces from the
> Moon that are not that much smaller than the light-pressure force you're
> considering, which will also have a similar steady direction on a daily
> basis (though rotating around once a month in the case of the Moon).
>
> But there's some math involved, the importance one way or the other
> isn't obvious to me right now...
of Earth Satellites
[lead in]
The main works devoted to the study of the effects of solar radiation
pressure on the motion
of artificial earth satellites are reviewed. The resonance case, when
the motion of the satellite
undergoes long-period variations with large amplitudes, is considered in detail.
snip
Yet, in
this case, the observed effect of radiation pressure was so
small that even toward the end of the two-year period the
magnitude of the effect was still determined with an accuracy
of not more than 30%. The accuracy of determining the
magnitude of the radiation pressure from observations of the
satellite "Echo 1" (1960 ii) was much greater, even during
the first month of observations, since the corresponding
variations in the orbit of "Echo 1" are much greater than in
the orbit of "Vanguard 1." These variations in the orbit of
http://www.aiaa.org/content.cfm?pageid@...
Which makes sense. Large light objects are blown around more by wind
or light pressure. Some recent power sat designs are not much more
substantial than Echo 1
Keith