# Space: Still the Final Frontier

Ask any American which country is the greatest in the world, and he’ll answer without hesitation. Ask him why, and he’ll likely respond, “What? You’d rather live in (fill in the blank with random oppressive regime)?” He’ll state this with the conviction of a modern-day Don Quixote, as if the logic were so irrefutable it should be taken as a mathematical proof.¹ Press him to explain. If you’re able to keep this game going long enough, you’ll eventually reach the “We’re the best country because we put a man on the moon” defense.

It’s been 38 years since our last trip to the moon, a fact that has been highlighted in recent headlines by the cancellation of NASA’s Constellation program. Much has been written about the pros and cons of manned space flights. If Oregon Trail taught us anything, it’s that exploring new environments can be deadly, and we should expect space travel to be no different. That said, even more catastrophic dangers are inherent with staying on this planet: asteroids, the Sun expanding into a red giant and swallowing the Earth, moonlike space stations attacking us with lasers, etc. Unfortunately, none of these threats are immediate enough for our collective human psychology to kick in and make us budge, so I’d like to offer some bits of mathematical motivation to push us in the forward direction.

Reason 1: Space Is a Great Energy Source

Space is filled with abundant sources of inherently green energy². I’ve previously written about how much energy you could obtain by building a wind farm on Jupiter, but even sticking with solar energy would be sufficient to power all of our earthly needs. In total, how much solar power exists?

Earth’s surface is constantly bombarded with electromagnetic radiation from the Sun. The solar flux (i.e. the power per square meter arriving at Earth’s surface) is about 1,370 W/m². Earth’s radius is about 6,371 km. From this info, we can estimate the total solar power falling on the Earth:

This is about 50,000 times larger than the total US power consumption, but it’s much smaller than the total power we could absorb from the Sun. Since the Sun radiates power uniformly in all directions, much of it misses the Earth. What fraction of radiation emitted by the Sun hits the Earth?

Consider an imaginary sphere centered on the Sun with a radius equal to the distance between the Earth and the Sun (~1.5×10^8 km). The Earth will take up only a small fraction of this sphere’s area:

This means Earth only absorbs about 0.00000000045% of the total power emitted by the Sun. Absorbing all this power for only one second would produce enough energy to run the entire world for almost 800,000 years. Clearly, there’s a lot more energy to be gained in space than there is on Earth.

Reason 2: Potential for Less Pollution

There’s a continent-sized patch of garbage floating in the Pacific Ocean. This thought is disconcerting enough, but it’s even scarier when you consider that developing countries and population growth will increase an already frightening amount of trash production. It may not be possible for recycling alone to keep up. A green Earth may need to transport its garbage elsewhere, but fortunately there are many places in the solar system we could use as our trash can. Let’s use Pluto since it’s not even a planet anymore³. How long would we have to dump trash on Pluto before it regained its planet status?

There’s quite a bit of ambiguity surrounding the definition of a planet. We know that Mercury, which at 3.3×10^23 kg is fairly svelte for a planet, is large enough to fit the IAU’s definition. Since Pluto’s mass is 1.3×10^22 kg, it would have to gain no more than 2.2×10^23 kg before regaining its planet status.

There are 6.7 billion people on the planet. If each person throws out one 5 kg of trash each week, there will be 1.7×10^12 kg of trash produced per year. Dividing this into the mass Pluto would need to gain, we can estimate how long it will take before Pluto becomes a planet again:

This is about 30 times longer than the age of the Earth, so it’s certainly a sustainable solution.

Reason 3: A Defense Project

“A thousand nations of the Persian Empire descend upon you. Our arrows will blot out the Sun!”

— A Persian in the movie 300

I’m not so naïve as to think that projects as passé as alternative energy sources and pollution reduction would ever gain support in Congress, but it may be possible to promote manned space flight as a military project. “How would space travel be a defense project?”you say. What are you, a commie? Don’t you support our troops? Do you want the terrorists to win? I digress.

While it’s unlikely to lead to the next dark ages, the giant cloud of volcanic ash stretching from Iceland to Greece is a major threat to people living in the affected areas. Without sunlight there’s no agriculture, and without agriculture there’s no food. While it sounds like a bad Dr. Evil plot, building a giant Sun screen to block out an adversarial nation is, at least in theory, possible. In addition, we could presumably turn it off as soon as it’s no longer needed and it wouldn’t have the adverse long-term effects that nuclear and biological weapons would. How large of a screen would be required to block the Sun from an entire nation?*

This clearly depends on (1) how big of a country you want to keep in the shade and (2) how far away you place the screen. We know that the Moon is large enough to block out the Sun during an eclipse, but you might be able to use something appreciably smaller if you put in a lower orbit around the Earth. Using fairly simple geometry, you can estimate the apparent size of the Sun and set that equal to the apparent size of an object in a low Earth orbit,

(D)Screen = (D)Country + (D)Sun (R)Earth-Screen / (R)Earth-Sun,

where (D)Screen, (D)Country, and (D)Sun are the diameters of the screen, country, and Sun, respectively, and (R)Earth-Sun and (R)Earth-Screen are the distances between the Earth and Sun and Earth and screen, respectively. To block out a 100 km long country with a screen in orbit 300 km above the Earth’s surface, you would need:

As you can see, the screen would only need to be about 3% larger than the actual size of the country. Admittedly, this is no small feat, but remember we’re already building giant solar panels to collect energy so it might be feasible.

There are countless reasons, both practical and downright science fiction-y, for funding manned space exploration. While balancing the budget and paying off the deficit are certainly important, doing so should not also prevent us from building the next great wonders of the world. What will be our Panama Canal? Our Moon landing? What will our generation point to and say, “Hey, check out what we did?” We’ve got 218 years until James T. Kirk is born, so there’s not a moment to lose.

[1] This, of course, would only be true if his oppressive regime of choice constituted the second best nation in the world, but I doubt he’ll provide convincing proof of this theorem.

[2] I say “inherently green” because any emissions would be generated in space, so they wouldn’t contribute to global warming.

[3] Yeah, kick it while it’s down!

* There are additional issues about how to maintain your screen’s location over the country of interest, but I’ll ignore those for now.