Update 2002-07-15

Climate modification using orbiting mirrors


Conclusion: Go for moon-based production plants.
Sample from the content: Some consequences of climate modification using orbiting mirrors are discussed such as the need for terraformation in order to prevent the sea level from changing.

NASA is dedicated to pure research and has declared that they prefer others to enter into commercial exploitations of space technology. Probably a wise decision.

In order to make something happen it is necessary that investors are made aware of the potential for profitable space technology.

Here we will discuss one area of space exploitation that seems promising.

Namely the collection and redistribution of solar energy by means of large areas of regulated mirror arrangements placed in orbit around the earth.

It seems like a pretty obvious application and I am sure that there are others who have analyzed similar ideas long before. But I am not aware of any particular work. The basic physics is not hard to handle and it is quicker for me to make an independent analysis here.

1 m2 of mirror area can redistribute several hundred watts of visible light and can prevent the dangerous UV radiation from reaching us. That part of the radiation can instead be converted photoelectrically for supplying the space-based equipment with power.
(For a 6000 K black body the spectral distribution is in %: visible/UV/Infrared: 46/14/40)

An ideal mirror material for that purpose would be highly reflecting for wavelengths beyond the UV and have a high transmission for UV light channelling that part of the energy into a layer whose function is that of a solar cell. Further an ideal material would also be strong and have a low density. Hexagonal supporting structures often turn up in similar contexts. Inventors will be able to find it out I am sure.

The idea to combine mirror and a UV driven photoelectric powersource would probably make the whole construction much more expensive and cost matters, (see the crude calculations below) so it is possible that one would have to accept a less efficient utilization of the available space and energy flux in the initial period.

In order to be able to orient the mirror using only photoelectric power it would be easier to connect the mirror in a frame and move the two internally whithout any external force acting.

For translation of the mirrors external radiation could be used exerting radiation pressure on the mirror from a suitable direction. Only slow adjustments would be possible but that would normally suffice.

Such a mirror may be assumed to be carefully oriented according to what is needed at any given time.

Considering a large number of such mirrors and sensors that determine the current distribution of clouds it is possible to finetune the incoming illumination and heating over large areas of the earth where previously there were entirely different conditions. For instance it would be possible to create mediterranean climate in the cold polar regions. The climate could be modified to any wanted degree. If such a system is built up to such an extent that the mirrors are capable of blocking the sunlight it would also be possible to cool selected areas such as hot and dry deserts. It is reasonable to assume that this would lead to increased precipitation and better conditions for plant growth etc. Presently I havent got very deep into climate models or anything. But one way or the other this could be realized by way of redistributing the energy in the contemplated fashion.

Before continuing lets just observe that if many such mirrors are placed in orbit one would have to consider how this affects satellite communication. If no particular preparations are made the mirrors might block some of the satellite communication when the mirrors rise in number.

Some of the mirrors might be equipped with suitable transponder systems to compensate. The mirrors need their own radio communication anyway since their orientation is assumed to be regularly adjusted according to fresh data from a global system of sensors, perhaps satellite based or using lightweight solarpowered aircraft flying on very high altitudes. Such sensors would among other things monitor the distribution of clouds.

If the polar areas are heated, in particular the Antarctic continent, we know from the debate on the greenhouse effect that the melting ice will give rise to an increase in the global sea level. People in Holland and elsewhere wouldn't fancy that. But there are ways to counter that problem. One way would be to deepen the atlantic ocean by moving matter from the bottom of the sea or from even deeper levels and placing that matter in unpopulated areas or elsewhere where it is needed. This argument seems equally valid in connection with the usual greenhouse debate. If 50 meters of sea bottom is to be moved it would correspond to an average increase of the height of the presently existing land by 3 times that height or 150 m. Since people wouldnt want to pile up that material in populated areas, the average rise in unpopulated areas would be correspondingly higher.

So presently existing forrests and mountain regions would gradually grow in height by several hundred meters

while the Antarctic ice layer is gradually melting. If this material would be used to broaden or heighten mountainous regions the result could be an increased availability of hydroelectric power.

Another possibility would be to somehow bind water chemically, a challenge for researchers in chemistry.

to find an economically sound solution.

Solar-powered methods of transportation for this terraforming operation could be contemplated since there is no hurry. Very slow walking vehicles would be adequate. They wouldnt need to move faster than a snail.

On the other hand if the Antarctic would be left as it is, there are many other areas where a modified climate could lead to important economic growth creating better conditions for farming and habitation.

Although the precise arrangement for this redistribution of solar energy would need to be carefully analyzed before any large scale changes are realized there is no fundamental reason why it wouldnt be a feasible plan.

The earths climate has varied alot in the past and some of the cold areas where it is suggested that the redistributed solar energy would be put to use have previously had a tropical climate which has been deduced from fossile records.

Since the mirror arrangement can be used both for cooling and heating the climate can be finetuned both locally and globally. There is of course a need for extensive research on reliable climate models.

Groundbased astronomical instruments will be rendered useless when those mirrors become numbered since they would unavoidable increase the background light level. The astronomers would have to use instruments permanently placed further away from the earth.

As a space based climate control system of the contemplated type becomes an important factor in our global economy its safe operation becomes very important. Space based service stations will surely play a role.

It might be a good idea to make sure that there is a great degree of overlap of the use of many mirrors for many nations so that everybody has a selfinterest in protecting the mirrors from sabotage or incompetent handling.

I am not sure what type of orbit would be the optimum choice for such mirrors. Formulas simplified to an arrangement where the group of mirrors mimic one big mirror of diameter D creating an authentic image of the sun.

T:Time of orbit in hours. R:distance from the centre of the earth to the mirror. R0:earth radius.

V: orbital velocity in km/s




The illuminated diameter on the ground would be at least D

It would be possible to let that area sweep like a moving spotlight or the mirrors could be readjusted in order to illuminate the same area constantly. If there are alot of mirrors available it would be possible to create a constant illumination for long times provided the clouds didnt prevent it.

The formulas above apply to a single large mirror. But in order to counter the problem of clouds that hinder the transmission of light it would be better to combine widely separated mirror elements.

Further one should expect that climate modification necessitates the combined action of widely separated sources anyway. Because a single spotlight directed to an otherwise very cold area would probably cause extreme weather changes that might not be of the wanted kind. As was stated earlier there is a need for advanced climate models and extensive research using those models.

Who knows, maybe there are conditions where this kind of spotlight weather modification would actually be useful, creating a lovely climate inside its active diameter while there would be intensive raining at the perimeter. Perhaps it would work at the polar areas.

To repeat, such a fixed spotlight would need to be built up from the combined action of many moving mirrors adjusted to direct the light unto the same area. That seems like an exotic situation and perhaps a more likely configuration would create an energy distribution, more resembling that created by the sun if the earth had been rotating in a different manner.

One possible outcome of carefully investigated climate models could be that there are ways by which the distribution of clouds may be controlled and ways to systematically create openings in it, using the space mirrors.

Very crude estimates of the economical balance situation

What is the economic value of this kind of artificial energy source?

For a small scale project, the value can perhaps be estimated in terms of an equivalent increase in available ground area for productive agriculture, habitation and recreation.

Perhaps the area would be say n=3 times that of the illuminated area from a plane mirror. This factor n compensates for the difference between perpendicular incidence and typical incidence of natural solar light. For an effective mirror diameter of 100 kms this equivalent ground area would be say 200 kms wide.

MMaintenance cost per unit area of mirror and year.
QProduction cost of the mirror per unit area.
IInstallation cost per unit area of mirror including transport.
Pproductivity per unit ground area and year.
jinterest %/year.
Leffective lifelength of a mirror.
hEffective mirror thickness.
tEffective mirror density.

I think conventional rocket transports cost c=$20000/kg of cargo. I have to check it out.
(I checked it out. Numbers like that were cited but I also found much lower values around $1000 or less for new tentative methods of transporation.
by Len Cormier, Member, AIAA Third Millennium® Aerospace, Inc. Reno, Nevada. Published as AIAA 97-3124, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference Washington State Convention and Trade Center, Seattle, Washington)


I=cht, n=3, j=8

Economic balance equation: Profit=nP-{M+((I+Q)/L)}F

Balance when cht+Q=L(nP/F-M) => h={L(nP/F-M)-Q}/ct < nPL/ctF

c=20000, h=hu microns, t=500kg/m3, L=30 years, => hu=3(2.8P-M)-Q/10<8P

P for agriculture on fertile ground could be perhaps $50/m2 and year?
(Such numbers are cited for modern agriculture but of course the ground cannot be entirely covered with plants and in order to hold on average there needs to be many other types profitable activities that depend on the artificial illumination and heating.)
(It corresponds to $1.5·1012 per 170km diameter and year and that surely sounds high)

maximum hu=8P=400 => h=0.4 mm (assuming Q<<84P=$4200/ m2)

Maintenance costs M<2.8P=$140/m2 of mirror area and year
For a 100 km wide mirror the limit would be <$140·1010 =$1.4·1012

M doesnt seem to be a problem. Q comprises the cost for the mirror, the electronics and mechanics

It would help to produce part of the equipment in space or on the moon to bring down the cost of transportation.

Perhaps the complete system could be manufactured on the moon and then thrown into orbit on a solar-powered race track. The time to store photoelectric energy to put one kg of payload in orbit from the moon would be t(hours)=v2/(2·3600·bIA) where I is solar intensity in W/m2, b quantum efficiency in photoelectric conversion including the losses in the conversion from the storage to kinetic energy

A area of photoelectric cell, v escape velocity, m:mass.

Putting I=1000, b=0.1 (meaning that 10% of the solar energy hitting the solar cell is ultimately converted into kinetic energy), v=1.5 km/s


In this estimate a photocell of 3m2 allows for the transportation of 1kg/hour.

The estimate of b may be a bit optimistic but transportation cost for putting the mirrors in orbit seems to be a minor problem if the necessary production plants have been established on the moon.

Lunar production plants may be expected to take over in the long run.

The calculation earlier shows that using presently existing technology and conventional earthbased rocket transport, the production per m2 of ground area needs to be much better than for potato crops, to put it mildly, to make sense economically. Hardly unexpected but to me its more surprising that the balance isnt less favorable and there appears to be several ways to arrive at an economically sensible solution even using groundbased production and rocket transport.

One problem is to improve the effective strength and cost of the needed materials. Another is to realize the lower transportation costs hinted at above.

In the above analysis no estimate was made of the effect of the artificial energy source on the general agricultural productivity around the earth. Or other effects on the economy.

Since a number of artificial sources like this makes it possible for plants to have their photosynthesis operating day and night the production can be expected to raise correspondingly. There is the problem of biological clocks and maybe there is a hatch somewhere. This has to be studied carefully of course. But in principle higher production can be expected and therefore the actual economic balance may be more favorable than in the previous estimates by as much as a factor of say 4 or more. If the total angle spanned by the mirror trajectory while it is illuminating the main target area is a in degrees, then the maximum improvement would be 360/a

But this maximum improvement assumes that the mirror could illuminate fertile ground everywhere along its trajectory. And since there is a lot of water the productivity of the sea would weigh into the result.

I assume the normal sea-bound photosynthesis is not as productive as modern agriculture.

This raises the question of whether there may come a day when this will be considered a problem and that the conditions should be modified in order to increase the seas productivity. There is already a problem with the fishing that has lead to political intervention.

Other consequences than those affecting agriculture could be that the weather would be noticably improved in some northern areas where tourism might increase as a consequence.

If all available energy is squeezed out of the mirror system there would be a net heating of the earth. More plantgrowth leads to higher oxygen content which in turn leads to more abundant fires everywhere.

Therefore there may be an actual need for using it to cool parts of the ground in particular in places where more precipitation is wanted. I will not try to go deeper into that analysis.

This document was written very quickly without any intention of being complete. The calculations in particular are very sketchy.

Update 2002-07-17
Summary of the update below:
Available experimental data on meteorites indicates many hits by meteorites but that the total damage may be insignificant if each hit creates holes not extremely much larger than the meteorite. Meteorites hitting at grazing incidence may need separate consideration and possibly some kind of protection around the perimeter should be considered.

Some data on cosmic dust that can be expected to damage the mirrors.
The relation shown below is a crude empirical fit to a diagram [1] showing the cumulative effort of many satellite measurements and groundbased measurements both on the earth and on the moon.
f(m) is a measure of the flux of meteorites having mass greater than the parameter value m
Flux f=f0(m/m0)k [m-2s-1/2psteradians]
Mass Range
{min , max}
f0 m0 -k
{ > 1 }6·10-170.070.623
{10-10 , 1}6·10-170.071.18
{10-14 , 10-11}1.5·10-510-110.56
{ < 10-14}5·10-4 - - - - - - - - 0

The impact velocity may be taken to be 20 km/s but it is not used here.
The empirical formula corresponds to a flux per unit mass range of:
df/dm=-k(f0/m0)(m/m0)k-1 [m-2s-1Kg-1/2psteradians] =10-15(m/0.07)-2.18
in the range m={10-10 , 1}
As stated above the data is only a crude estimate and cannot be used for precise calculations. But it suffices for our purposes.
For time T and mirror area A there will be
n=2pATf(m) hits by meteorites of mass > m:
Example: mirror diameter D=300 km
D=300 km
Meteorite size[mm]
assuming r=1000
D=100 m

I have no prior experience of this kind of data and I am surprised that it would be so much. The case of 100 m diameter looks like the conditions for a space station. And it would be hit by a handful of 1 mm projectiles travelling with a speed of 20 km/s.
But for the contemplated mirrors this kind of erosion would seem to necessitate substantial maintenance procedures.
Since each hit may produce debris, there is the additional problem of secondary hits. There is no air or anything to stop fragments from travelling long distances at high speed.
But if each meteorite creates a hole that isnt much bigger than the meteorite size (The mirror is assumed to be very thin over most of its area) then the total damaged area dA constitutes a small fraction of the total area. Integrating over the mass range [10-10, 1] we get dA/A=8·10-15T or a fraction of 2·10-7/year
However there is a possibility that a meteorite hitting at grazing incidence might cause much more damage in the plane of the mirror, even when it is built up out of many independent pieces. The fraction of 'perfect' grazing hits can be estimated from pd1/D where d1 is the diameter of the meteorite.
Example m=10-10, total nr of hits/year N=3·1012, d1=0.06 mm, nr of grazing hits/year N2=Npd1/D=2·103
A more accurate calculation would consider other angles and various types of damage inflicted. But I leave it for another time. It seems natural to consider the function of some kind of protecting cover around the perimeter.
It is a challenge to create material structures that can stop projectiles travelling at 20 km/s with the least possible amount of material.
Maybe entirely different ideas will be considered as space exploitation proceeds. There is the possibility of deflecting electrically charged space dust. Either naturally charged or otherwise. Another possibility would be to deliberately mechanically scatter larger projectiles one or several times. Using grazing incidence the scattering surface wouldnt take significant damage. Large regions could be cleared from meteorites.

[1] Fig 3 in the article Moon Dust and the Age of the Solar System, Dr. Andrew A. Snelling and David E. Rush (1993) http://www.answersingenesis.org/home/area/magazines/tj/.../moondust.asp

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