Devoted reader, friend of the blog, and noted person-who-has-the-same-parents-as-me, Maggie S., no doubt motivated by certain recent events, submitted this question via Twitter:

Can we launch all fraternities into the sun? I got at least a grand to contribute to this. Please advise

As in all truly worthwhile human endeavors, the answer is that yes, of course we can, provided we're willing to dedicate the required ingenuity and resources. If we're willing to accept simply launching all of the members of every fraternity into the Sun, preserving their infrastructure (buildings, etc.) for more noble purposes, than it's a fairly simple problem of mass; packing humans into a normal sized payload fairing should be very doable, although it's left to the reader to decide upon the optimal arrangement.

The problem of mass, while simple, is substantial. This summary from the North American Interfraternity Conference suggests there are 397,000 undergraduate men in fraternities in the United States. This is from 2011, and I can't seem to find a newer number, so let's allow for some accumulation, and maybe for independent fraternities that aren't in the NAIC, and call it 450,000 even. According to the NHANES II Survey, conducted by the CDC, the average weight for an American male in his twenties is about 76 kilograms, but that was in the 1990s, so uh, let's round that up to 80 kilograms. 80 kilograms multiplied by 450,000 fraternity members gives us the mass of our payload: 36,000 metric tons.

That's a very large payload. The heaviest lifting rocket ever to fly thus far, the Saturn V, could "only" lift 118 metric tons into low Earth orbit. And we want to put our payload not just into low Earth orbit, but on a trans-solar trajectory, which takes even more energy. Clearly we're not going to be doing this in just a few launches.

We need a very heavy lifter. If all goes well with development of SpaceX's Falcon Heavy, which is more or less three Falcon 9s strapped together, it should be able to put 53 or so metric tons into low Earth orbit. Assuming it flies in 2015, it will be the heaviest lifter available. We should probably aim higher than that, though. NASA's SLS, in its Block II configuration, is intended to lift 130 metric tons to low Earth orbit. Better. Not great, and this configuration probably won't fly until the 2020s, but there's nothing planned any further down the line that's going to give us better lift, so it's probably our best bet.

As I said though, our goal is to get our payload onto a trajectory that intersects the Sun, not just low Earth orbit. This entails producing enough change in velocity (delta-v) to:

• Achieve escape velocity from Earth, putting our payload in a heliocentric (sun-centered) orbit
• Reduce the perihelion (point closest to the sun) of our solar orbit until it intersects with the sun

Or, illustrated, we need to do this:

This is exaggerated and not to scale, but you get the idea. We escape Earth orbit and lower our orbital energy relative to the Sun until our orbit intersects it.

This takes a lot of change in velocity. After launch, when our payload is in low Earth orbit, it will be traveling about 7.7 km/s. Escape velocity from Earth is about 11.2 km/s, which means we'll need (11.2 km/s - 7.7 km/s) = 3.5 km/s delta-v to get us from low Earth orbit to Earth escape velocity. Once we achieve escape velocity, we'll be in an orbit of the Sun that's roughly similar to Earth's. Earth orbits the Sun at a speed of about 30 km/s, and so that will be roughly our sun-relative velocity. If we were to cancel out all of that velocity by performing an engine burn of 30 km/s delta-v, we'd fall in a straight line right into the Sun. That's unnecessary, though, as illustrated above; we just need to lower our orbit enough to touch the corona, where the multi-million degree temperatures should do the trick.

I laboriously did the math for you. No, actually, I googled someone who had already done the math (see note 1 from Mark Adler): it will take 26.9 km/s delta-v. Adding in the 3.5 km/s it took us to get to Earth escape velocity, that makes it 30.4 km/s total delta-v to get from low Earth orbit to a trajectory that kisses the Sun.

Like I said, that's a lot of delta-v. The Dawn probe, as I discussed in this post, set a record by producing over 10 km/s delta-v with its propulsion alone, and our payloads are too massive to use Dawn's ion thrusters. Missions that have to achieve anywhere close to the kind of delta-v we need, such as ones on an escape trajectory from the solar system, use gravity assists from massive bodies like Jupiter and Saturn.

We're going to need a substantial propulsion module to produce all that delta-v once we're in low Earth orbit. As I mentioned above, using SLS will allow us to put 130 metric tons into low Earth orbit. Some of that will be our payload of hapless fraternity members; some of it (a great deal of it, considering our mission requirements) will be an engine, a tank, and the propellant we need to produce our 30.4 km/s delta-v. The more efficient our engine is, the less propellant we'll need, and the more of our 130 metric tons we can devote to our payload. We want a very efficient engine for this, an engine with high specific impulse (ISP). So instead of using conventional chemical rockets, which typically max out at around 450 seconds ISP, I propose we use a nuclear thermal rocket. These heat up and accelerate hydrogen propellant using a nuclear reactor, achieving much higher exhaust velocities than traditional rockets and therefore much higher ISP.

There's a minor rub here, and it's that a nuclear thermal rocket has never actually been flown on a spacecraft. The concept has been extensively researched, though, and plenty of test articles have been developed to demonstrate it. It's just that every project to develop them has eventually run dry of funding or legislative support. But let's resurrect one in the name of the mission. In the early 1990s, a Department of Defense project called the Space Nuclear Thermal Propulsion Project worked on developing low mass nuclear engines that would operate only in the vacuum of space. Their final report (link goes directly to PDF) elaborates the design for an engine that masses just 621 kilograms, produces 197.5 kN (kilonewtons) of thrust, and has an ISP of 1000 seconds. We're going to use three of these engines, to capitalize on their efficiency but also produce enough thrust that our burn is completed in a reasonable amount of time.

Our humble upper stage engine, three of which will perform the burn that takes us from low Earth orbit to an orbit that intersects the edge of the Sun. The nuclear reactor uses 37 uranium fuel rods with a beryllium/lithium-hydride moderator. SNTP engineers dubbed it, rather dryly, "LV03," but for our purposes I propose we christen it Qatrikias, the proto-Irish name of St. Patrick, who drove the snakes out of Ireland. Note that the Qatrikias engine is 13 feet long from top to bottom.

So now we know the mass we have in orbit (130 metric tons), the efficiency of our engine (1000 seconds), and the delta-v we need to achieve (30.4 km/s), we have enough information to calculate, via the Tsiolkovsky rocket equation, how much of our initial 130 metric ton mass we can devote to our payload. And again, I briefly considered doing the difficult math but instead located a web application that calculates it. Long story short, at the end of our engine burn we will have 5.9 metric tons of mass left, and you have to subtract from that the mass of our 3 engines (621 kg * 3 = 1,863 kg) and empty propellant tank, which means probably about 4 metric tons of payload on our Sun-bound orbit. By our earlier estimate of an 80 kilogram average male, this means 50 fraternity members per payload (and I really have to lodge a minor objection here; I'm sure at least 20 of those are upstanding young gentlemen).

Now that we've got the details nailed, let's review our mission profile. The SLS rocket launches our payload, a tank full of liquid hydrogen, and our 3 Qatrikias engines into low Earth orbit. It would look something like this, except mentally replace the pointy bit at the top with a container full of frat dudes:

With our payload and propulsion module separated from the SLS launch vehicle, we're ready to inject into our Sun-intersecting orbit. At the point in our orbit where we're traveling opposite the direction in which the Earth orbits the Sun, we will perform our trans-Solar Injection burn. Firing our 3 Qatrikias engines at this point in the orbit will raise our velocity relative to the Earth to escape velocity and beyond, but at the same time will lower our velocity relative to the Sun, lowering our resulting heliocentric orbit as I illustrated above. The engines will burn 125 tons of hydrogen propellant at a combined rate of 64 kilograms per second, taking 32 minutes to produce our required 30.4 km/s of delta-v.

After the engines cut off, we can jettison them and the propellant tank, and our frat guy payload will enjoy a 65 day free fall into the Sun's corona. You may recall from the recent Spacebag that in eccentric orbits such as that of our payload's, the velocity is greatest at periapsis (point in the orbit that's closest to the body being orbited), and that for massive objects such as the Sun, this can equate to tremendous velocities. Well, our perihelion happens to touch the Sun, and, consequently, our payload will be traveling 616 kilometers per second just before it meets oblivion (New York to Los Angeles in about 6 seconds).

Mission accomplished! But remember how we have 450,000 fraternity members, for a total payload of 36,000 metric tons? At 4 metric tons to trans-Solar injection per launch, that means nine thousand launches of the SLS to meet our goal. At an estimated cost per launch of $500 million, that brings the total cost of Maggie's project to 4.5 trillion dollars, or approximately the gross domestic product of Japan. But as the adage goes, nothing that's worth doing is easy.

Image credits: Cover Image -- Southern Methodist University; Trans-Solar Trajectory Diagram -- Azimuth; SNTP Engine Diagram -- Department of Defense.