Quote:Original post by Raduprv
For the time being we do not have the technology to do this, but with the advancements in nano technology and new materials, wouldn't it be possible in the future (maybe 500 years from now) to build some very elastic and flexible pipe between those two planets, and pump the CO2 from Venus to Mars?
Disclaimer: All of this is armchair calculations from Google, Wikipedia, and my handy CRC Reference Manual of Chemistry and Physics, 86th Edition.
Let's crunch some numbers to figure out the following:
(1) How big would this be?
(2) How much would building this cost?
Any such pipe would have to be made out of an arrangement/mesh of molecules with no lattice spaces large enough for CO2 to diffuse through. Otherwise, any pumping efforts would be utterly useless (they'd just drain right back out to wherever they were being pumped from). Since CO2 is one of the smallest molecules around, however, this material will need to be quite tight.
Carbon nanotubes would do the trick, since they're just carbon, and carbon fibers can keep CO2 out (this is what some CO2 scrubbers use to trap CO2 from recycled air). Let us suppose that the pipe has a cross-sectional diameter of 200 meters, approximately the length of Grand Central Station in New York City, and a wall thickness of 1 meter. The cross-sectional volume of an infinitely thin slice of the tube is therefore (201^2 - 200^2) * pi * dx = 401*pi*dx cubic meters, where dx is the thickness of the slice.
According to your modified plan, we'd anchor up the tubes whenever the planets passed close to each other, and then start pumping. Let's make a tremendous simplifying assumption and suppose that by the time 2505 arrives, we've already invented the technology to stabilize objects in space relative to some reference point, so that we can either fix the position of the tube relative to Venus or relative to Mars (or relative to the Sun, but that wouldn't be very useful).
The orbital period of Venus is about 225 days, while the orbital period of Mars is about 687 days. This means that they are closest to each other (assuming a perfectly circular orbit) about three times per Mars-year, or about once every 7.5 months in Earth time. Both Mars and Venus have orbital eccentricities less than 0.1 and ecliptic inclinations less than 5 degrees, so we will consider them circular for this purpose.
The Young's modulus (or "stiffness") for carbon nanotubes is approximately 1,000, which means that it takes approximately 1,000 times more stress to cause it to change shape than polypropylene, about 100 times more stress than oak wood, and about 10 times more stress than tempered titanium. As such, we won't have much time to start pumping once we attach the tubes; carbon doesn't stretch very well.
Let's suppose that we can stretch the tubes about 5% before they would approach their elastic limit and deform or break. Mars is about 9.553 AU in orbital circumference, while Venus is about 4.545 AU. The distance between Mars and Venus at their closest passes is therefore about (9.553 AU - 4.545 AU)/(2*pi) = 119,244,565,800 meters. With a 5% margin of error, that means we have about a window of about 16 Earth days every 7.5 Earth months before the planets are out of range, or about 26 (amortized) days every year.
Now we have enough information to answer (1). If the closest-pass distance is about 119 Gm, then the tube will need to be at least this long to connect the atmospheres of the two planets. Since the volume of a slice of width dx is 401*pi*dx cubic meters, the volume of a slice of width 119 Gm is
1.50221759 × 1014 m3.
The density of chiral carbon nanotubes (the kind we'd want for a super-long tunnel) is approximately 1.4 g/cm3, or 1,400 kg/m3. Therefore it would require a mass of carbon equal to DV = m = (1,400 kg/m3) * (1.5022 x 1014 m3) = 2.103 x 1017 kg, roughly equivalent to retrieving 7 inches of carbon from every point on the Earth's surface. For reference, the mass of the Earth is on the order of 10^24. (And forget about asteroid mining; the total mass of all asteroids in the Mars-Jupiter asteroid belt is less than 1/1000 of the Earth.)
The best source right now for cheap carbon is undoubtedly carbon dioxide, for which the current price is approximately $40 per ton. Since carbon comprises only about 38% of the mass of carbon dioxide, though, the effective price of the carbon in carbon dioxide is actually $106 per ton.
At $106 per ton, the cost of the raw materials is therefore USD 24.572 quadrillion. The current world GDP in USD is approximately $55.5 trillion (of which the United States alone contributes $11 trillion). The world's countries would need to invest 100% of their output over the next 254 years to be able to afford that much carbon (assuming a GDP growth rate of 4% per year). Considering it's a major challenge for most countries just to balance their budget, it might be hard to get them to invest in a gigantic space pipe. You can almost see the special-interest group attack ads: "Senator Wilkins is squandering your child's education dollars on a
GIANT SPACE TUNNEL TO NOWHERE!"
Assuming a 2% rate of inflation over the next 500 years, the world would be paying the unimaginably titanic sum of
USD 1.107 sextillion (1 followed by 18 zeroes) for all this carbon, which gives us the answer to (2). (And that's just the raw materials, to say nothing of the cost of moving all that carbon into space.)