Earth rings for planetary environment control

Acta Astronautica 58 (2006) 44–57www.elsevier.com/locate/actaastro

Earth rings for planetary environment controlJerome Pearson∗, John Oldson, Eugene Levin

Star Technology and Research Inc., 3213 Carmel Bay Drive, Suite 200, Mount Pleasant, SC 29466-8513, USA

Received 25 April 2003; received in revised form 1 February 2005; accepted 23 March 2005Available online 27 June 2005

Abstract

An artificial planetary ring about the Earth, composed of passive particles or controlled spacecraft with parasols, is proposedto reduce global warming. A flat ring from 1.2 to 1.6 Earth radii would shade mainly the tropics, moderating climate extremes,and counteract global warming. A preliminary design of the ring is developed, and a one-dimensional climate model isused to evaluate its performance. Earth, lunar, and asteroidal material sources are compared to determine the costs of theparticle ring and the spacecraft ring. Environmental concerns and effects on existing satellites in Earth orbit are addressed.The particle ring endangers LEO satellites, is limited to cooling only, and lights the night many times as bright as the fullmoon. It would cost an estimated $6–200 trillion. The ring of controlled satellites with reflectors has other attractive uses,and would cost an estimated $125–500 billion.© 2005 Published by Elsevier Ltd.

Keywords: Artificial planetary rings; Climate control; Global warming; Greenhouse effect; Asteroid materials; Lunar resources

1. Introduction

For 95% of its past, the Earth’s climate has beenwarmer than it is now, with high sea levels and noglaciers [1]. This warmer environment was interrupted570, 280, and 3 million years ago with periods ofglaciation that covered temperate regions with thickice for millions of years. At the end of the currentice age, a warmer climate could flood coastal cities,even without human-caused global warming. In ad-dition, asteroids bombard the Earth periodically, withimpacts large enough to destroy most life on Earth.

∗ Corresponding author. Tel./fax.: +1 843 856 3590.E-mail address: [email protected] (J. Pearson).

0094-5765/$ - see front matter © 2005 Published by Elsevier Ltd.doi:10.1016/j.actaastro.2005.03.071

A recent world concern is the effect of industrial green-house gases in raising the overall global temperature,melting the polar caps, and raising sea level. Govin-dasamy et al. [2] estimated that the expected dou-bling of CO2 in the atmosphere over the next cen-tury will warm the Earth by about 1–4 K and raise sealevel by about 1 m. Not all scientists are convincedof human-caused global warming, but the tempera-ture will rise, regardless of human action, as the worldcomes out of the current ice age. Reducing solar inso-lation by ∼1.6% should overcome a 1.75 K tempera-ture rise. This might be accomplished by a variety ofterrestrial or space systems. Teller et al. [3] providean excellent review of the basic physics of a wholerange of climate control techniques, with first-order

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J. Pearson et al. / Acta Astronautica 58 (2006) 44–57 45

Table 1Summary of climate control methods

Author Description Requirements Mass (kg) Maintenance

Earth-atmosphere methodsDyson and Marland [4] SO2 from coal-fired plants Smokestack additives Exhaust control requiredBrady [5] Al from rockets Rocket design Rocket controlTeller et al. [3] H2-filled Al balloons 0.02 �m walls; 108 Replenish as necessary

“anti-greenhouses”

Earth orbit systemsMautner [6] Saturn-like particle rings R = 1.2–1.5RE 3.4 × 1011 Replenish asPearson et al. [8] R = 1.3–1.6RE 2.1 × 1014 necessary

2.3 × 1012

NAS [9] Orbiting mirrors in 55,000 mirrors, Uncontrolled;random LEO orbits A = 100 km2 collisions, debris

Pearson et al. [8] Controlled spacecraft 50,000 to 5 million spacecraft 5 × 109 Active control

Solar orbit systemsEarly [9] L1 lunar glass from D = 2000 km, 1011 Active controlMautner [6] mass driver 10 �m thickMautner and Parks [10] L1thin-films 31,000 solar sails, 5 × 1014 Active control

3 × 1012 m2 eachHudson [11] L1 parasol Active controlTeller et al. [3] L1 metallic scattering D = 638 km 3.4 × 106 Active control

T = 600 A

McInnes [12] L1 metallic reflector D = 3648 km 4 × 1011 Active control

Other conceptsKorycansky et al. [13] Move Earth using 150-km object; 1019 Actively moved,

Kuiper-belt-objects One encounter every low delta-V6000 years

Criswell [14] Lower sun’s mass to Remove plasma from 2 × 1028 Continualslow brightening magnetic poles spacecraft ops

evaluations of their mass and cost. Table 1 summa-rizes these and other proposals for climate control andtheir parameters. They are grouped into Earth-basedsystems, Earth-orbit systems, and solar-orbit systemsat the Earth-sun L1 Lagrangian point.

Scattering devices or reflectors in the stratospherewould avoid the costs of space launching. Dysonand Marland [4] proposed scattering of sunlight bySO2 from exhaust stacks, and the eruption of Mt.Pinatubo in the Philippines demonstrated this coolingpower of such aerosols in the atmosphere by lower-ing the Earth’s temperature ∼0.5 K. Brady et al. [5]proposed cooling by adding 0.1 �m-diameter aluminaparticles to exhaust stacks, or by a special combustorof aluminum powder at high altitude, to loft alumina

dust into the stratosphere. Teller et al. suggestedtiny hydrogen-filled balloons with diameters of 8 mmand aluminum walls 0.2 �m thick, to float at 25 kmaltitude and scatter sunlight.

In Earth-orbit-based systems, Mautner [6] proposeda thin film like a belt around the Earth, and rings ofgrains. The National Academy of Sciences [7] pro-posed 55,000 orbiting mirrors of 100 km2 area each,aligned horizontally, but in random orbits. Pearson etal. [8] proposed a particle ring and a ring of controlledsatellites. The current paper describes both the particlering and the ring of controlled satellites.

For solar orbit systems, Early [9] proposed placinga shield at the sun-Earth L1 Lagrangian point, about1.5 million kilometers sunward from the Earth, as a

46 J. Pearson et al. / Acta Astronautica 58 (2006) 44–57

∼1011-kg refractor composed of lunar glass. Mautnerand Parks [10] proposed thin-film solar sails at L1, andHudson [11] proposed a ∼1011-kg opaque thin filmat L1. Teller et al. proposed a ∼106-kg small-anglemetallic scatterer at L1, and McInnes [12] proposed ametallic reflector.

Other, more ambitious schemes include the proposalby Korycansky et al. [13] to move the Earth to a moredistant solar orbit, and by Criswell [14] to remove ma-terial from the sun’s poles, lowering its mass, extend-ing its stay on the main sequence, and thereby post-poning the red-giant phase by billions of years. From adifferent perspective, Fawcett and Boslough [15] sug-gested that grazing asteroid impacts have created tem-porary debris rings that cooled the Earth for 105 years.They find fossil evidence for such a ring associatedwith an asteroid impact 33.5 million years ago (al-though not with the dinosaur-killer of 65 million yearsago); another temporary ring may have caused the pe-riod of heavy glaciation about 570 million years ago.

The Fawcett and Boslough climate modeling resultsshow that such rings could drastically lower the plan-etary temperatures. Muller and MacDonald [16] evenproposed that past ice ages were caused by a ring ofdust in the Earth’s orbital plane. The meteorologicalcommunity is developing improved climate modelsthat could be useful in detailed analyses of the climateeffects of these systems [17]. There has been at leastone study looking at the economic effects of globalwarming on the US economy [18].

2. Artificial Earth rings

This paper proposes to create an artificial ring abovethe Earth to reduce solar insolation. An equatorial ringlocation was chosen from the standpoint of stabilityand reduced perturbations. We describe two differ-ent options: a ring of passive particles, derived fromthe Earth, moon, or asteroids, and a ring of attitude-controlled spacecraft with large, thin-film reflectors.The optimum ring size, location, and material proper-ties are addressed, using a climate model to determinethe desired reduction in insolation. Ring materials andcost of emplacement are evaluated, and methods arediscussed for controlling ring deterioration from par-ticle loss due to air drag and ring spreading or fromsatellite malfunctions.

Fig. 1. Earth ring concept, R∼1.3–1.7RE, with shepherding satel-lites.

2.1. Earth ring concept

Our baseline concept is to create an Earth ring inequatorial orbit, similar to Saturn’s B ring, but closer.The concept is shown in Fig. 1. We looked at radii be-tween 1.2 and 1.8 RE. The ring can be composed ofparticles or of individual spacecraft, and is character-ized by its radial extent and by its density, or opac-ity. This low-altitude ring shades the tropics primar-ily, providing maximum effectiveness in cooling thewarmest parts of our planet. The shadow oscillates likea sine wave over the Earth, from a minimum line overthe equator at the equinoxes to a maximum shadingarea in the winter tropical zone at the solstice, whichis the time represented in Fig. 1. This amplifies sea-sonal effects, just as Saturn’s rings do [19].

2.2. Ring shadow

To allow for the climatic effects of the ring shadow,the shadow area and position must be calculated. Referto Fig. 2 for this derivation.

The area of the ring shadow in the YZ plane (blockedsunlight area):

A = RH(u2 − u1) sin �,

where R is the ring radius, H is the width of the ring(H>R), sin � = sin i sin �, i is the inclination of thering plane, and u1 and u2 are solutions to the equation

Y 2 + Z2 = R2E,

where RE is the Earth radius, and Y = R cos u sin � +R sin u cos i cos �, Z = R sin u sin i.


Fig. 2. Calculation of ring shadow area.

The equation for u can be re-written as

sin 2u sin 2� cos i

+ cos 2u(sin2 � − cos2 i cos2 � − sin2 i)

= 2R2E/R2 − (sin2 � + cos2 i cos2 � + sin2 i)

or

cos(2u − �)

= [2R2E/R2 − (sin2 � + cos2 i cos2 � + sin2 i)]/D,

where

D = [(sin 2� cos i)2 + (sin2 � − cos2 i cos2 �

− sin2 i)2]1/2,

� = arctan[(sin 2� cos i)/

(sin2 � − cos2 i cos2 � − sin2 i)].Now, it appears that

u2 − u1 = arccos{[2R2E/R2

− (sin2 � + cos2 i cos2 � + sin2 i)]/D}and the shaded area is

A = RH sin i sin � arccos{[2R2E/R2

− (sin2 � + cos2 i cos2 � + sin2 i)]/D}. (1)

If the ring is not narrow, Eq. (1) must be integratedover the range of R, assuming H = dR. This area is

then calculated for each of the latitude bands for inputto the climate model.

2.3. One-dimensional climate model

The average insolation over a 24-h period at specificlatitudes and solar declinations [20] is given by

I = (S/�)(T sin � sin � + cos � cos � sin T ),

where all angles are in radians, and � is the solardeclination, � is the latitude, T is the half-day lengthin radians, S is the solar constant, and T is thearccos(− tan � tan �).

The insolation value at the equator for the equinox,T =�/2, sin T =1, so I =S/�, as expected. The Earthring shading was modeled and used to calculate theinsolation values for each latitude band for input intoa global climate prediction model, shown in Fig. 3.

The one-dimensional climate model of McGuffieand Henderson-Sellers [21] was used. The model be-gins with the solar constant, 1370 W/m2 outside theatmosphere, and develops the insolation values for10◦ latitude zones in terms of a sunlight weight fromthe formula above. An initial temperature and albedoare chosen for each latitude zone. This model takesthe average insolation in latitude bands and appliesthese inputs to a simplified energy balance model ofthe Earth’s climate system; the result is a set of aver-age temperatures for the latitude band, and a result-ing overall planetary temperature. The model allowsfor changes in albedo due to the formation of ice andsnow, and uses an iterative calculation in an Excelspreadsheet to perform the analysis in 50 integrationsteps. This kind of model does not show altitude vari-ations in temperature, nor does it take into accountocean currents or other second-order effects. However,it does show the latitude dependency of the temper-atures resulting from various ring configurations, aswell as the global results. The model can also be mod-ified to show the seasonal effects, giving results forwinter and summer temperatures as functions of thering parameters.

The iteration in Fig. 3 uses the nominal solar con-stant (SC) of 1370 W/m2 outside the atmosphere, ap-plies the geometry to produce the sunlight weight foreach zone, and through the iterative process (two stepsare shown) gives the zonal temperatures. These are


ENERGY BALANCE MODELA 204 aice 0.6 Frac.SC 1B 2.17 a 0.3 SC 1370 Step_1 Step_2K 3.87 Tcrit -10 Workspace >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

cos(lat)Zones SunWt Init_T Init_a Final_aFinal_TR_in R_out Tcos Temp Albedo Tcos Temp Albedo80-90 85 0.5 -15 0.6 0.6 -12.9 171.3 176 0.09 -1.31 -13.9 0.6 -1.2122 -13.5431 0.670-80 75 0.531 -15 0.6 0.6 -12.2 181.9 177.5 0.26 -3.88 -13.2 0.6 -3.4165 -12.84 0.660-70 65 0.624 -5 0.3 0.3 0.524 213.7 205.1 0.42 -2.11 -0.474 0.3 -0.2003 -0.11533 0.350-60 55 0.77 5 0.3 0.3 6.319 263.7 217.7 0.57 2.868 5.321 0.3 3.05234 5.67995 0.340-50 45 0.892 10 0.3 0.3 11.16 305.5 228.2 0.71 7.071 10.16 0.3 7.18721 10.5226 0.330-40 35 1.021 15 0.3 0.3 16.28 349.7 239.3 0.82 12.29 15.28 0.3 12.5205 15.6431 0.320-30 25 1.12 18 0.3 0.3 20.21 383.6 247.9 0.91 16.31 19.21 0.3 17.4141 19.5728 0.310-20 15 1.189 22 0.3 0.3 22.95 407.2 253.8 0.97 21.25 21.95 0.3 21.2051 22.3116 0.30-10 5 1.219 24 0.3 0.3 24.14 417.5 256.4 1 23.91 23.14 0.3 23.0558 23.5024 0.3

Global Mean Temperature 14.87 5.74 Mean_T 13.32 13.8758

Fig. 3. One-dimensional energy balance climate model.

averaged by the zonal areas to produce the currentpredicted global mean temperature, 14.87 ◦C.

Because an equatorial ring system shades the win-ter hemisphere, which tends to produce more extremeseasonal temperature changes, the rings should be infairly low Earth orbit, to limit the shielding to the trop-ics, or perhaps as far as the desert belts at 25◦–35◦latitude. The effectiveness of six different ring alti-tudes was measured using the one-dimensional climatemodel. Rings extending from R = 1.2–1.3, 1.3–1.4,1.4–1.5, 1.5–1.6, 1.6–1.7, and 1.7–1.8 RE were eval-uated to find their overall effects. Because these ringsdiffer in overall area, their opacities were adjusted,from 1.0 for the innermost ring to 0.6757 for the outer-most ring, corresponding to a constant ring mass. Thering shadings in each latitude band were calculated bynumerically integrating Eq. (1).

Fig. 4 shows the resulting temperature changesby 10◦ latitude band for these 6 narrow rings, plot-ted at the central latitude of each band. The globalcooling from each ring is plotted at the zero latitudepoint; these range from −1.63 ◦C for the inner ring to−1.16 ◦C for the outer ring. The greatest cooling isat 0◦–10◦ latitude for the inner ring, 10◦–20◦ latitudefor the next three rings, and at 20◦–30◦ latitude forthe outer two rings. These results imply that rings ofR = 1.2–1.6RE would be most effective, and wouldmoderate the Earth’s temperature extremes. This cor-responds to circular equatorial orbits ranging from1300 to 3800 km in altitude, above LEO satellites.

Temperatures by Latitude Bands

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0 10 20 30 40 50 60 70 80 90

Central Latitude (0 = Overall)

Tem

per

atu

re, C

1.2-1.3

1.3-1.4

1.4-1.5

1.5-1.6

1.6-1.7

1.7-1.8

Fig. 4. Temperature reductions versus ring altitudes.

3. Particle ring

3.1. Particle lifetimes

Burns [22] notes that ring particle collisions col-lapse their orbits to the Laplacian plane of maximumangular momentum of the planetary system. Gravita-tional interaction between ring particles slows downthe inner particles and speeds up the outer ones, lead-ing to ring spreading. The spreading continues be-cause of these interactions, until the particles are farenough apart that they no longer collide; the rate of thisspreading is directly proportional to the particle diam-eters. Aerodynamic, plasma, and Poynting–Robertson


drag reduce the ring orbital diameter, but the rate isinversely proportional to particle size; consequentlylong-lived rings must have particles neither too big nortoo small. Natural rings seem to be generally kept inplace by shepherding moons located just beyond thering edges [19].

To estimate the orbital lifetime of a particle, we mayuse the following approximate formula:

T = V H a�mD/(3��a), (2)

where T is the orbital lifetime, V is the orbital ve-locity in the initial orbit, Ha is the scale height of theatmosphere in the initial orbit, �m = particle density,D = particle diameter, � = Earth’s gravity constant,398, 603 km3/s2, and �a = air density in the initialorbit.

As an example, assuming Ha = 100 km and �a =1.5 × 10−15 kg/m3 at an altitude of 1000 km, we getan estimate of T = 23 days for D = 10−6 m, �m =5000 kg/m3. This means that a particle has to be 16 �min diameter to survive 1 year when initially placed ina 1000 km orbit, and it has to be 1.6 mm to survive100 years.

The totals for N particles of the same size are asfollows. The total shading area is

S = GcN�D2/4,

where Gc is some geometry coefficient, depending onthe orbit parameters and over-shading of the particles.

The total mass is

M = N�m�D3/6, (3)

and therefore,

M/S = �mD/(1.5Gc), (4)

or

�mD = 1.5GcM/S.

After substituting the expression into the formulafor the orbital lifetime, we obtain

T = V H aGc(M/S)/(2��a),

or

M = 2T S��a/(GcV H a). (5)

This is a useful formula because it does not include anydetails of the ring composition, particle size or density.

It can be interpreted as a minimum ring mass requiredto provide a given shading area for a given period oftime. The minimum is reached when the sizes of allparticles in the ring are optimized for the given orbitallifetime. The formula says that the minimum ring massis proportional to the orbital lifetime, shading areaand the air density at the ring altitude (assuming itis narrow). If there is an altitude where �a/(GcV ) isminimum, this will be the optimum position of thering, providing a minimum ring mass for any givenlifetime and shading area.

If we ignore the over-shading of the particles, thenthe geometry coefficient is roughly

Gc = arcsin(RE/R)/�,

where RE is the Earth radius and R is the ring meanradius. If we assume that the air density �a drops expo-nentially with a scale height of Ha>R, then the ratio�a/Gc will not have a minimum. This means that theminimum mass of the ring will decrease with the ringradius because the optimum particle size will drop.

Thus, the best positioning of the ring must be a re-sult of considering the trade-offs: large particles areineffective because of low S/M ratios. Small particlesare more effective, but they must be placed far enoughto provide a reasonable lifetime. Also, for micron sizeparticles, solar pressure will significantly deform or-bits. Small particle collisions will produce even finerparticles, which quickly drop out of the main ring andinfest low orbits.

3.2. Particle heating and RE-radiation

Assume spherical (or randomly-shaped andrandomly-oriented) particles that are far enough apartthat particle-to-particle heating and shading can beneglected, compared to their effects on the Earth andvice versa. First it is necessary to estimate the viewfactor of the Earth from the particle. If the orbit radiusof the particle is R = Rr/RE, then from Carroll [23],the view factor is

F =(

1 −√

1 − (1/R)2)/

2.

For R = 1.3, 1.5, and 1.7, the view factors are 0.18,0.13, and 0.10.


For dark particles, most of the sunlight striking themis absorbed and re-radiated as long-wave radiation.The Earth’s absorptance for this is higher (∼0.95) thanit is in the visible (∼0.65). And this radiation is re-radiated isotropically, rather than preferentially sun-ward, as albedo radiation would be. That gives it abetter chance of reaching the Earth, since the sunlitside faces away from the Earth rather than toward itduring most of the sunlit period. On the other hand,most long-wave radiation is intercepted higher thanshortwave radiation is (no “greenhouse effect” comesinto play). Let us guess that it reduces the surfaceheating effect from 0.95 to 0.65. That would suggestthat long-wave radiation has a net effect comparableto shortwave radiation.

Next, let’s analyze sunlit and eclipsed particle casesseparately. This is relevant for both small particles andthin films, because they will heat up or cool downquickly compared to the orbit period. Any energy car-ryover would simply have the effect of reducing day-time temperatures and increasing nighttime tempera-tures, rather than changing the net energy balance. Forthe daytime case, the long-wave effect caused by theenergy intercepted by a black particle should reducethe shading by 0.10–0.18. But keep in mind that the il-luminated particle count is much higher than the countof particles that actually cast a shadow on the Earth:about three times larger for R = 1.5, and by smallerand larger amounts for R = 1.3 and 1.7. This suggeststhat long-wave radiation from the particle may reducethe shadowing impact by ∼40%.

In addition to this, the particles provide a smallheating effect at night, by intercepting and re-radiatingback to Earth a small fraction of the outgoing radiation.The average blackbody temperature of the night side ofthe Earth is probably ∼240 K. With Earth view factorsof 0.10–0.18, the particles will absorb and return to theEarth a long-wave radiation of 2–6 W/m2 of particlesurface, or 8–24 W/m2 of “daytime shadow area”. Ifthe particles are in circular orbit, the time spent in thismode (shadowed by Earth) should be the same thatthe particles spend shadowing Earth, so the reductionin net cooling due to night time re-radiation back toEarth should be 0.6–2% of the shading effect. Hencedaytime re-radiation towards Earth should be far moreimportant than nighttime re-radiation towards Earth.It appears to reduce the net effectiveness of shadingby roughly 40%.

Temperatures by Latitude Bands

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0 10 20 30 40 50 60 70 80 90

Central Latitude (0 = Overall)

Tem

per

atu

re, C

1.2-1.5

1.3-1.6

Fig. 5. Temperature reductions from two broad Earth rings.

3.3. Particle ring design requirements

Now let us design two conceptual particle rings andcompare them. To overcome a doubling of the car-bon dioxide in the atmosphere over the next century,a cooling of about 1.75 K is required, which can beachieved with about a 1.6% reduction in insolation.We choose one ring extending from R =1.2 to 1.5RE,and the other from R = 1.3 to 1.6RE. For 1.6% in-solation reduction, the required opacity is 0.356, asviewed normal to the ring. Fig. 5 shows the climateeffects. The lower ring has a much greater effect inthe 0◦–10◦ latitude band, and less in the other latitudebands. This will moderate the climate extremes, butas we shall see later, it requires much more mass.

We can calculate the lifetimes of particles from Eq.(2). The ring should have a lifetime of about 1000years, to cover the expected era of fossil fuel burn-ing. For rocks of average density of 2700 kg/m3, theparticle sizes required are

R 1.2 1.3 1.4 1.5 1.6D 4.3 mm 54 �m 1 �m 1 �m 1 �m

Because particles smaller than 1 �m may be sweptout by non-gravitational effects, that diameter is usedas the lower limit. For a lifetime of 1000 years, thelower ring edge, R = 1.2, must have particles 4.3 mmin diameter, ranging down to 1 �m. Integrating Eq.(2) over this range gives an average diameter of5.2 × 10−4 m. Similarly, the upper ring particles,R = 1.3–1.6, range from 54 to 1 �m, with an av-erage diameter of 4.7 �m. From Eq. (4), the lowerring mass is 2.1 × 1014 kg, and the upper ring mass


is 2.3 × 1012 kg, (only 1% as much), allowing fora 40% reduction in efficiency from particle heatingand re-radiation. The ring mass is seen to be stronglydetermined by the largest particles.

3.4. Particle ring side effects

This revolutionary system will have planet-wide ef-fects as the intended result. In addition, there will beunwanted or unexpected side effects that must be dealtwith. The rings will reflect sunlight onto the twilightand night portion of the Earth during the summertimeof each hemisphere, providing additional evening illu-mination, extending twilight, and reducing the need forcity and highway lighting. The total nighttime illumi-nation at 45◦ latitude will be that of a dozen full moonsat midnight and 48 full moons at 9 pm and 3 am. Atsunset at 30◦ latitude, it will arch like a silver rainbowacross the southern sky, spanning 11◦–26◦ altitudemaximum at due south, and shining with the equiva-lent of 22 full moons. This will significantly reducenighttime lighting requirements, by extending twilightand eliminating complete darkness. It may also haveadverse effects on animals, especially nocturnal ones,and on plant growth. The ring will shade the “winter”portion of the tropics, enhancing the annual tempera-ture differential there without directly deepening thewinter in the temperate and polar regions.

The Earth ring will extend into the Van Allen radi-ation belts, and absorb the charged particles trappedin the belts. This will lower the intensity of the radi-ation belts, and reduce the radiation experienced byspacecraft and humans venturing beyond LEO. Thering will also reflect radio waves, acting as an artificialionosphere for international communication, and in-terfering with GEO satellite communication to pointsexactly on the equator.

The particle ring particles have limited lifetimes inLEO, and there will be a continual loss of materialfrom the lower edge. Even a ring with a million-yearlifetime will lose 10−6 of its mass per year—about2.3 million kg per year raining down and impactingall LEO satellites as they cross the equator twice eachorbit. This means that a particle ring must have a shep-herding object at its lower edge to catch these parti-cles, or they will destroy all LEO satellites. The shep-herd needs to have a diameter equal to the thickness ofthe ring. Saturn’s rings are estimated to be 40–1100 m

thick, and the ring thickness scales with the orbitalvelocity [22]. Earth rings, at one-third the velocity,would be ∼15–400 m thick.

A 1-km shepherding asteroid at 2700 kg/m3 wouldhave a mass of 1.4 × 1011 kg, just 6% of the total ringmass. A shepherding satellite could be much lower inmass. In addition to shepherding the ring particles, itcould remove the ring if its orbit were gradually raisedpast the ring. Also, a pair of shepherding satellites,at the top and the bottom, could create the ring andcatch the stray ring particles, continually replenishingthe ring.

Without shepherding, an alternative solution wouldbe to make the ring out of random pieces of a very thintape or film, e.g., 1 cm pieces of 0.01 mm thickness, assuggested by Mautner [6]. These pieces will providehigh S/M ratios, like a film of the same thickness, butthe number of pieces will be orders of magnitude lessthan the number of particles, the ring can be muchmore uniform, and the pollution of low orbit will bemany orders of magnitude less than with unshepherdeddust particles.

3.5. Particle ring development scenario

A natural Earth ring could be formed by simplybringing small asteroids into the desired orbits and let-ting collisions provide the ring material. The asteroidswould be retrieved over decades by emplacing propul-sion systems on them, and bringing them into Earthorbit at the outer and inner radii of the planned parti-cle ring. These shepherding asteroids could also act asa source of additional ring material to replace materiallost by diffusion. They would be processed for theirraw materials, and the tailings would be tailored to theproper diameters to form a long-lived ring. The rem-nants of the two asteroids then become the shepherdsthat prevent ring spreading and loss of ring material.

The lower shepherd, with a sufficient diameter sothat it is wider than the thickness of the ring, will pre-vent the constant loss of ring material from the loweredge, with its resultant sandblasting of LEO satel-lites. Similarly, the upper shepherd will prevent ringparticles from spreading into higher orbits, where theparticles could interfere with GEO satellites. To pro-vide ring shepherding with less mass, the shepherdingmoons might be replaced by spacecraft with large ar-eas to catch the decaying or spreading ring particles.


The relative velocities of the particles leaving the ringswill be very low, so there will be no structural diffi-culty in withstanding the forces.

4. Controlled spacecraft ring

4.1. Spacecraft ring design requirements

Without shepherding, the particle ring would pro-duce additional meteoroid intensity for LEO satellites,and would be more difficult to remove if it has un-expected deleterious effects. An alternative approachis to create a ring of controlled reflecting spacecraftin LEO. Putting spacecraft with multiple reflectors, orparasols, in a few dedicated orbits is more organizedand easier for other spacecraft to navigate. The con-cept is based on the use of lightweight spacecraft usingelectrodynamic tethers and thin-film reflectors, whichcould be solar arrays [24]. These satellites have ma-neuvering capability (from electrodynamic forces onconductors in the Earth’s magnetic field) to keep themproperly spaced without using propellant.

4.2. Tethered spacecraft constellation design

Two parasol spacecraft designs can be envisioned,based on the tethered spacecraft concept. The first isto use long vertical tethers to hold parasol segmentsnormal to the tethers. It is not clear what size gives theminimum mass per unit panel area, but the spacecrafttether could be 5 km long, with parasols 200 m wide,giving 1 km2 of surface area per vehicle. The seconddesign is a large disk of thin-film reflecting material,bounded by a ring conductor that develops electrody-namic forces to control the orientation of the reflector.A hanging electrodynamic tether could control the or-bit. The disk parasols must be kept taut, which mayrequire a perimeter current to keep them open and nor-mal to the magnetic field. The spacecraft could be putinto equatorial orbit, as shown schematically in Fig. 6,where they would shade the winter hemisphere, likethe dust ring.

As an alternative, the spacecraft could be put intomedium-inclination retrograde orbits, high enoughthat nodal regression is once per year (1.6–1.8RE, forinclinations of 30◦–40◦). The ascending node couldbe phased so the tethers are north of the equator dur-

Fig. 6. Concept of the Earth ring using a tethered spacecraftconstellation.

ing the day during northern summer. This gives a lowsolar beta angle, which means that steerable parasolsegments are needed. Then during northern winter(and southern summer), the orbit plane would havea high solar beta angle, and the shadows will mostlymiss the Earth. Steerable parasol segments could havetheir undersides reflect light onto the winter hemi-sphere, mostly around dusk and dawn, to extend thehours of daylight. However, this is a less efficientuse of the total shading area than the equatorial ringof spacecraft, and would only be used if the wintershading were unacceptable.

The spacecraft can be very lightweight. Existingaluminized film weighs ∼3 g/m2. The film polyethy-lene naphthalate (PEN) is made in weights down to3 g/m2, and aluminization thick enough to be opaqueweighs a tenth of this. Future improvements may allowthe whole spacecraft to approach 1 g/m2, or 1 mega-gram (Mg) per square kilometer. Applying the space-craft ring in place of the particle ring at R = 1.2–1.5with an opacity of 0.356 gives a total area required of3.7×107 km2. Because the spacecraft parasols can bepointed at the sun rather than staying in the plane of thering, the effective area is reduced to about 5×106 km2,or about 3.9% of the Earth’s cross-sectional area. Ata mass of 1 Mg/km2, this gives a total required massof 5 × 109 kg.

If each spacecraft has a parasol area of 1 km2, thenwe will require 5 million individual spacecraft of 1 Mgeach. If each actively controlled spacecraft can bemade to last for 100 years, we will need to launch anadditional 137 spacecraft per day, each with a massof 1 Mg. We will also have to remove 137 malfunc-tioning spacecraft from orbit each day. This is not asmall task; to reduce the requirements, we may want


to build gigantic spacecraft with 100 km2 area, reduc-ing the total number to 50,000, and the replacementrate to just 10 per week. However, the launch capac-ity required would still be a total payload of 1000 Mgper week, orders of magnitude greater than our currentspace launch rates.

4.3. Spacecraft control

Some force is needed to prevent the individual para-sol segments, which need to be thin films of about1 km2, from folding. This can be done by spinning thetethered configuration, or by driving a current througha wire at the perimeter of the disk configuration, tokeep the film stretched and normal on average to themagnetic field. It is possible to maintain reasonablesolar pointing of the tethered petals, by modulatingtheir natural oscillations about the radial direction. Anuncontrolled parasol presents an effective area ratioto the sun of 2/�, or 64%. A simple one-axis controlsystem can increase this to about 90%. Because ofthe cosine relationship, this does not require precisioncontrol, but only moderate accuracy. A pointing errorof 20◦ reduces the shaded area by only 6%.

Beletsky and Levin [25] describe hanging EDTpetals in near-equatorial orbits. Basically, they tend toorient perpendicular to the magnetic field lines. Filmswired on the perimeter are expected to behave simi-larly. It would be a petal-like parasol with a perimeterwire and a small satellite with a power source andcontrol system. At least one electron collector area atthe far side of the petal would be needed to producethrust.

To combine the solar shading of these spacecraftwith the production of solar power would add an ad-ditional control element for the Earth’s temperature.If a significant amount of solar power is beamed downto the ground, reducing the requirement for fossilfuel burning in the atmosphere, the total amount ofshading mass is reduced. There is thus a tradeoff be-tween power production and shade production fromthe spacecraft. If it became necessary to actually in-crease rather than decrease the Earth’s insolation, theoptimum placement would probably become twilightsun-synchronous orbits. That will primarily increasesolar input in early morning and late afternoon, whichwill probably cause the least problems with localoverheating. The time required to move from equa-

torial to polar using the spacecraft electrodynamicthrust could be years, but that is fast enough on thetimescale of climate changes.

4.4. Spacecraft ring side effects

The major side effect of these spacecraft would beto provide a multitude of bright “stars” in the morningand evening skies, which could interfere with astro-nomical observations from the ground. However, thereduction in launch costs from emplacing these satel-lites could be used to launch many space telescopesat much lower costs. The satellite ring will have oc-casional failures, requiring a constant replenishmentof the satellites, and a continuing demand for newlaunches.

The spacecraft ring may lower the Van Allen radia-tion enough to allow the shading spacecraft to becomesolar power stations. This combination would greatlylower the cost of space solar power, at the expense ofrequiring actively pointed receiving antennas on theground.

4.5. Spacecraft ring development scenario

This system can be developed and deployed gradu-ally, one step at a time, without a complete commit-ment up front, and the program can be stopped at anytime, or delayed for whatever reason, making it muchmore manageable.

The first step would be aimed at designing a low-altitude test system weighing about 50 kg, with a para-sol of about 100 m in diameter, orientation controlledby a 300-m wire loop, with an option to use a 100-m segment of wire to produce a low electrodynamicthrust. The parasols might even be used as electroncollectors, improving efficiency of the electrodynamicthrust. Deployment can be assisted by the ampere forceon the wire loop (an “inflating” loop that pulls the filmout of the storage canister).

The satellites would be launched into LEO, andthen would ascend to the proper orbit under their ownpower before deployment to full extent. Any failurewould result in re-entry without damaging the existingring of spacecraft. The ring could consist of multi-ple controlled satellites in different orbital altitudebands, with gaps between the orbits. Thus, if thereis a spacecraft control system failure, the errant


spacecraft could be repaired, using service vehicleskept in orbit for that purpose, before it had time tomove to an altitude that would interfere with otherspacecraft.

4.6. Spacecraft ring additional applications

A spacecraft design could have various electrody-namic propulsion elements distributed and embeddedinto the film surface, including thin-film solar arrays,electron and ion collection areas, and tape conductors.The parasol is designed like an electronic board, withdistributed elements connected together. The space-craft then becomes much more resistant to micro-meteoroid damage, and becomes a solar power satel-lite with control of its orbit and attitude.

With such a controlled spacecraft, we could in-crease or decrease sunlight as desired over certainareas of the Earth. If the shading objects are below2000 km altitude, the shaded or illuminated regionscan be < 50 km across in most cases, and the shad-ing is effective within 10◦ of the equator. This wouldallow local directed nighttime lighting for ∼3 h aftersunset, and could help burn morning fog off the fieldsin large agricultural areas during the growing season.

The spacecraft areas involved in shading the Earthare larger than those envisioned for solar power satel-lites. That means that even very inefficient power gen-eration would make solar power available for beam-ing to the ground over latitudes up to ±45◦. Theremay be a weather-related control of parasols aimedat maximizing shielding/shining efficiency over clear(not clouded) areas, while using time over cloudedareas to better control the orientation. Mautner andParks [10] even suggest that energy could be focusedon incipient cyclones and the El Niño phenomenon toimprove local weather.

The launch of the spacecraft for the ring will requirecontinual launching of many rocket vehicles, and it ispossible to use these launches to reduce the need foras much solar shielding. The addition of aluminumto the rocket exhaust, to create small aluminum oxideparticles in the stratosphere is an additional methodfor global cooling. The optimum mix might be to usesufficient spacecraft to dissipate the radiation belts byabsorption, and use them for solar power, thus lower-ing the greenhouse gas emissions. This will lower thetotal spacecraft area needed. The addition of aluminum

oxide to the rocket exhaust might further reduce thespacecraft requirements. If the rocket exhaust parti-cles and lowered emissions accomplished most of therequired cooling, then the number of spacecraft mightbe drastically reduced.

5. Materials and launch costs

To achieve the result of cooling the Earth by plan-etary rings, we must emplace the required mass of 5billion kg of spacecraft or 2 trillion kg of rocks. Thematerial can come from the Earth, the Moon, or theasteroids. We will examine the costs of each of thesesources.

5.1. Launching Earth material

Launching the ring material from the Earth’s surfacewould require the development of very large boosters,perhaps larger than the Saturn V booster that was usedfor lunar launches in the Apollo program. It wouldalso add to the pollution of the atmosphere from rocketexhausts.

Koelle [26] developed a cost methodology for cal-culating cost per kg into orbit, and Pearson et al. [27]used this to calculate the costs for launching Earthmaterial into orbit in terms of the size of conventionalrockets and the number of launches required. For amission requirement of 108 kg, for example, the mini-mum cost is achieved at 500 launches of a 200,000-kgpayload vehicle, and is about $2800/kg, as shown inFig. 7.

Pearson et al. [28] proposed a ram accelerator andorbiting tether to achieve $250/kg to LEO. Even thislatter combination would cost $1.25 trillion to launch

Cost vs Mission Requirement

1,000

10,000

100,000

1,000,000

100 1,000 10,000 100,000 1,000,000

Vehicle Payload, kg

To

tal C

ost

, $/k

g

1 million kg

10 million kg

100 million kg

200 Launches

Fig. 7. Cost per kg of launching Earth material for the ring.


Table 2Material sources and system emplacement costs

Launch technique Unit cost of material launching ($/kg)

Earth Moon Asteroids

Conventional rockets 1000–3000 100–1000 —EM or gun launch plus orbiting tether 100–500 24 —Ion rockets — —Rotating space tethers — 10–100 1–10Electromagnetic (EM) mass drivers — 10–100 25

the spacecraft ring and $500 trillion for the particles.The cost of launching Earth materials is seen to be ex-tremely high, even with advanced launch techniques.

5.2. Retrieving lunar material

For the use of lunar material, a system for launch-ing lunar material from the moon’s surface would berequired, with a catcher in Earth orbit. Gerard O’Neill[29] envisioned the use of lunar materials for the con-struction of space colonies, and proposed lunar massdrivers to send lunar material into high Earth orbit.With each mass driver delivering 109 kg/yr, the 3 ×1011 kg of mass required could be obtained by using 10mass drivers, each operating continuously for 30 years.To bring back lunar materials on a large scale, Pearson[30] proposed a lunar space elevator, and Hoyt and Up-hoff [31] proposed a system of rotating tethers. Early[8] estimated a total cost of $1–10 trillion for a 1011-kg solar shield using lunar materials, or $10–100/kg,which he proposed to achieve by using robotic tech-niques and a minimal human presence on the moon.

5.3. Using asteroid material

For asteroidal material, a system for capture or pro-cessing asteroids in situ would be required, plus thecatcher and processor in Earth orbit. Asteroids thatpose a danger cross the Earth’s orbit, and therefore alsorequire only a relatively low delta-V for rendezvousand retrieval. Semi-autonomous and remote-controlledspacecraft could carry propulsion systems to candidateasteroids for in situ long-term retrieval operations.

Several potential propulsion techniques could beused to retrieve asteroids. A mass driver [32] proposedby O’Leary could be assembled in Earth orbit and

launched to the target asteroid, using a high-specific-impulse ion propulsion system. This system could berobotically emplaced on the asteroid, fire asteroid ma-terial to stop its rotation, and then be aimed to providethe required delta-V to bring back the asteroid. Oncethe material is brought into Earth orbit, it must be pro-cessed into the proper form and placed into the properorbit to provide a long-lived ring. A simple grind-ing and sieving operation may suffice to give suitablemillimeter-sized particles [33].

Alternatively, an ion-propelled spacecraft couldsimply rendezvous with the asteroid, load a largeamount of material in its cargo bay, and then use itsion propulsion or a rotary “rock” rocket proposed byPearson [34] to return part of the asteroid to the Earth.Multiple trips by multiple spacecraft could provide aconstant supply of asteroid material. Once sufficientmass is removed from the asteroid, the remaindercould then be propelled into high Earth orbit.

In an appendix to O’Leary et al. [33], Robert Salkeldcompares the cost of retrieving asteroidal material ver-sus lunar material, using the O’Neill scenario of amass driver on the moon and a catcher in lunar or-bit [28]. Salkeld concludes that we could bring back1.1×106 ton of asteroid for $25/kg, and we could bringback 2.4 × 106 ton of lunar material for $24/kg; bothfigures include RDT&E costs. These results assumean Earth-to-LEO transportation system based on anuprated Shuttle with transportation costs of $240/kg.

5.4. Earth ring cost estimates

The costs of material launching from Earth, moon,and asteroids are summarized and compared inTable 2, and the costs of the Earth rings are summa-rized in Table 3.


Table 3Cost of Earth rings

Type of ring Mass of system (kg) Launch cost versus source of materials

Earth Moon Asteroid

Particle ring 2 × 1012 $200–2000 trillion $20–60 trillion $6–50 trillionSpacecraft ring 5 × 109 $500 billion–1 trillion $500 billion $125 billion

6. Discussion

The particle ring could be composed of materialfrom dangerous asteroids, thereby achieving two ob-jectives. This source of material could result in lowerlaunch and emplacement costs than Earth surfacelaunching. It would also open a new source of rawmaterials and resources. It would also reduce the VanAllen radiation belts by absorption and provide areflector for worldwide radio communications. How-ever, it could have deleterious environmental effectson LEO spacecraft, and it would reduce nighttimedarkness, with potentially harmful effects on noc-turnal animals and on the growth cycle of plants. Itwould also be difficult to remove.

The controlled spacecraft ring could be lighter inweight for the same shielding effectiveness, and couldperhaps be fabricated from asteroidal or lunar mate-rials as well. It would provide better environmentalcontrol than the particles, allowing directed light toselected parts of the ground, and providing additionallighting to counter ice ages as well shielding to counterglobal warming. The spacecraft ring could also per-form as solar power satellites, reducing the amount offossil fuel burning in the atmosphere, and the overallrequirement for shading. It would also reduce the ra-diation belts, but could have far less effect on night-time darkness. It would be incremental, controllable,and reversible if required.

7. Conclusions

The use of an Earth ring for climate control wasexamined. A ring composed of particles or multiplespacecraft can be used to provide sufficient opacity toreduce insolation by 1.6%. The lower altitude is lim-ited by atmospheric drag at about R = 1.15RE, andthe efficiency drops beyond R = 1.85RE. A ring ofparticles would be optimum at R = 1.3–1.6RE, and a

ring of active spacecraft at R = 1.2–1.5 RE. The par-ticle ring was designed to last for 1000 years, by us-ing larger particles at the lower altitudes, ranging from2.3 mm diameter to 1 �m at the top. Unless the ring iscontrolled with shepherding satellites, it will producea severe micro-meteoroid flux on LEO satellites, andis difficult to reverse in the event of unforeseen sideeffects. However, it can be constructed of lunar or as-teroidal materials at a lower cost than Earth launching.The ring of spacecraft allows orbit and attitude control,higher efficiency, and less of a problem for other satel-lites, but requires multitudes of Earth launches or theprocessing of asteroid material in Earth orbit for con-struction. One advantage of the spacecraft ring is that itcan be constructed and tested on a small scale, and thesatellites themselves can be used for other purposes,such as solar power. The required shading may be re-duced if solar power production becomes significant,as the amount of fossil fuel consumed in the biospheredeclines. The required shading may also be reducedby using rocket launches to place particulates in thestratosphere for part of the shading. A near-term testof the satellite constellation would have other payoffs,including advancements in thin-film satellite technol-ogy for solar arrays and solar sails, and new capabili-ties in electrodynamic propulsion for LEO satellites.

In the broader context of world climate control,such schemes would have widespread and perhapsunexpected results, from changing rainfall, sea cur-rents, and wind patterns to even creating or destroyingdeserts, grassland, forests, and glaciers. No such plan-etary engineering would be possible without extraor-dinary precautions, careful engineering, and attentionto a myriad of international and regional concerns.

Acknowledgement

The authors express their thanks to J. Carroll forinvaluable comments on the manuscript.


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