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kfsorensen
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« Reply #12 on: 03/12/2006 10:09 PM » |
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An excerpt from Martyn Fogg's excellent book "Terraforming" might clear some of this up.
From page 173-178:
4.2.6.1 Shadowing the Earth
Space-based devices that absorb or reflect sunlight could be used as geoengineering tools for a number of applications . Most recently they have been discussed in the context of bringing about a negative radiative forcing to combat global warming. The Earth's surface would be shadowed from some fraction of solar radiation sufficient to offset the positive forcing of greenhouse gas emissions and, in this sense, the technique works in the same way as the dust/aerosol layers discussed in the previous section. Assuming, for simplicity, that the Sun is a point source of light at infinity, the size of the shading area required to screen out 1% of the Earth's insolation is 1% of the planet's projected area, i.e., as = 0.01*pi*re^2 = 1.28 x 10^12 m (where re is the radius of the Earth) . This figure is actually a minimum as the size gradually increases with distance from the planet and not all the shading area may be correctly aligned between the Earth and Sun at any one time, reducing its shadowing efficiency to es < 1 and requiring an increase in area of 1/es. If constructed as a single object, even this minimum area is equivalent to an enormous parasol about 1280 km across, roughly the area of a country the size of Peru. Yet the scale of the project is not as daunting as this analogy suggests. Sunlight can be interrupted by very thin layers of opaque matter and lightweight, flimsy structures that would collapse on Earth could hold their shape perfectly well in the airless, free-fall conditions of space. Ultra-thin films made from common materials are therefore the key to fabricating devices with large areas and relatively little mass. Examples of thin films that everybody is familiar with include aluminum cooking foil (13-25 µm thick) and plastic wrap (13 µm thick). Material designed for solar sail spacecraft has to be much thinner than this to maximize the acceleration the sail is capable of: one design for such a material is only 2 µm thick, consisting of aluminum-coated polymer. We may be able to provide films for space reflectors with areal densities of rhoa < 5 g/m^2 and a total mass, for the area given above, of ~6 million tons . Handling this amount of processed material is already well within the capabilities of civilization and it is interesting to note that it is on the same order as estimates for the mass of stratospheric dust required in the albedo enhancement scenario. The disadvantage with the dust is that it must be continually replenished every year, whereas if one's reflective surface is a fabricated, semi-permanent structure in space, then it might require renewal on a much longer time scale. Of course, structural support for space reflector material will add to its overall areal density and mass, but this might be offset by more "high-tech," thinner material, possibly perforated at a submicron scale so that it will still interrupt visible light.
Four categories of orbit can be envisaged for space parasols and are listed, along with their relative merits, in Table 4.7. Use of the first two, low Earth orbit (LEO) and geostationary orbit (GEO), are hampered by many severe difficulties that will probably rule them out as viable choices for the purpose in question. The principal problem is that since parasols would be circling the Earth, they would be positioned between the Earth and Sun during only a small part of their orbit. Their shadowing efficiency would therefore be low, particularly in the case of GEO where es ~ 1.5 x 10^-3, requiring the shading area (as) to be multiplied by ~670. This is obviously not the way to proceed as it greatly increases the resources, industry and expense involved in cutting down the insolation by the desired fraction. Other objections include the overcrowding of orbits already used by regular satellites; the intrusive visibility inherent in the screen being so close overhead; the reflection of unwanted sunlight onto the planet's night hemisphere; and the complexity of maintaining such extended objects correctly oriented when subject to planetary tidal forces, gas drag, and light pressure. Close orbits do have one dubious advantage and that is, if we are faced with a climatic emergency, and there has been no development of extraterrestrial resources, then LEO could be filled with fleets of parasols launched from the surface of the Earth. However, it is difficult to imagine such a panic measure being practical; it would require a huge increase in launch capability (>1 million 50-ton launch increments) and would thus significantly contribute to environmental stress in its own right.
Since it takes 22 times less energy to launch a payload off the Moon than Earth, and there is no atmosphere to worry about, it makes sense to obtain and process the raw materials for the parasol from the Moon or convenient near-Earth asteroids. The manufacture of large quantities of thin film in space should not present an overwhelming obstacle, especially if it can be made from commonly occurring substances. (Scenarios of space manufacturing in the context of the construction of space habitats envisage the fabrication of much more complex items.) Subsections of parasol might then be conveniently and cheaply launched into their shadowing orbit where they might deploy automatically, or be assembled into larger structures.
A much better choice of shadowing orbit would be available if we could permanently interpose a parasol (or fleet of parasols) between the Earth and the Sun . This would ideally involve a stable orbit that co-revolves with the Earth such that, to an observer on the ground, the parasols would stay fixed relative to the Sun (except for an oscillation across the solar disc in response to a parallax effect caused by the planet's rotation). However, for a parasol to possess the same angular velocity as the Earth, at a smaller orbital radius where the Sun's gravity is stronger, an additional outward force is necessary. It so happens that one of the Sun-Earth libration points (where centrifugal force and the forces of solar and terrestrial gravity balance) is situated inward from the Earth on the Earth-Sun line. This point is called L1 and is shown along with the other libration points L2 - L5 in Fig. 4.13. An object placed at L1 will co-revolve with the Earth about the Sun because of the additional outward force provided by the Earth's gravity.
The situation is in fact more complex than this because L1 is only a semi-stable region, resisting perturbation perpendicular to the Earth-Sun line only. Additionally, a wide, thin object such as a solar sail will also be subject to an extra outward pressure due to sunlight, displacing its equilibrium inward of L1 . For a planar, totally reflective sail, the equilibrium point is determined from the following balance of forces. When the photon pressure is zero, we obtain the L1 point distance of 1.5 million km (~0.01 AU (about four times the distance to the Moon)).
Since the photon pressure on a solar sail is proportional to its area and not its mass, the acceleration is inversely proportional to its areal density, rho. Thus, the thinner and less massive the solar sail, the further it is displaced from the L1 point, stability being achieved for Re's = 0.02 AU and 0.05 AU for rho = 29 g/m^2 and 11 g/m^2, respectively . Thus, the more we lessen the mass of the parasol by using sails of higher performance, the less we are able to exploit the semi-stable properties of the L1 region. The ideal parasol for the L1 point is therefore not a solar sail at all but a thin disc that would be minimally reflective on its Sunfacing side and with a high infrared emissivity on its Earth-facing side. The photon thrust from radiated infrared energy could be used to offset the thrust from absorption.
A particularly elegant solution to this problem was proposed by James Early of the Lawrence Livermore National Laboratory. He suggested fabricating a 2000-km-diameter parasol (his aim being to cut out 2% of sunlight) made from 10-p.m-thick glass which would be scored with a pattern of parallel grooves on one side. It would thus act as a prism, deflecting sunlight through just half a degree, sufficient to miss the Earth. Because the structure is transparent, it is subject to a very low photon pressure, with a calculated equilibrium point of R e's = 1.58 million km, very close to L1 . Another advantage of glass as the main parasol material is that the raw materials from which to make it are readily available in lunar soils, although the feasibility of producing good quality, ultra-thin glass sheets on the Moon remains to be demonstrated.
Most conceivable space reflector systems are going to need some kind of active positional control. The first reason for this is that the L1 point is only semi-stable and a station-keeping mechanism will be required to prevent displacement along the Earth-Sun line. Even so, thrust requirements are very low and could be easily done by making a small fraction of the parasol's area adjustable so that it can function as an attitude-control device, minutely varying the applied photon pressure. It would be a task that would be much less tricky than the fly-by-wire systems of modern fighter aircraft and could therefore be handled autonomously by a simple on-board computer. The second reason for active positional control is that the structures being proposed can be unstable due to their sheer size. Early's parasol, for instance, is a single object that is balanced only where it intersects the Earth-Sun line; all other parts would experience a small radial acceleration toward the center that would be balanced by rotating the structure about the Earth-Sun line at a rate of 2 cycles/year. A slightly faster rotation would give it an outward radial stress that would maintain it as a flat disk. However, in Early's words this situation itself creates another difficulty: "The disk rotation will unfortunately act as a gyroscope which keeps the disk oriented with its axis pointed in one direction. Since the disk axis must always point toward the Sun, a torque must be applied to the disk by a control system to cause the disk to precess at one cycle per year. it is not clear if this control system is simpler than using solar sails at the perimeter of the disk to supply a radial tension to balance the radial gravitational acceleration.
A space-based solution to the symptoms of the Earth's unwanted radiative forcing in the next century is scientifically feasible and merely requires us to develop and become experienced at space-based engineering. Influencing the Earth's climate from L1 or levitated orbits has some obvious advantages over measures that are implemented within our planet's biosphere. The technique would be non-invasive, non-polluting (if most industrial activities are confined to space), and manipulation of insolation can be very precise. Screen fleets can be maneuvered in and out of position comparatively rapidly; negative forcing being adjustable and predictable over shorter time scales than intrinsic geoengineering techniques, the effects of which have to work their way through various physical and biogeochemical processes. Not surprisingly, estimates for the cost of a space parasol project are very crude and vary widely. Early's estimate is $1-$10 trillion and the PIGW report (which considers only the unattractive case of LEO parasols) came to $5.5-$55 trillion. The economics of extrinsic geoengineering are therefore critically dependent on screen lifetime. If we assume that the scenarios referred to above can mitigate the warming equivalent of 4000 billion tons of CO2, and screen components or individual mini-parasols have a 10- to 40-year lifetime, yearly costs range from $0.0006 to $1.4 per ton of CO2. While the space program's track record of underestimating costs would probably drive the real expense into the higher end of this bracket, a collateral benefit of such a project could be that its necessary extraterrestrial operations could lay the foundations for the permanent habitation of space.
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