The amount of sunlight removed by a particle is quantified by a cross section, Q_extπr_p², where r_p is the particle’s radius, and Q ext = Q abs + Q sca (2) is the extinction efficiency factor, broken down in terms of absorption and scattering efficiencies (Q_abs and Q_sca, respectively). Light scattered by reflection and refraction is characterized by a phase function, Φ(θ), giving the amount of incident light that is scattered at angle θ relative to the direction of travel of the incident beam. The anisotropy parameter, g = ∫ cos ( θ ) Φ ( θ ) d Ω / ∫ Φ ( θ ) d Ω , (3) where the integration is over all solid angles, indicates whether light is, on average, back-scattered (−1 ≤ g < 0), forward-scattered (0 < g ≤ 1) or neither (g = 0, as for an isotropic scattering). While the effectiveness of a particle as a sun shield is governed by Q_ext, the scattering anisotropy may also be important. A small particle that is impacted by radiation pressure feels a stronger force if it back-scatters photons, reversing their angular momentum, than if the particle forward-scatters them, with only modest changes to the flow of photon momentum [22].

Scattering outcomes depend strongly on particle size. For particles larger than a micron, bigger than the typical wavelength of sunlight, λ ∼ 0.5 μm, the scattering efficiency is Q_ext ≈ 2; particles of this size block incident sunlight as a result of their geometric cross section A_p, equal to π r p 2 for spheres, augmented by interference effects from their internal response to the incident radiation [23]. At distance d₁, the Earth-L₁separation, even objects as large as λ d 1 ∼ 10 m will be in the Frauenhofer diffraction regime [24].

Particles with sub-micron radii are smaller than the typical wavelength of sunlight. The interaction of these small grains with light can be complicated, though the theories of Rayleigh, Lorentz, and Mie are powerful starting points. From Rayliegh theory, the efficiency factors for nanoparticles are Q abs ∼ - Im ( K ) r p / λ (4) Q sca ∼ | K | 2 r p 4 / λ 4 , (5) where K = (n² − 1)/(n² + 2) and n is the index of refraction. In this limit, scattered light is isotropic. For smaller particles in this regime, extinction efficiencies are low; for example, 0.01 μm silver nanoparties have Q_ext ∼ 0.01 [25]. Small molecules, with physical radii of a few tenths of a nanometer and absorption cross sections typically smaller than 10⁻⁴ nm² when averaged across the solar spectrum, have extinction efficiencies below roughly 10⁻³.

In the intermediate regime, where grains have radii of 0.1–1 μm, the extinction efficiencies are higher and admit the possibility of forward scattering. We use Mie theory to estimate scattering properties of these grains, incorporating the miepython package (github.com/scottprahl/miepython) to obtain average Q_ext, Q_sca, and g for particles of coal dust, sea salt, glass, and gold in sunlight, modelled with a blackbody spectrum running from 300 nm to 1500 nm. Table 1 provides a list of parameters.

Other dust or grain configurations include particles with elongated shapes (e.g., ice crystals) or in fluffy agglomerates. When the geometric limit applies, the average scattering cross section of a randomly oriented, long cylinder (length L and diameter D) is Q ext ( c y l ) Q ext ( s p h ) ≈ 1 . 6 ( L / D 10 ) 1 / 3 ; ( L ≫ D ≫ λ ) . (6) When the wavelength of light is comparable to D, the cross-section is much larger [27].

Fluffy aggregates with high porosity may also increase the scattering efficiencies compared to objects with the same bulk composition and mass. The Bruggeman mixing rule allows for an estimate of n_eff the effective index of refraction of a non-absorbing composite material through the solution of ( 1 - f ) 1 - n eff 2 1 + 2 n eff 2 + f n 2 - n eff 2 n 2 + 2 n eff 2 = 0 , (7) where f is the filling factor, defined to be a volume fraction of the aggregate material within the fluffy particle.

By varying composition and structure (shape, porosity), the optical properties of a material may be adjusted to optimize effectiveness as a solar shield.

If a light-scattering particle lies directly between Earth and the Sun, it will diminish the solar irradiance at Earth by an amount that depends on its angular size, which depends on the cross-section and the distance from Earth [13]. In the limit where the particle is very close to Earth, just above the atmosphere for example, every photon scattered or absorbed by the particle would have hit Earth. The attenuation in sunlight, defined here as the fractional reduction of the total radiative power of the Sun received by Earth, is then the ratio of the cross-section of the particle to the area of the illuminated face of our planet. When the particle is farther from Earth, well beyond the L₁ point, its shadow, a penumbra, may extend beyond the Sun-facing disk of Earth. Many of the photons that the particle deflects would not have reached Earth. The attenuation in this case is comparatively small.

In general, the attenuation of solar irradiance at Earth, stemming from a particle with geometric cross section σ, is A p = f • Q ext σ π R ⊕ 2 (8) where f_• is the fraction of solar photons deflected by the particle that would have otherwise reached Earth. This “shadowing efficiency” quantifies the effects of geometry, specifically the fraction of the particle’s penumbral shadow that is occupied by the Sun-facing disk of Earth.

Toward estimating f_•, we define R_•, the radius of the particle’s penumbra when projected onto the surface of a sphere about the Sun that contains the center of Earth: R • ≡ R ⊙ d p / ( a semi - d p ) , (9) where a_semi is the Earth–Sun distance, and d_p is the distance from the Earth’s center to the particle. Close to Earth, R_• is small, and grows as the particle is moved toward the Sun. At some optimal distance from Earth, d • ≈ a semi R ⊕ / ( R ⊙ + R ⊕ ) ≈ 0 . 91 d 1 (10) the penumbra exactly covers the Sun-facing disk of Earth. As in the rightmost expression in the equation, d_• is curiously close to the distance between Earth and L₁, d₁ ≈ R_Hill [13].

When Earth, the Sun, and a light-scattering particle are not aligned, the center of the penumbral shadow of the particle will fall some distance from the center of the Earth’s Sun-facing disk given by b = 1 a semi | d → p × a → semi | , (11) where d → p is the particle position relative to Earth, and a → semi is the Earth’s displacement from the Sun. With these definitions, the shadowing efficiency is f • ( d p , b ) = { 0( b > R • + R ⊕ ; no shadow ) ; max ( 1 , R ⊕ 2 / R • 2 ) ( b < | R • - R ⊕ | ; complete shadow ) ; { R ⊕ 2 cos - 1 ( b 2 + R ⊕ 2 - R • 2 2 b R ⊕ ) + R • 2 cos - 1 ( b 2 + R • 2 - R ⊕ 2 2 b R • ) + - 1 2 [ ( b + R ⊕ + R • ) ( b - R ⊕ + R • ) × ( b + R ⊕ - R • ) ( R ⊕ + R • - b ) ] 1 / 2 } / π R • 2 ( otherwise ) . (12) When a light-scattering particle is interior to d_• ≈ 0.008 au and aligned with Earth and the Sun. the shadowing efficiency is unity. Further out, at L₁ (b ≤ R_•−R_⊕, f_• ≈ 0.82). To estimate the impact of dust on the solar radiance, we consider the attenuation from a spherical particle with a radius of 1 μm, located at L₁ and aligned with Earth and the Sun: A p ≈ 2 . 0 Q ext [ r p 1 μ m ] 2 × 10 - 26 (at L 1 ) (13) While this value is small for an individual absorbing particle, a substantial ensemble of dust particles may have a significant impact on the solar radiation received on Earth. If the particle were moved toward the Sun to a new distance d_p > d₁, then the attenuation would fall off roughly as the square of d_p. This decrease with distance may be an important consideration when establishing a swarm of particles at some new L₁ point in response to non-gravitational forces like radiation pressure.

A scatterer near L₁ in line with Earth and the Sun attenuates solar radiation by deflecting light out of the narrow cone aimed at the illuminated face of Earth. Light scattered into this cone, with a solid angle ΔΩ, amplifies the sunlight received by Earth by a factor B ≈ π r p 2 d p 2 ⟨ Φ ( θ ) ⟩ | Δ Ω , (14) where angular braces denote the phase function averaged over solid angle ΔΩ in the Earth’s direction. For a particle near L₁, aligned between Earth and the Sun, Earth appears as a disk with an angular radius of ΔΘ = R_⊕/d₁ ≈ 0.24°, filling a solid angle of ΔΩ ≈ 5.7 × 10⁻⁵ steradians; the phase function in this case is evaluated around a scattering angle of 0°. In practice we estimate the average value of the phase function in ΔΘ using the miepython routine i_unpolarized and a 7-point Simpson’s 3/8s rule integrator, since the phase function can be sharply peaked at θ = 0°. For micron size grains at L₁, the amplification is generally below 0.1% of the level of the attenuation, even for strongly forward-scattering particles (g ≳ 0.8). For larger particles with r_p ≳ 10 μm, the phase function is so sharply peaked at θ = 0° that the amplification can exceed over 10% of the magnitude of attenuation.

Particles that forward-scatter light amplify the sunlight received on Earth even when they provide no shade at all. While the magnitude of the effect is small compared with attenuation, an accumulation of dust particles just beyond the disk of the Sun from the Earth’s perspective could overwhelm the impact of attenuation by those orbiting in front of the Sun. It is important to avoid a situation where a significant mass in dust lingers just outside the solar disk, brightening the terrestrial sky. Two factors mitigate this risk. First, as particles move away from alignment with Earth and the Sun, the scattering angle toward Earth increases, typically leading to a drop in the amplification. Second, particles displaced from L₁ tend to move away from that point quickly as compared with the metastable orbits at the Lagrange point. It seems unlikely to accumulate much dust in the broad space between Earth and the Sun.

A swarm of purely absorbing dust particles could provide an effective sun shield [15, 16, 19]. However, with an attenuation of solar radiation by a factor of 10⁻²⁶ per micron-sized grain, climate-impacting reduction in solar radiance at Earth requires a large cloud of dust. To estimate the amount of material required to achieve Earth-climate impact, we first analyze a face-on, disk-like cloud with a radius R_cloud, depth Z in the Earth–Sun direction, and dust uniformly distributed within it with number density n. The cloud’s optical depth along a path perpendicular to the disk is τ ( R ⊥ ) = { Q ext A p n Z ( R ⊥ < R cloud ) 0 ( otherwise ) (15) where R_⊥ is the path’s distance from the cloud’s central axis. When the cloud lies on the Earth–Sun axis, directly above the Earth’s subsolar point, its attenuation is A = F ( R cloud ) [ 1 - exp ( - τ ) ] R cloud 2 d 1 2 a semi 2 R ⊙ 2 ( on-axis disk ) (16) where F ( X ) = 1 π X 2 ∫ 0 X 2 π x f • ( x ) d x (17) is a measure of the average shadowing fraction provided by the penumbra of the disk. If the disk is comparatively small, so that R_cloud ≤ R_•(1 − d₁/a_semi) ≈ 650 km, Earth lies within the penumbra of the entire cloud. Then, F ≈ 0.82, its maximum value.

For Earth-climate impact, A ≈ 1 . 8 %. An optically thick cloud (τ ≫ 1), provides this level of shade when its physical radius is R cloud ≈ 940 km ( ECI shield radius at L 1 ) ; (18) For comparison, a disk radius of about 7000 km is required to totally eclipse the Sun from the perspective of the Earth’s subsolar point. If a 940-km “cloud” were instead a sheet of aluminum with a thickness of 100 nm and areal density of 0.3 g/m², as in the insulating films on current spacecraft, the total mass would be 7.6 × 10⁸ kg, equivalent to a sphere of about 40 m in radius. For structural support, though, the films on existing and proposed spacecraft have areal densities over an order of magnitude higher [13, 14].

An optically thin disk with a larger radius, for example 1500 km, requires M cloud = 1 . 6 × 10 9 [ Q ext 2 ] - 1 [ ρ p 2 . 7 g/cm 3 ] [ r p 1 μ m ] kg ( at L 1 ) (19) where the numerical value of the bulk density ρ_p applies approximately to both aluminum and silicate dust, and the scattering efficiency has a strong dependence on material properties and particle radius, r_p. At 1 μm, both aluminum and silicate grains have a high scattering efficiency (Q_ext ≳ 2 based on Mie scattering), and have similar mass requirements to reach the same attenuation target. Because aluminum is strongly absorbing, its extinction efficiency remains near Q_ext = 2 even when the grain size is reduced to 0.1 μm, cutting the required cloud mass by a factor of ten. By comparison, the extinction efficiency of silicate dust with r_p = 0.1 μm is only 0.7, reducing M_cloud by a factor of four. Coal dust is promising, as its density is comparatively low, yet like aluminum, it is absorbing and so retains a fairly high extinction efficiency (Q_ext ≈ 1.2 for grain radii of 0.1 μm). A cloud of coal dust would require a mass of 1.3 × 10⁸ kg to have climate impact. Modifications to grain porosity and shape can also increase the attenuation per unit mass. Fig 1 illustrates these dependencies.

As in the figure, the peaks of the attenuation curves for spherical particles as a function of grain size are fairly sharp at just under a micron for most of the materials considered. This result provides a guide to how dust might be mined, sifted or milled to achieve a desired level of attenuation, especially for natural materials that have a broad size distribution. Particle shapes of also impact attenuation by allowing more massive grains with elongated or porous configurations to scatter sunlight more effectively. Since more massive dust particles are less susceptible to the effects of radiation pressure and the solar wind, there may be a benefit to producing dust clouds with these “designer” materials, as discussed below. Production and delivery costs would differ, also impacting the feasibility of each grain type as a solar shield.

The attenuation calculations illustrated in Fig 1 assume that the cloud of dust is located at L₁. Non-gravitational forces (e.g., radiation pressure) may prevent the cloud from maintaining a stable position, although a sustained L₁-like orbit maybe be possible further away from Earth. If the distance between a cloud and Earth were increased beyond 1 R_Hill, yet retains alignment with the Sun so that Earth is fully in the penumbral shadow, then f_• falls off roughly as the square of f • ( 0 ) ≈ 0 . 82 [ d p 0 . 01 au ] - 2 ( d p ≥ d • ) ; (20) This value and the corresponding averaged shading factor F in Eq (3) generally diminish with increasing distance beyond L₁. We consider detailed grain orbits next.

Radiation pressure, Poynting-Robertson drag, and the solar wind contribute to the orbital dynamics of micron- and submicron-size particles [22, 30–32]. The acceleration of a single dust grain from these effects is d r → ng d t = L ⊙ Q A p 4 π c r 2 m p { [ 1 + η Q u c - ( 1 + η Q ) v → · r ^ c ] r ^ - ( 1 + η Q ) v → c } (21) where L_⊙ is the luminosity of the Sun, particle position r → and velocity v → as well as u ≈ 450 km/s, the speed of the solar wind, are relative to the Sun, c is the speed of light, Q is an efficiency factor for radiation pressure, and η ≈ 1/3 is the strength of corpuscular pressure from the solar wind relative to radiation pressure [22, 32]. The efficiency factor encodes the physics of scattering and absorption: Q = Q abs + ( 1 - ⟨ cos θ ⟩ ) Q sca ; (22) where the first term on the right is the fraction of radiation that is absorbed by the particle and the second term takes into account scattering. If light is completely back-scattered, 〈cos θ〉 ≡ g = −1, hence Q = 2Q_sca. When light is totally forward scattered (g = 1), Q is zero; radiation passes right through the particle [22].

Radiation pressure and the solar wind can strongly modify the orbits of small particles. The dominant term in Eq (21) is the radial, velocity-independent force of radiation pressure from the Sun. By convention, the parameter β ≡ L ⊙ Q A p 4 π G c m p M ⊙ (23) ≈ 0 . 213 Q [ ρ p 2 . 7 g/cm 3 ] - 1 [ r p 1 μ m ] - 1 ( spheres ) (24) indicates the strength of this force compared to the Sun’s gravity. Because radiation pressure depends on the flux of sunlight, ∼L_⊙/r², β depends on grain properties and not heliocentric distance. Thus, for β < 1, a grain orbits in a central force that still varies as 1/r², although with diminished strength as the Euler constant GM_⊙ becomes GM_⊙(1 − β). For β ≥ 1, dust grains are ejected from the solar system.

For particles initially orbiting at the L₁ point, a non-zero β can lead to a rapid drift from the ideal, purely gravitational orbit. We define a persistence time, T per = 1 f • ( 0 ) ∫ f • ( r → , t ) t d t , (25) to represent the equivalent time that Earth is fully shaded by a grain. Fig 3 illustrates how the persistence time depends on β for spherical grains with several different radii. At small β, and for particles with radii much larger than a micron, the persistence time is long, at least months. Sub-micron grains have short persistence even when β is small, since they are swept away from L₁ by the solar wind.

We can increase persistence by noting that the reduction of the strength of the central force when 0 < β < 1 means that Earth can shepherd dust at an “L₁-like” point closer to the Sun. An estimate of the distance between Earth and this new, size-dependent L₁ is derived from equating the orbital speed of Earth with that of a dust particle on an inner orbit: G M a semi 3 = [ ( 1 - β ) G M ⊙ ( a semi - x ) 2 - G M ⊕ x 2 ] 1 M ⊙ a semi / M - x , (26) where M = M_⊙ + M_⊕. For β ≤ 0.1, the solution to the above equation is well-approximated by d p ( β ) ≈ d 1 + 0 . 1047 β + 1 . 6215 β 2 ( β ≲ 0 . 1 ) . (27) We numerically determined the location of these L₁-like points, which can be several times more distant from Earth than “true L₁”. Fig 4 provides examples. We verified that particle orbits may be sustained there for at least one year, balancing gravity, radiation pressure and solar wind in the ideal case when all quantities are constant.

The next step is to combine the orbits described in this section with the physics of dust scattering discussed earlier.

We first consider a monodisperse dust cloud at true L₁, as in Fig 2. The optimal attenuation for a cloud perfectly centered between Earth and the Sun is A 0 = f • ( 0 ) 3 Q ext M cloud 4 π ρ p r p d 1 2 a semi 2 R ⊙ 2 , (28) where r_p, ρ_p, and Q_ext are the radius, bulk density and scattering efficiency of individual dust grains, respectively. Fig 1 provides examples of the attenuation as a function of dust particle size for a variety of materials. Coal dust, which is an efficient absorber, provides the strongest attenuation when dust particles are approximately a few tenths of a micron in radius. Glass, when formed into elongated, hollow tubes, has a peak attenuation when the volume-equivalent radius is about ten microns.

When providing shade to Earth, both the attenuation and the persistence of each grain at L₁ matter. A simple measure of this joint effect, the cumulative attenuation defined as T per × A 0, gives an estimate of the effectiveness of a grain type and quantity for impacting Earth climate. For example, a ten-year reduction of sunlight at Earth equivalent to the Maunder Minimum would have a value of 0.025 attenuation-years, or about 9 attenuation-days. For comparison, Fig 5 shows the cumulative attenuation for 10⁹ kg of of dust composed of materials listed in Table 1. Coal dust with radii near 0.1 μm is most effective, in part because of its low density and high scattering efficiency. With a maximum cumulative attenuation of 0.03 days, approximately 300 times more dust of this size and composition (∼ 1.5 × 10¹¹ kg) would need to be delivered to L₁ to reproduce the Maunder Minimum.

For context, 10¹¹ kg of materials considered here would fill a sphere with a radius of roughly 200 m, comparable to the amount of material excavated per year in a single open-pit mine. The total mass launched into space over human history is considerably less, with estimates under 2 × 10⁷ kg.

We ran simulations of fluffy glass aggregate particles with a volume-equivalent radius of 2 μm and filling factor of 0.1, launched from a platform on the L₁ orbit in Fig 2. We assessed two scenarios: (i) release all the particles at the start from L₁ with some small velocity dispersion (σ_v = 10 cm/s), and (ii) launching them from that same platform continuously over a one-month period in a directed jet. In the first case, the cumulative attenuation is about 0.085 days with a 10⁹ kg cloud of dust; it is short because radiation pressure causes individual grains to drift from disk of the Sun. In the second case, this same cloud is launched with a velocity dispersion of 10 cm/s within a jet of mean speed 10 m/s directed at an angle θ_v = 65° relative to the Earth’s direction of travel. The persistence is approximately doubled, increasing to 0.15 days, since the jetted particles have initial speeds that compensate for the drifting motion away from the solar disk. Fig 6 is a snapshot of a particle jet launched in this way.

With the possibility that dust can orbit at an L₁-like point more distant than true L₁ when it experiences non-gravitational forces, we introduce a second base-line attenuation factor for an optically thin, monodisperse cloud of dust with a total mass M_cloud: A β = f • ( 0 ) 3 Q ext M cloud 4 π ρ p r p R ⊕ 2 (29) where d_p is the distance between Earth and the cloud’s location at the corotating, L₁-like point. We assume perfect alignment between the Sun, Earth, and the cloud, so that f_•(0) is the fraction of photons removed by a grain that would have otherwise struck Earth.

The cascade of dependencies in this equation begins with the scattering properties of each grain. Its extinction efficiency determines how many Earth-bound solar photons it can eliminate, but that factor, along with the scattering anisotropy, sets β (Eq 23), the degree to which radiation pressure can affect its orbit. Higher values of β require larger distance between the cloud and Earth, substantially reducing the angular size of each dust grain, and diluting the shade provided to Earth. To compensate, the mass of the cloud could be tuned for a desired level of attenuation.

As an alternative to changing the total mass of the cloud to achieve high attenuation, we consider particle size and optical properties. Grains are most efficient scatterers of sunlight when they are around 1 micron in size. Yet micron-size grains typically have high β, possibly to the point where radiation pressure makes these grains unbound to the Sun (β ≥ 1). Material with significant forward scattering, g → 1, is less susceptible to radiation pressure than back-scatterers. More massive grains, by virtue of increased density or size, have smaller β than less massive ones. Numerical experiments suggest that silicate spheres with r_p ≳ 100 μm are massive enough so that radiation pressure does not impact orbits over the course of a year. The down side to this choice is that there are fewer grains for a fixed cloud mass. For a fixed cloud mass, the attenuation generally falls with increasing grain/pebble size.

For sub-micron grains, the extinction efficiency falls with decreasing radius; individual very small particles do not scatter light well. However, they also do not feel much radiation pressure [22], so β is also low, as d_p → d₁. Furthermore, for a fixed cloud mass, the smaller the particles, the more numerous they are. In balance, extinction efficiency, dominated at small particle sizes by absorption in the Rayleigh limit (Q_ext → Q_abs ∼ r_p), compensates for the increase in particle number when r_p is reduced. The attenuation from very small grains is independent of grain size for a fixed cloud mass.

Fig 7 illustrates these effects for spherical grains with properties in Table 1 (left panel) as well as the suite of “designer” glass particles in Fig 1 (right panel). The cloud mass is fixed for all materials at M_cloud = 10⁹ kg. For spherical grains, sea salt seems most promising in the 5–10 μm size range, followed by lunar dust of similar size. While the attenuation is two orders of magnitude lower than the eci level of 0.025, the persistence of all grains here is roughly a year, so the cumulative attenuation will be close to 0.04 days. Still, the total amount of dust to reach even an attenuation-day must thus exceed 10¹³ g. The availability and location of lunar dust, presumably mined from the lunar surface [18], suggest that this material might be the best choice for generating a massive, persistent cloud at an L₁-like location.

The designer glass grains offer a different scenario. The right panel of Fig 7 shows that a cloud of “fluff balls”—high-porosity glass or aggregates with a filling factor of (0.1)—for example, made from an aggregate of smaller particles—has a cumulative attenuation of approximately 3 days if it remains near d_p for a year. Tubular or rod-like shapes with aspect ratios of L : D = 100 : 1, lead to cumulative attenuation around 0.2–0.4 day with 10⁹ kg. Substituting aluminum for glass does not substantially change these results.

Numerical experiments highlight that persistence is difficult to achieve even with L₁-like orbits, both in the precision required to initialize them, but also because non-gravitational forces can affect particles of slightly different sizes in significant ways.

Because of issues of persistence at L₁ and L₁-like locations, we considered other strategies, including particles launched from the surface of the Moon, on orbits that are optimized to block the Sun as they stream toward L₁. Fig 8 illustrates the path of a burst of lunar dust with radius 0.2 μm from a ballistic launch at 4.7 km/s from the northern pole of the Moon. The cumulative attenuation in this case is 0.11 days for 10⁹ kg of dust.

A similar numerical experiment with larger, 1 μm grains yielded a cumulative attenuation of 0.03 days. Radiation pressure is less impactful than for smaller particles, so these larger grains can achieve an orbit that intercepts Earth and the Sun with slower launch speeds (2.8 km/s). However, despite the longer time that they spend shadowing Earth along their trajectory, their scattering efficiency is relatively low (Fig 1); a cloud of 10⁹ kg provides a cumulative attenuation of only 0.025 d.

Fortuitiously, the distribution of grain sizes in the lunar regolith peaks around 0.2 μm, the size with the highest scattering efficiency. In Apollo samples, approximately 20% of the lunar regolith mass is in the form of dust smaller than 20 μm park2008, with a lognormal distribution peaking at a grain size of about 0.2 μm. About 30% of this small-sized material is in grains between 0.1 and 0.3 μm (Fig 3 in [33]). Either sifting the existing regolith for the desired grain size or milling the larger bulk could provide a substantial reservoir of dust. The prospects for mining lunar dust with grain sizes suitable for shielding Earth are promising.

Because of the simplicity of this strategy—a ready source of dust, a ballistic launch with no subsequent orbit corrections—and its low cost in terms of energy compared with a launch from Earth, it could provide a good alternative to maintaining sun-shielding material at L₁.

Roughly 10¹⁰ kg of dust per year is needed for Earth-climate impact, which is approximately 700 times more mass than humans have launched into space. A lower bound on the energy requirement of delivering this material comes from the potential difference between the Earth’s surface and L₁, ∼ 6.3 × 10⁷ J/kg. Thus, 10¹⁰ kg of material for a solar shield from Earth would require close to 10¹⁸ J, more than the energy spent in 20,000 Saturn V launches.

The potential difference between L₁ and the Moon’s surface is about 4% of the L₁-Earth value. From our numerical experiments, launch speeds of 3–5 km/s are needed to send micron-size dust from the Moon on orbits that shade Earth for up to a week. Launching 10¹⁰ kg of dust at these speeds requires up to 10¹⁷ J, equivalent to roughly 2500 Saturn V launches. This amount of energy is produced annually by an efficient array of solar panels with an area of less than a few square kilometers. A bank of electromagnetic mass drivers [34, 35], already envisioned for launches from the Moon [36, 37], could place large amounts of dust on Earth-Sun-intercept orbits.