Disconnects in Logic (4) - We don't do Physics

Ever come across the "space mirror"? If not (where were you, on Mars?), let me provide a little illumination. The mirror concept comes in several flavours, from the sublime to the ridiculous single large "sunshade" to trillions (I kid you not) of small sunshades, between the Earth and the life-giving deadly solar rays from our Sun. The intention is to reflect or filter or diffract a portion of the incoming insolation to offset "global warming" caused by life-giving deadly CO2 and other "pollutants" in Earth's atmosphere. Before I continue, I suggest you put down any drink, fragile artefact or large heavy object you might be holding, and swallow anything in your mouth - gum, toothbrushes, pens, thumbs and similar objects excepted - these should be removed. I fear for your safety, dear reader, should you laugh, chortle, guffaw or splutter while reading on.

One of the earliest ideas was for sunshades in orbit around Gaia, a simple and relatively inexpensive concept, one which could be phased over decades, and involve all those countries capable of putting such objects in orbit. International co-operation involving spending large sums is so easy to organise, as we all know. This would cost tens of billions of dollars per year over the coming decades. If you were paying attention, you might have noticed that I referred to this as "relatively inexpensive", which should give you a clue as to the cost of the other schemes. A major disadvantage is of course that roughly half of the orbiting parasols would be on the shady side of Earth at any given time, performing no useful function, and also spoiling things for astronomers beneath. Somewhat disconcertingly (and rather alarmingly) none of the articles I've read mention this problem. Logic disconnect number 1.

Because of the 50% redundancy and consequent additional cost involved, those engineers and scientists who had a well-thumbed copy of "101 things you didn't know about the Solar System" came up with a cunning wheeze to exploit something called a "Lagrange Point". Any object orbiting between the Earth and Sun would have a shorter orbit and greater speed, so would rapidly move away from the Earth, re-visiting in less than a year, if orbiting in contra-rotation (going the other way round) relative to Earth. Johannes Kepler (God rest his soul) discovered this and published his law  in 1619. If the orbiting object is not-too-far from Earth, gravity pulls it back a little, and if the distance is "just right" reduces the orbital speed to keep it stationary relative to the Earth.

Lagrange Points - Source: Montana State University, Department of Physics

L1 is the obviously useful one, the others being most useful if you want to remain a long way from your mother-in-law, though L3 is best to hide from the forces of loranorder. One concept is for a single, large (obviously) "wire mesh" disc at L1, to deflect 1% of the incoming sunlight. Lowell Wood and others have calculated that a screen made of one-millionth of an inch diameter aluminium wire forming a mesh of 1 thousandth spacing would act as a diffraction grating, and "bend" infra-red light away from Earth.

The flies in the ointment are that it must have an area of 1,600,000 sq. km (more than twice the area of Texas) with a diameter of 1427 km, and even with the too-thin-to see wire, with an estimated average mass of 1 gram/sq. metre including "ribs", weigh 1.6 million tons (I'll use the imperial ton,  tonnes are much the same). It's been estimated that using US launch vehicles, the cost of putting anything into Earth orbit is currently $44,000 per kilogram, or $440,000 per ton, and that doesn't include the cost of boosting mirror (parasol or sunshade) parts to the Lagrange point 1.5 m km. further out. Using the space shuttle would cost $175,000 per kilo just to Earth orbit. The mirror would weigh some 1,600,000,000 kilos. Assume the deployment costs reduce tenfold over time and do the sums yourself - I don't think my calculator display is big enough.

Don't employ these guys as fly-swatters because they've missed a few already, as I will show. First, all the diagrams I've seen show the parasol at 90° to the Sun-Earth axis, and the designers and most proponents seem to think it'll stay that way. I have news for them - without giving it a "twist" of one rotation per annum, the parasol would be parallel to the axis in 3 months, having no effect whatever. How it's possible to impart a rotation of exactly 360° per annum to a thinner-than a hair parasol 1427 km across I don't know. Someone suggested a steerable "hub", but hasn't heard of inertia. The parasol might have zero weight but it would have a mass of 1.6 million tons, and it would take some hefty steering jets to shift it. The "ribs" would have to be stiff enough not to flex unduly, adding considerably to the total weight to be lofted from Earth, perhaps doubling it. Brilliant idea, shame about the (lack of) physics. That faint sound is Newton turning in his grave.

There's more (of course there's more!) - the Lagrange points move. The system is not just Sun-Earth, but Sun-Earth-Moon. Objects in space orbit around their centre of mass, not their geometric centres. The centre of mass Sun-Earth is relatively very close to the centre of the sun, but the centre of mass of Earth-Moon (barycentre) is inside the Earth about 1,700 km. below the surface The Earth wobbles slightly therefore, changing the Sun-Earth distance, and also the Moon is either closer to, or further from the Lagrange point as the lunar month progresses. The important L1 and irrelevant L2 are most affected, oscillating by several km a month. In addition, the Earth's orbit ain't a circle but an ellipse, moving closer to, then further away from the parasol, compounding the problem. Our parasol now needs to be moved this way and that constantly to stay close to the elusive Lagrange point L1 and avoid us having to wave goodbye to it, and the trillions of dollars spent getting it up there. Then there's all the inevitable millions of tons of space junk orbiting the Earth at various distances, and the effect of all the CO2 and other gasses emitted during the construction of the parasol, the rockets or shuttles, their fuel, and the burning of that fuel in the atmosphere, none of the aforementioned even hinted at by the rose-tinted spectacle brigade. Unintended consequences, anyone?

The other scheme by astronomer Roger Angel involves 16,000,000,000,000 (16 trillion) pierced transparent 0.6 sq. metre 1-gram discs, forming a cylindrical cloud some 60,000 miles long orbiting in what he calls "L1 orbit". I see several difficulties, quite apart from the obvious, which you should be able to identify for yourselves. First, there's strictly no such thing as "L1 orbit", and even if there was, a 60,000-mile long cylinder oriented towards Earth would leave most of his "flyers" away from that orbit, meaning they'd drift Sunwards or Earthwards, speeding up or slowing down in orbit, and so spreading in all directions. At least he though of the effect of "radiation pressure" which would push the discs earthwards, and introduced a compensating mechanism. The "big parasol" team overlooked this, and also the Solar Wind of atomic particles, which Roger Angel seems to have ignored. Secondly he (Angel) says a 2% reduction in insolation over the entire surface would be "enough to balance the heating of a doubling of atmospheric carbon dioxide in Earth's atmosphere". A reduction of 2% averaged over the surface is around 7 W/m², or twice the IPCC AR4 estimate for a doubling of CO2. That 7 W/m² would be, from what I've absorbed from several years of surfing the net and absorbing concepts of radiative forcing like a solar parasol absorbs sunlight, enough to take the Earth into the next ice-age. Oops. Strong on ideas, short on physics and celestial mechanics, and should read more.

Here's my own "Cool It" plan

I reckon it'd be easier and cheaper just to deposit all that dosh in orbit. A dollar bill has an area of 103.4 sq. cm., and weighs a bit less than a gram, so a trillion of them would cover roughly 10,000,000,000 sq.metres or 10,000 sq. km. and weigh a million tons. Assuming each is oriented at 45° to the Sun on average, the effective area would be around 7071 sq. km. They wouldn't need complicated and expensive rockets, but could be blasted there in "super guns" - quite technically feasible (I know my history). The other advantage is that it doesn't actually cost 1$ to print a 1$ bill. Banknotes are paper and ink, and in some cases include a thin thread of metal (about as thin as the thread of logic in the other schemes). Banks wouldn't have to actually issue the notes as currency.

Each country could contribute a special "Cool It" note, with a picture of the incumbent political leader imprinted thereon. Just think - The US would have "Drill, baby, drill!" Obama waving his birth certificate, the UK would have "The NHS is safe with me" Cameron, Australia could have "No carbon tax" Gillard with a long nose, and Russia would have "It's me again!" Putin. I'm certain both democrats and republicans (though maybe not in equal numbers) would like to see Obama blasted into orbit, and citizens of other countries would be happy to contribute to see their beloved leaders actually doing something useful for a change. A side-advantage is that as the notes drift out of orbit they'd never fall fast enough to burn up, would float to the surface, and still be reflecting sunlight, increasing the albedo. Polar explorers would never run short of toilet paper... the list just goes on. Just think of all the thousands of "green-back" jobs Obama could point to as the election draws nigh. The Pentagon would be allocated funds to develop a "super gun" for the army, and the other services would be green with envy.

There's a Nobel Prize, or at least "Climate Crusader of the Year" in this for me, I'm sure. I may even get my handsome visage (He lies - Ed.) on a special edition banknote and join the political elite in orbit. I've changed my mind - geo-engineering is FUN!