The reality of global warming is receiving growing acceptance. Even the Bush Administration seems to be modifying its previous hard-line position rejecting the idea. Projections of the Intergovernmental Panel on Climate Change indicate an average global temperature rise of between 1.5 and 4.5 degrees C by the year 2100. Climate change simulations suggest that we may be approaching (or may already have passed) a tipping point in global warming. Data records show a progressive increase in average temperature starting about 1920, with the average temperature of the Earth now about 1 degree C higher than it was in 1920.
There are predictions that fertile farmland, for example in the Great Plains region of the USA, will be replaced by new deserts, that temperate zones will become more tropical, that the ecology of the ocean will be radically altered, that glaciers will melt, that the level of the ocean may rise by up to 20 feet, perhaps drowning costal cities around the world. Over the coming decades, the Earth may become a very different and less pleasant place.
Is there anything that
can be done to avert this global calamity? Several technical
fixes have been suggested. One of them is based on the
cooling effects of volcanic eruptions. The progressive
increase in average temperature over the past few decades shows a pronounced dip
of a few tenths of a degree C spanning a decade that corresponds to the eruption
Prof. Roger Angel of the
To understand the proposal, let’s start with what Lagrange points are. The Italian-French mathematician and mathematical physicist Joseph-Louis Lagrange (1736 –1813), in attempting to solve the gravitational three body problem, discovered that in a simplified Solar system in which the Earth orbits the Sun with no other planets or moons, there are five points of stability. They are now called “Lagrange points” and labeled L1 through L5. If a massive object is at one of these Lagrange points and displaced slightly in a particular direction, there may be a restoring force that pushes it back toward the stability point. The “Trojan” Lagrange points L4 and L5, which are in the Earth’s orbit 600 ahead and behind the Earth, have such stability in all three directions in space. However, Lagrange points L1, L2, and L3, which lie on the line through the centers of the Earth and Sun, are stable only in the two directions perpendicular to the line connecting the two gravitating bodies, but are unstable to “radial” displacements along that line.
L3 is the “contra-Earth” Lagrange point on the far side of the Sun from the Earth. Its stability is more mathematical than real, because an object orbiting at L3 would be strongly perturbed and soon kicked out of its orbit by the other inner planets of the Solar System, particularly Venus. L2 is the “Earth-shadowed” Lagrange point on the side of the Earth away from the Sun. The Wilkinson Microwave Anisotropy Probe (WMAP) is located at L2, and it is also the location of the planned James Webb Space Telescope, to be launched in 2013.
The L1 Lagrange point, about 1.5 million kilometers above the Earth in the direction of the Sun, could be called the “sunshine” Lagrange point. It is closer to the Sun than The Earth, but the “back-pull” of the Earth partially cancels the Sun’s gravitational pull, so that it has the same orbital period as the Earth. It is stable to perturbations perpendicular to the Earth-Sun axis, but it is unstable to perturbations along that line, so that some active thrusters are occasionally required to maintain a satellite in this orbit. The Solar and Heliospheric Observatory (SOHO) and the Advanced Composition Explorer (ACE) are presently located at L1.
Roger Angel’s sunshield would be placed just beyond the L1 point. Because the Earth and Sun have about the same density, the penumbra shadow of blocked sunlight from an object placed at L1 almost precisely covers the disc of the Earth. Thus, it is the ideal location for an object blocking Earth-bound sunlight. Angel estimates that a reduction in the intensity of solar radiation by about 1.8% would full reverse the effects of a doubling of atmospheric CO2.
However, in maintaining an orbit at L1, the action of light-pressure is a problem. A square meter of radiation absorbing material (assumed to be 1.06 mm thick and to have an average density of 2.35 g/cm3) at the orbit of the Earth and perpendicular to the Earth-Sun axis receives a push from solar radiation of 4.6 mN (1 mN = 10-6 newtons). The gravitational pull of the Sun on the same square meter of material is 15 mN, so light pressure would cancel about 1/3 of the gravitational pull, and maintaining an orbit precisely at L1 would be impossible.
Roger Angel’s solution to this dilemma is to make several innovations. First, make the material transmit most of the light that strikes it and to scatter about 4% of the light at an angle of a few degrees, just large enough to miss the Earth but not large enough to absorb much momentum. The remaining light pressure still requires him to put the object in an orbit a bit closer to the Sun (about 1.8 million kilometers above the Earth) to achieve a stable L1-type orbit. The downside of intercepting only 4% of the light is that you need 25 times more area than if you intercepted all of the light. As we’ll see below, that raises the cost.
What goes into the L1 orbit and how much will it cost? The cheapest solution would be to place a light-absorbing dust cloud there. However, light pressure and the radial instability of L1 orbits would rapidly dissipate such a cloud. Therefore, one must instead use a “cloud” of autonomous sunshade spacecraft with “station-keeping” capabilities. Angel’s unit sunshade spacecraft design is essentially a navigable sheet of silicon nitride containing holes with their centers placed 15 mm apart in a vast hexagonal planar array, so that light passing through the holes is coherently deflected in an interference pattern by a few degrees. Each unit has a mass of about a ton (1000 kg) and has a shade area of about 2.4 square kilometers.
The total area that must be occupied by these sunshades is very large, about 4.7 million square kilometers. The total mass of the spacecraft needed to cover this area is estimated to be 20 million tons (2.0 ´ 1010 kg).
Angle tries to get the launch cost down by suggesting the construction of an electromagnetic launcher, a “space cannon” mounted on a high mountaintop and having a “muzzle velocity” of 12.8 km/s. He describes a 2 km long magnetic coil launch system using peak magnetic fields of 24 tesla and requiring an energy input of 65 billion joules that is projected to provide such a capability.
Suppose it was decided that the effects of global warming must be mitigated in a 10 year period using this method. Angel estimates that with flyer payloads of 1000 kg each, about 20 million launches would be needed to deploy the sunshade system. He envisions 20 of the electromagnetic launchers, each costing about $30 billion, launching one flyer every 5 minutes for 10 years. A stretch-out to more decades of launch would require a smaller number of launchers operating for a longer period. The total capital cost of the launchers would be about $600 billion and the electrical energy cost about $150 billion. Added to that, the production cost of the flyers would be about $1 trillion. These figures do not include the development and operations costs, estimated to be less than $5 trillion. If the lifetime of the project is 50 years, than average annual cost would be $100 billion, about 0.2% of the world’s gross domestic product.
Is this sunshade project, or one like it, likely to become a world priority and to be implemented? It’s difficult to say. Concern about global warming is rising in all parts of a planet, but such concern would have to rise much higher to reach a level at which the megaproject envisioned by Roger Angel would be seriously undertaken. The resources of the planet have never been mobilized in a coherent way on such a massive scale, and it is not easy to visualize the political processes that might bring this about.
Nevertheless, it’s an interesting idea, and it certainly has implications for science fiction as well as geopolitics.
SF Novels by John Cramer: my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .
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