Wednesday, December 29, 2010

My 2010 Review

I started this year thinking the Augustine committee had nailed the Moon shut. Considering that I was a proponent of Constellation before the Augustine committee, that's pretty significant. If I go back to that time and see what I was saying to people, most of it was explaining the flexible path as an alternative to sitting on the ground waiting for a booster and a capsule and a lander to be developed by NASA.

I end this year thinking that the Moon isn't nailed shut. SpaceX has demonstrated that making a capsule and booster need not be expensive. Armadillo Aerospace and the other contractor's work on Project M (now Project Morpheus) demonstrated to me that going to the Moon need not be expensive. Tim Pickens and the Rocket City Space Pioneers have successfully restored my faith that the Google Lunar X-Prize will be won. Paul Spudis has actually become a robotic exploration advocate! In a few years time it won't be absurd to suggest that a commercial effort could send a rover to characterize the polar ice, make money by selling data to NASA, and later start selling lunar derived propellant in orbit.

I don't mean to suggest this negates the need for heavy lift. Actually, quite the opposite. I mean this to demonstrate that my belief that lunar exploration was necessarily expensive is slowly going away. With that frame of reference, I have to admit that maybe my belief that heavy lift is also necessarily expensive may have to go away. SpaceX have suggested they can do 130t to LEO for $2.5B in development costs and $300M per flight.

But the other problem with heavy lift is that it's a gate keeper. The advocates are perfectly happy to say that the Moon (or any beyond Earth target really) is off limits without heavy lift. This is simply wrong. We don't need heavy lift to send rovers to Mars so I think it is pretty clear that we don't need heavy lift to send rovers to the Moon.

Humans weigh less than rovers.

The problem is the can't-do attitude.

Monday, December 20, 2010

Soonest Space Solar Power

Space Solar Power has a bad rap, caused predominately by advocates who can't separate the exciting long term vision from the short term facts. In his recent paper, Al Globus has tried to rectify this by investigating what can be done with demonstrated launch vehicles, solar collectors and power beaming (and without on-orbit assembly, manned outposts, lunar materials, etc). His conclusion is that it appears space solar power is now ready for niche markets, such as forward military bases, where the price of power can be as much as $1/kWh.

The low cost launch vehicle of choice is, of course, SpaceX's Falcon 9. High specific power solar collection is achieved using thin-film heliogyros as demonstrated by the Japanese Ikaros satellite. The power beaming technology is infrared laser with custom solar panel receivers, as demonstrated by LaserMotive in their win at the Space Elevator Games last year.

A minor improvement in Globus' architecture is apparent. The mass of the spacecraft was estimated based on the throw capability of the Falcon 9 to geostationary transfer orbit (GTO), presumably because a solar sail style flight is expected to circularize the orbit, and solar sails can't start from low earth orbit (LEO). This is an implicit trade over a solar electric style flight from LEO, which I'm guessing is intended to utilize the solar collector for double duty in order to avoid additional mass. I'm not sure this trade wins. Even with a SMART-1 performance thruster, starting from LEO places 7751kg in GEO, 3.2 tons more than the estimated mass in the paper. If a NEXT thruster is available, the improvement goes up to 5.2 tons. However, this improvement only doubles the performance of the system, perhaps halving the price of power at the meter, which still doesn't make it competitive with the grid.

The problem is scale. Globus should be commended for describing a space solar power system that is achievable with current technology and could even make a profit in some niche markets, but let's think just a little bit further ahead for a moment. LaserMotive continues to improve the performance of their laser power beaming systems, so the 8% efficiency suggested may soon be on-par with the often quoted 10% efficiency of microwave power transmission. The paper suggests that SpaceX could reduce their prices by a factor of 3.6 if one ordered 1000 launches, but this claim is a few years old now. A more recent claim by SpaceX is that a super heavy lift vehicle could be built that delivers 130t to LEO for $300M per flight, a factor of just 2.3 - but the improved logistics of a single launch may offset that.

It should come as no surprise that reducing launch costs makes space solar power more feasible. What does surprise me is that sufficient specific power improvements in solar collection has been demonstrated which makes it reasonable to choose a lower efficiency beaming technique, with the resulting effect on the mass of the spacecraft making it launchable on existing boosters. This is a revolutionary idea which not only makes sense right now but defines a path for future work that will bring space solar power to the meter.

Thursday, December 16, 2010

Non-Rotating Artifical Gravity

If you put a long boom on a satellite, it will align to the "local vertical". This was first demonstrated on the GOES 3 probe in 1978. It works because the forces of gravity and the "centrifugal force" balance at the center of mass.

Today, long life space tethers are available, using existing materials they are light enough for long lengths to be launched on a cheap launch vehicle like SpaceX's Falcon 9. A length of 500 km, with a lifetime of 10 years, would have mass of just 1275 kg. The tether would stretch from the altitude of the International Space Station (~340 km) up past the altitude of the Hubble Space Telescope (~595 km), out to where the polar orbiting satellites do their job (~700 km+). Within equal masses on each end of the tether, a force of 0.1g would be experienced, with no rotation of the structure required.

Of course, this only works while in orbit around a planetary body. Around the Sun, say for generating artificial gravity for a trip to Mars, a much longer tether would be required and it quickly becomes infeasible. So what good is it? Currently, we have very little data on how the human body responds to partial gravity. Sure, we know lots about how it responds to 1g, and we have some ideas about how it responds to "zero g", but we don't have any data at all about anything in-between. 0.1g is just enough gravity for a human to stand upright and walk around (although Joe Carroll recently suggested that 0.06g was sufficient). If we could put some astronauts on a station with this level of partial gravity for a few months it would give us some vital data for determining whether people can actually live on the Moon or Mars or even asteroids for long periods of time without serious health issues.

Having the low end of the tether at the same orbit as the ISS, and having it not rotating around at high speed would make getting to the experiment very convenient. The high end of the tether could simply be the upper stage of the launch vehicle. SpaceX has already demonstrated that their second stage can be relighted, and flying to a circular orbit of 800km seems well within their capabilities. A 500km tether reel could fit in the trunk of the Dragon, which can remain connected to the second stage after separation.

Considering the availability and low cost of the hardware, the low risk of non-spinning artificial gravity, and the massive scientific payoff, NASA should be pursing this.. now.

Wednesday, December 08, 2010

A New Sputnik Moment?

Stephen Smith has an post over at his blog questioning President Obama's rhetoric that the down tick in the economy is having the same effect today as Sputnik had on the USA in the 50s and 60s. He's not convinced and neither am I, but near the middle he asks an interesting question: What would be the equivalent of a "Sputnik moment" in today's world?

The shock in the US caused by Sputnik was not so much that it was a military threat - although it was - but that it was a significant technical feat achieved by what most of the western world considered a backwater of scientific thought. Today, there are many technologies that are slowly being developed around the world which are primed for a breakthrough. Earlier this year North Korea claimed a fusion power breakthrough which certainly would have been a Sputnik moment if it hadn't turned out to just be a claim about fusion bombs, not fusion power.

This highlights a very important part of the Sputnik formula: how does the protagonist country dramatically demonstrate their technological achievement so there's no misunderstanding and no way to refute it? Sputnik did this fabulously by broadcasting an unmistakable signal that could be confirmed by amateurs and professionals alike. Any attempt to put the genie back in the bottle with Sputnik would be met with howls from the populous.

Suppose some manufacturing backwater suddenly started turning out superb jet engines, or even a whole new fighter plane. Just as a matter of competitive interest, other manufacturers would no doubt arrange to get their hands on a few samples and check out their quality. I expect that more than a few "national security" inquiries would also be made. What they discover blows their mind: the fan blades, the compressor, the combustion chambers, even the cowling, are all made from materials they've never seen before. Parts of the combustion chambers even appear to be made of perfectly shaped diamond.

By releasing these products onto the market, the protagonist has demonstrated a highly functional molecular nanotechnology manufacturing system. This is a massive breakthrough, and it would be completely unexpected. The current state of the art in molecular nanotechnology is basically: designing stuff we can't actually build. Here's some examples done with the open source nanotechnology CAD tool NanoEngineer-1:

There has also been some interesting work done by Ralph Merkle and Robert Freitas Jr. into making a "tool set" that might some day be usable to slowly make small objects in single quantities using hydrogen and carbon.

If some backwater country was to demonstrate that they had a molecular manufacturing system that could build anything they can design, using a handful of atoms - aka, not "just" a hydrocarbon metabolism - and do so on the macro scale, it would instantly make them a super power and set the stage for a worldwide scramble to duplicate their efforts and come up with some reasonable defense. I could imagine immediate calls for non-proliferation of the technology, etc.

That would be the equivalent of a "Sputnik moment" in today's world.

Friday, December 03, 2010

Apollo 8 Solo

In 1927 Charles Lindbergh flew non-stop from Long Island to Paris. He was catapulted to instant fame by doing so and won the Orteig Prize. He didn't have a co-pilot. He didn't have an army of engineers monitoring his plane or a flight surgeon monitoring his heart rate, it was just him and his trusty single-engine monoplane, the Spirit of St. Louis. His achievement is heralded today as kick-starting the commercial aviation industry and opening up the skies to the everyman.

But what of space? Could a modern Lindbergh fly an impossible journey and change the way we look at spaceflight forever? I think it can be done, and for cheaper than you might imagine.

In 1968 the first humans left the vicinity of Earth, flew 6 days and nearly a million miles to the Moon and back. Their mission not only was the first, it also proved the feasibility of the missions to follow. Apollo 8 would have been much easier to achieve had they only wanted to swing-by the Moon, and still a significant achievement. Instead, they entered lunar orbit, circling it 10 times before returning home.

If the flight is to be attempted today, the cheapest available launcher is the Falcon 9 from SpaceX. It can put 10,450kg into LEO. The Dragon capsule is also available - they say the crew configuration is not much different from the cargo configuration - and after removing the 310kg Common Berthing Mechanism, and another 60kg of miscellaneous mass savings, a dry mass of 1926kg is achievable.

For a single crew member, assumed to be less than 90kg, the consumables requirements for one week are: 11.839kg cabin air and pressurization, 25.83kg oxygen candles, 52.71kg LiHo CO2 scrubbers, 45kg food and water. Adding this to the dry mass gives a final mass to run the rocket equation on: 2152kg.

The delta-v required to leave Earth orbit and head towards the Moon is a whopping 3107m/s. Entering low Lunar orbit requires another 837m/s, and returning home requires another 837m/s. So we need a grand total of 4781m/s.

All the propulsive maneuvers are achieved using the Draco thrusters on the Dragon capsule, which I estimate to have a specific impulse of 309 seconds. dv = 9.8 * 309 * ln(10450 / 2152) gives us an uncomfortable 4m/s of margin. :) [edit: it occurs to me that the Dragon dry mass already includes a life support system, and a 78.54kg reduction in mass has a massive effect on delta-v. So this is more like 115m/s of margin, which should make anyone happy.]

In order to win the Orteig, Lindbergh had the Spirit built custom for his needs. Benjamin Mahoney is said to have built it for cost. Perhaps Elon Musk could be similarly persuaded, but at current prices it'll cost around $130M.

Sunday, November 28, 2010

I Guess "It's Not Junk" Is Just Too Visionary

Last week I attended a different kind of space conference. It was populated with very intelligent people who are active in doing "real" space, working payloads to get them accepted to fly on government vehicles - often up to the International Space Station - or as free flying satellites. I recorded 17 videos of the event, which I found enthralling, but I'm weird like that.

The best talk (in my opinion) was given by Dr Alice Gorman of Flinders University (Australia) about achieving an international agreement on Space Heritage. The presentation was aimed at preserving historic sites related to human spaceflight so that future generations have some physical connection with the past. This is something we do well in Australia, with "heritage listing" enforced by law. Of course, there's not that many sites that one might consider space heritage in Australia, a few radio telescopes that were used during Apollo - one that has already been heritage listed - but that's about it. The presentation went on to suggest that objects in orbit and on the surface of the Moon deserve as much respect as objects on the ground and the international agreement being sought was on how to define a "heritage site" that is off the Earth.

After the talk, some rather pointed questions were asked, and some rather pointed answers were given, then we broke for coffee. Over biscuits I stuck my head into a conversation with a PhD from Australia, another PhD from Europe and the head of a Japanese space company - his major objection was the use of the words "common heritage of all mankind" in the discussion of space heritage and all of a sudden I was feeling at home.. I expected to hear the old arguments about the United Nations Convention on the Law of the Sea, and the International Seabed Authority.. and I wasn't disappointed. What soon followed was some discussion about the private ownership of celestial bodies and yadda, yadda, yadda, you've heard all this before right?

In a way, it's nice to know that the "smart kids" are having the same conversations as the rest of us.. in a way. An argument which hasn't completely entered the standard model just yet is the suggestion that recycling satellites, spent propulsive stages and other sorts of "space junk" may be a critical part of a future space-faring civilization. No doubt, my presentation of the argument was probably a little rough, but I was surprised to lose just about everyone after the first breath. The fellow Australian was the first to break the silence suggesting that "it's going quite fast you know" as if I had just suggested the use of warp drive to catch the attention of a passing Vulcan spaceship.

Perhaps I shouldn't have labored the point, but I couldn't help myself. I started talking about the delta-v requirements of deorbiting GEO junk vs placing it into a super-synchronous graveyard orbit.. their eyes glazed over. Really? I'd just listened to four hours of ISS payload integration, the difficulties of sterilizing seeds for export, space weather detection, etc, and a little orbital mechanics is too boring?

This isn't the first time I've heard people scoff at the notion of recycling already on-orbit assets. At the New Space conference back in July a number of people said they had switched off when one of the panels started talking about it, as "they clearly don't understand orbital mechanics". It's frustrating. I don't claim to be an expert on the subject, but having actually done sufficient study (and written code) to calculate trans-lunar injection and other maneuvers, predict the trajectories of asteroids, and even change them to be more favorable for human missions, I really can't see what's so wrong with the idea of recycling valuable space assets.

If you're living in a space colony in GEO, it seems obvious that you would take whatever mass you could get for free, especially if it is highly refined solar panels and other materials. If you're living at one of the Lagrangian points you'd have to have vehicles capable of 4 km/s of delta-v and a steady supply of propellant or the means to produce it from water stocks, why wouldn't you go scavenging in the graveyard orbits for tanks and rocket nozzles to keep those vehicles operational without paying for expensive replacement parts from Earth?

Although I appreciate and respect the practicalities and even the horse trading of real space, I don't think we need to close our minds to future possibilities, as the decisions we make today, with good intentions or bad, will make that future.

Monday, November 15, 2010

The Space Industry

Here's a great video by Bob Stover, Tim Walters and Todd Halvorson.. one of the best I've seen.

Thursday, October 07, 2010

Thoughts on a SpaceX Lunar Architecture

It's no secret that the SpaceX Dragon capsule has a very impressive heat shield believed to be capable of direct lunar return. Official statements from SpaceX that they intend to add deployable landing gear and leverage the thrusters in order to land on land in the future prompts an obvious suggestion: if it can land on Earth, could it land on the Moon too?

The Dragon capsule has thus far been launched on the Falcon 9 booster, and although that booster is able to put 2473kg into lunar transfer orbit, after using the Draco thusters on the Dragon to enter low lunar orbit the total mass would be under 1876kg.. this seems a bit light for a crewed configuration, especially when you consider that only 1422kg of it could be returned to Earth. And that's just lunar orbit.

We need a bigger rocket, and the official SpaceX plan right now is called the Falcon 9 Heavy. One should not be confused by the name, the F9H is not "heavy lift" in the sense often used by space advocates and policy makers - who should more correctly be using the term super heavy lift. So how heavy is the F9H? Comparison is usually done in terms of lift to LEO, but for our purposes lift to LTO is more interesting at 10622kg. A slight improvement on the Delta IV Heavy at 9984kg.

Now we can imagine a Dragon-lander flying direct from lunar transfer orbit to the surface, it would have a mass of 3766kg when it landed which is quite respectable. For a cargo flight this is fine, delivering 2737kg of payload, but it's unlikely the vehicle would have enough fuel left to attempt an ascent.

Having determined that a single stage direct descent vehicle is unlikely, we're now forced to choose a mission mode. The size of the launch vehicle has already dictated that LEO should be bypassed, so our choice comes down to lunar-orbit rendezvous (the mode used by Apollo) or lunar-surface rendezvous, aka, refueling on the surface. So much has been said about LOR already, so let's run the numbers for LSR.

Having landed a crewed Dragon-lander on the surface, and assuming no fuel is left, we would require 6014kg of propellant to return to Earth. This is not too bad, at 3 fuel landings, but we can do better. If we can carry just 540kg of fuel in reserve we can eliminate the third fuel landing. Another alternative is to throw 338kg of payload out.

Of the 2737kg payload delivered, we have to determine how much is needed for the crew and their supplies, and how much can be fuel. The pressurized volume of the Dragon is 10m^3 requiring 11.839kg of air to fill. Without an airlock we may wish to cycle that a few times, so let's say 118kg total. Next we need a one week supply of oxygen candles at 25.83kg per person, and LiOH to scrub the CO2 at 52.71kg per person. Finally there's food and water at 45kg per person. For a total of 488kg for a crew of three. Too easy! This leaves 1708kg for spacesuits and equipment.

Once on the surface, the crew would vent the chamber, get out and refill the fuel tanks. Having gravity, transferring the propellant is well understood. Return to Earth would be direct, with no need to enter lunar orbit or perform a rendezvous. As no parts fall off the Dragon-lander on the way it could be fully reusable, providing a stepping stone to in-situ produced propellants.

I estimate a Falcon 9 Heavy / Dragon-lander cargo configuration would cost around $40k/kg to the lunar surface. With the two fuel emplacement flights, this makes crew transport something like $130M/seat for crews of 3, but you could conceivably get that down to $55M/seat if you were delivering 7 at a time - most likely to some kind of base as they would have reduced volume for equipment.

Most of my calculations were done with this rocket equation calculator and I used an inert mass fraction of 0.15 for the lander.

Saturday, October 02, 2010

Revolutionary Thinking in Nuclear Rockets

A few months ago I started talking to Jim Dewar about his latest book, which I reviewed in August. My suggestion to him was that he needs to write a better introduction that assumes the technical knowledge of rocketry but not the nuclear industry. He took on the task and recruited a number of people to serve as reviewers, myself included. So far, it hasn't been published anywhere, but he's given me a copy and invited me to publish it here.

To avoid confusion, I've put it on my website:

A Technical and Economic Introduction to Nuclear Rockets

It's long but divided into sections, and I think Dewar has done a great job, so check it out.

Jim tells me he would like to hear feedback.

Friday, October 01, 2010

Affordable Deep Space Exploration

For too long the aspirations of NASA have not matched the budget allocated. Building the International Space Station has been a decade long effort, now finally reaching completion, and until just recently the plan was to splash it into the ocean before moving on to "the next thing". For a while, that was a return of humans to the Moon, but the recognition that the necessary budget would not be forthcoming has pushed that goal so far into the future that it doesn't even make much sense to talk about it anymore.

Today, the focus is on making a new heavy lift vehicle, finishing a big heavy capsule to go on it, and considering the possible missions that could be done with that hardware should it ever be finished. At the same time, technology development and commercialization of ISS resupply promise to free up some existing budget dollars to pay for the lunar landers and prepare for the next next thing: Mars.

This has prompted many to ask: what if we didn't need heavy lift? What if NASA could do deep space exploration without it? I know what you're thinking, propellant depots, right? Not this time. I've talked about propellant depots, enough, let's talk about something completely different.

In this paper David L. Akin has made the case for ISS crew rotation, two lunar missions per year, and a "flexible path" mission every second year, using only storable propellant stages and the existing Delta IV Heavy. He's done the sums and says the whole thing could be done for less than the current NASA budget for human spaceflight.

Here's how it works. First off, the Delta IV Heavy (or some similar launcher should it become available) needs to be human rated. That's expected to take $2B and 5 years. A five ton crew module is developed - it's about 70% larger than the Soyuz - for $2.5B. With just these two components ISS crews can be rotated and this will likely happen anyway under the commercial crew development program. One thing to keep in mind, though, is that the heat shield has to be able to do direct reentry from the Moon, something only the SpaceX Dragon and the Orion is planning at this time.

Simultaneously, an Orbital Maneuvering System is developed. This is similar to the service module on most crew spacecraft, in that it uses storable propellants and is expended after use. A common configuration is used for multiple maneuvers: lunar orbit injection, lunar descent, lunar ascent and trans-Earth insertion. A modification of the Orbital Maneuvering System is required to do the final landing on the Moon. Landing legs need to be added obviously, deep throttling and possibly restarts will need to be supported. These changes are significant enough that it deserves a new name, so Akin calls it the Terminal Landing Stage.

And that's it. The paper explains a few of the more interesting details. For example, for non-ISS missions LEO is completely bypassed, with direct lunar injection of the stages. All the rendezvous and docking happens in low lunar orbit, and by careful management of the loading of propellants stages, can be fired sequentially to generate the necessary delta-v for each maneuver - there's no need to transfer propellant from stage to stage.

Peak funding comes at the end of the development of the program (where it belongs!) and is less than $3B/year. Yes, that's right, Akin says we could have ISS crew rotation, 2 lunar missions a year and a flexible path mission every alternate year for less than what was being spent on the Shuttle program during it's peak. That's the value of leveraging existing hardware.

Read my lips: no new launch vehicles.

* Thanks to Ralph Buttigieg for sending me this very interesting paper.

Saturday, September 18, 2010

Mining The Moon: Closing The Business Case

I recently read Platinum Moon by Bill White, in just 4 days, it's just that much of a page-turner. Clark Lindsey has written an extensive review, which is mostly positive but has this little dig at the end:

A kilogram of pure platinum today sells for something like $53,000/kg. On the Moon even rich PGM ore would have have to be extensively refined to get anywhere close to that purity. A kilogram of raw ore would be worth a tiny fraction of that.

Until there are fully reusable vehicles flying frequently enough to LEO to bring costs there down to the low hundreds of dollars per kg, it's difficult to see how space mining can even begin to be viable.

My first reaction is to suggest that obviously high purity enrichment of platinum should be done on the Moon, and only "pure platinum" returned to the Earth - but I should first point out that Platinum Moon made the realistic argument that lunar platinum would be worth a lot more than market value in the form of commemorative coins and other trinkets - at least initially.

Extraction of oxygen from lunar regolith is a critical part of the plot in Platinum Moon and it's not unreasonable to expect a platinum enrichment facility to be capable of doing it as a side process. Similarly, extraction of aluminum from lunar regolith is an easy process which would also be available. Spinning that aluminum into tanks is simple manufacturing that could be done in-situ, and during lunar night the oxygen would naturally liquefy to make filling easier.

The landing vehicles in Platinum Moon use the fuel RP-1, a form of kerosene which is often approximated as dodecane in chemical formulas - this means it has 12 carbon atoms and 26 hydrogen atoms per molecule. On the Moon, carbon is about as rare as hydrogen, and the biggest deposits are in cold traps at the lunar poles. A simpler hydrocarbon, with higher performance, is methane with just 1 carbon atom and 4 hydrogen atoms. Liquid hydrogen could also be used as a fuel for a reusable lander. It seems inevitable that a complete propellant production plant - both fuel and oxidizers - would be an early infrastructure goal of an operational lunar platinum mine, but it would likely be separated from the mining and refining sites; requiring suborbital hops to refuel.

Estimating the size of a propellant production facility is difficult at this time. Current NASA estimates for a "pilot demonstration" plant to produce oxygen from lunar regolith are in the ~300kg range, producing up to 500kg/year. A similar sized plant in a cold trap could be expected to produce thousands of times as much, and would more likely be bound by the availability of tanks; which I imagine being transported from the distant platinum enrichment facility.. whether local production of tanks is more efficient depends on the flight rates.

Sticking with the "gateway" architecture presented in the book, lunar production of both fuel and oxidizer is game changing. Launching fuel for Earth departure stages from stockpiles on the lunar surface, via EML1, is cheaper than launching from Earth's deep gravity well. Storage of cryogenic propellants in the cold traps of the Moon until needed brings just-in-time delivery economics to spaceflight. This would allow the launch of larger processing plants and more sophisticated mining vehicles that can increase the production in a virtuous cycle.

If one could obtain pure platinum from the surface of the Moon, would it be profitable to return it to Earth at current market prices? I've previously shown that the SpaceX Dragon has a downmass of 3000kg at $28,330/kg, returning pure platinum from LEO at a profit of $24,670/kg. With the architecture described, cislunar transport is essentially free, but to make a profit, the initial costs of the architecture have to be amortized over every kg returned.

If the architecture costs low billions to setup then around 100,000kg needs to be returned over several years. For comparison, only 239,000kg of platinum was sold in 2006. The initial premium for lunar platinum would quickly fall to market levels, but would the market value of platinum fall significantly thereafter? I have had long arguments over whether or not platinum is an elastic market that is significantly effected by the opening of a new mine.. it's simply not clear what the demand for platinum is because the supply is so low at present, but it should be clear to see from the growing price of platinum over the years that more and more demand is out there for a very limited supply.

Saturday, September 11, 2010

Some Retrospective Space Policy

It's been a while since I said anything about space policy. This is primarily because the whole ball of wax can be summarized as, well, a big fat mess. As many of you are likely aware, I was an avid viewer of the Augustine committee when it was on, all 37+ hours of it, and still think they did a fantastic job with what they had to work with.

However, in retrospect, I think Norm Augustine hit the nail on the head when he started talking about "blue plate" options vs the alternatives that stuck within the existing NASA budget. I bet if they had to do it all over again they would have changed the balance to include more of the affordable options and less of the blue plate options.

Perhaps they could have worked out the completion dates and total prices of the various components of Constellation program under the "restricted" budget (aka, the "real" budget) including the options of splashing the ISS in 2015 and without. As Augustine himself said "ongoing programs should only be changed for compelling reasons".

From there they could have easily made the case that doing the booster and the capsule before starting work on the lander was a prudent course of action, and suggest the missions that could be done in that time.

The policy makers would have clearly gotten the message that the Flexible Path isn't an alternative to surface operations, but a prelude.

Commercial crew would not have been seen as a threat to the "government option" but as an enabler to moving budget away from routine servicing of LEO and into the exploration architecture.

And technology development could have taken its rightful place as the great hope that the exploration architecture could someday be accelerated from its plodding schedule.

But, as they say, hindsight is 20/20.

Saturday, September 04, 2010

Engineering An Asteroid Close Approach

I've been posting lately about the threat large asteroids pose to Earth, human missions to smaller asteroids, and the opportunities that will exist in the next few decades to do so. Up until this point, my analysis has been mostly for my own education and amusement, but I'd like to make a suggestion now which I haven't seen published in the literature or seriously discussed in either NASA working groups or even in the space advocacy community.

I'd like to suggest that we need not wait for an appropriate asteroid to come within range of Earth and plan human missions around just those opportunities - we can engineer a perfect close approach.

Next year, at the start of June, the asteroid 2009 BD will pass within the orbit of the Moon. Even though it is not a rare occurrence, few opportunities such as this have been identified, and realistically, no-one is going to be ready to send a human mission to an asteroid for years to come.

It seems a shame to let this close approach go to waste, with just 40m/s of tweaking, the orbit of 2009 BD could be changed to this:

(click to open the viewer)

The blue part indicates the part of the orbit which is within 20 lunar distances of Earth: over 965 days in the next 6 years. The delta-v required to change the orbit of this asteroid could be delivered by a single impulse, and the most advanced technology available to do that is to simply run into it.

Calculating how to change an asteroid's orbit has been an educational exercise which would not have been possible without the JPL Horizons system and the SPICE toolkit.

Friday, September 03, 2010

Rusty Schweickart Explains The Asteroid Threat

I don't think he's given a better lecture than this.

Wednesday, August 25, 2010

Rock Envy

With the exception of Hayabusa, all asteroid missions to-date have been to targets bigger than 1 km in "spherical radius".

DateEncounterAsteroidRadius (km)Spacecraft
1991Flyby951 Gaspra6.1Galileo
1993Flyby243 Ida15.7Galileo
1999Flyby9969 Braille~1Deep Space 1
2000Flyby2685 Masursky~8Cassini
2001Landing433 Eros8.42NEAR Shoemaker
2002Flyby5535 Annefrank2.4Stardust
25143 Itokawa0.165Hayabusa
2006Flyby132524 APL~1.1New Horizons
2008Flyby2867 Šteins~2.8Rosetta
2010Flyby21 Lutetia95.8Rosetta

This has led a number of people to express dismay that all the asteroids which have been identified for human exploration missions have significantly smaller estimated sizes.

DateAsteroidRadius (m)
20162008 HU4~5
20171991 VG~45
20192008 EA9~6
20202007 UN12~4
20251999 AO10~35
20262008 JL24~2.5
20282006 RH120~2.5
20292000 SG344~22.5

Notice that the scale has changed from km to m. Of course, exactly why these rocks are small is most probably what makes them optimal for a human mission. Their close approaches to Earth most likely would have ended long ago if they were any bigger. Collecting samples from these asteroids will help us to understand why they are not in the main asteroid belt, which is very important to know as their larger cousins threaten the Earth.

Some mission planners at NASA and elsewhere have expressed a desire to exclude any target with a radius smaller than 25m, being referred to as "mere building sized" asteroids. This reduces the targets in the table above to just two, although the last typically scrapes by due to a lack of options. Exactly why this policy is being suggested is unknown. Some speculation includes:

  • the belief that more targets will become available with greater funding directed to finding them, so it's best to downplay the available targets.
  • the difficulty of approaching a small rapidly spinning body.
  • lack of mass for sample collection.
  • lack of surface area for exploration given extended mission duration.
  • overall "spectacle".
These are all terrible reasons, and I'd hate to be accused of putting up a "strawman" to knock down, but they are the only reasons that I have read about. If you've heard more, let me know.

The first reason is just bad politics, and it's completely unnecessary. No-one can reasonably say the asteroid surveys are getting "enough" money, but they're certainly getting some, and they're getting valuable priority time on telescopes, both optical and radio. Hopefully this is just an ugly rumor.

Approaching a spinning body is something astronauts have done before. Dale A. Gardner and others used the Manned Maneuvering Unit (aka, the astronaut jetpack) to match rotation with satellites in LEO to return them to Earth on the Space Shuttle. With this in mind, it would seem engineering and astronaut experience is more applicable to small spinning bodies than it is to large ones.

The lack of mass argument should be immediately recognized as a failure of imagination. Referring to these asteroids as "small" in the first place is suggestive of this. The smallest asteroid on the list above has an spherical radius of ~2.5m, about the size of this:

The biggest asteroid on the list above, 1991 VG, is about half the size of this:

And unlike these reference objects, asteroids are solid with few to no internal voids. So there's plenty of mass, and when it comes to surface area and mission duration, I actually think making the case for short mission duration makes a lot of sense, and besides, suggesting that just a few days is too much time to spend exploring one of those London bus sized objects is just silly. A meteorite of such a size would be investigated for years.

In regards to spectacle, I recommend watching the video I linked to above of Dale A. Gardner catching that satellite. Even with a London bus sized object you're in for one hell of a show.

Tuesday, August 24, 2010

Early vs Late Human Missions To Deep Space

Anyone who has enjoyed my recreational attempts at designing a human mission to a near-Earth asteroid should check out the newly released mission to an asteroid by a team at Lockheed Martin*. The report ends with these important words:

The Plymouth Rock study shows that the first visits to asteroids can be easier and earlier than we have previously thought. The United States does not need to wait for more advanced technologies or develop expensive dedicated deep space vehicles. We can explore the asteroids within a decade, using spacecraft already being developed and tested.

This is a reasonable statement which I agree with. As far back as Apollo the question of "are we ready?" has been asked, and despite the success of Apollo it is still being asked. I have tried to make the argument that a Dragon capsule would be sufficient for a bare-bones mission to an asteroid, assuming some modifications to life support systems, dual use of propellant and supplies as radiation shielding and a whole lot of vigorous hand-waving. This Lockheed Martin study makes the same argument, obviously using their own hardware, and with a level of detail and rigorous breadth of study that puts my amateur efforts to shame. If we don't go we'll never be ready.

That said, they make some statements that go a little further than I have previously, or probably would. For example, consider this statement, which at first blush seems to be making a purely technical argument, but is certainly saying something a little more rhetorical.

As a consequence of their orbital similarity to Earth, there are only a few opportunities per decade to visit known asteroids. The number of opportunities will likely increase as more asteroids are discovered, but for now the limited number of opportunities has profound implications for asteroid mission planning.

It drives the timing of a human asteroid program since it may not make sense to plan a program which provides an initial operational capability during a period such as 2021-2024 when there are no known mission opportunities.

The small number of opportunities means that it may not make sense to design a spacecraft system dedicated to asteroid missions. Rather, asteroid missions would be performed occasionally by spacecraft that are also designed to perform other missions, such as going to the Moon or other deep space destinations.

While I can't find fault with the logic, I think I see a deeper message here. The second paragraph, while representative of a simple fact that I too was surprised to discover in my Prospector's Skymap efforts, is unnecessarily vague about what, precisely, it is recommending. I don't think it is saying NASA should not bother to field an asteroid mission until 2025, as is the President's current plan. This paragraph meant to hint that NASA should hurry up, perhaps even aim for the (2008 HU4) approach in 2016, the year the Senate's proscribed heavy lift vehicle is supposed to come online, lest the schedule slip and slip into the 4 year "asteroid gap".

The third paragraph above, however, is an outright stab at supporters of technology development, and is the "take home" message - going to the near-Earth asteroids is not a technology development program.

Bob Zubrin of the Mars Society recently made this argument in a little more alarmist way - it would be a terrible thing if VASIMR and propellant depots became "gateway technologies". The fear is that missions to deep space targets, Mars obviously being the intention, will be delayed until these technologies come online. "We can't go to Mars because we don't have VASIMR yet" they'll say. Unfortunately people are saying that, and the Plymouth Rock study comprehensively shows why it is not the case, at least for 6 month asteroid missions.

However, buried in the technical detail of this study is the answer why NASA is not yet ready to go all the way to Mars with existing technology and vehicles currently under development. The delta-v requirements are bigger for Mars missions than near-Earth asteroid missions, this is true, but the technology development required for a bigger Earth departure stage is minimal - with or without heavy lift. To see the real need for technology development we have to turn to page 13 of the report, and the section titled "Mission Duration".

Unlike Apollo or the Space Shuttle, the Orion spacecraft includes design features which support long missions, such as solar arrays rather than fuel cells for power, and regenerative amine beds rather than single-use lithium hydroxide canisters to remove CO2. Orion is designed to support four astronauts for 18 days going to and from the Moon, with a 180 day unoccupied period in lunar orbit while the astronauts are at the lunar outpost, plus 30 days of contingency loiter capability for a mission extension. This built-in long duration capability is a critical enabler for an asteroid mission.

Orion hardware is already designed for the same mission duration needed for an asteroid mission, addressing issues such as reliability, leak rates, hardware radiation tolerance, and micrometeroid protection. Micrometeroid and orbital debris (MMOD) protection has turned out to be one of the most challenging requirements to meet for long duration missions, since longer missions have higher cumulative probability of impacts.

The duration of a Mars mission is more like 32 months - 8 months there, 500 days on the surface (or, for a Phobos/Deimos mission, in orbit!), and 8 months back, and the crew size is almost certainly going to be bigger than an asteroid mission. The next section on "Life Support" addresses this.

Despite Orion's long duration capability, a five to seven month mission requires more food, water, oxygen, and nitrogen than Orion is presently designed for. Reducing the crew size from four to two astronauts and pairing up two spacecraft quadruples the number of days the astronauts can be supported, to approximately 80 days. A further factor of 2 to 2.5 increase in consumables is required for a 6 month class mission.

And goes on to state that although the Orion's open-loop life support system is adequate and the right choice for 6 month duration missions, it acknowledges that it is on the knife's edge and a closed-loop life support system is inevitably going to be necessary for the much longer duration missions.

Finally, no discussion of deep-space human missions is complete without addressing the radiation exposure problem. Section 10 on page 32 takes the problem head on and contains a great summary of the analysis Lockheed Martin took in the placement of components in the Orion spacecraft to provide good coverage for radiation shielding without adding additional mass. It also advocates an on-need strategy for deployment of supplies as additional shielding in the event of a solar storm. Flying asteroid missions is suggested as an important precursor to a Mars mission, and on this criteria alone that's a good argument.

In short, I think there's a false choice here. Although I agree with the basic statement that NASA doesn't need to design a dedicated vehicle now, and doesn't need fundamentally new technologies to reach the more favorable near-Earth asteroids in early missions, a sustained technology program to improve capability will widen the choice of near-Earth asteroids that are favorable and beat the path to Mars.

* If it's not already up there it should be soon. Thanks to Josh Hopkins for an advance copy of the report.

Thursday, August 19, 2010

Smacking Asteroids For Resources

Video by Eric Brueton

Summer studies of space settlements by Gerard O'Neill and NASA in the 70s and again in the early 90s both determined that significant amounts of mass is required for passive radiation shielding. Although structurally, most designs call for refined steel, it has been suggested that mass for the shielding could just be raw lunar regolith, left-over slag from future on-orbit industrial processing, or obtained from the asteroids. The asteroids are seen as preferable as, in terms of delta-v, they are most easily available. The typical argument is that a long duration mission to rendezvous with a near-Earth asteroid or comet (collectively, near earth objects, or NEOs) could skip a lot of launches from deep gravity wells, either digging into the NEO or
dismantling and processing it to make a nearby structure, or both.

The wrinkle, however, is in that "long duration" part. In terms of delta-v, there are NEOs which are easier to hit than the Moon, but all currently known NEOs require months to year long travel times. This rules out manned expeditions for the time being, as long duration human spaceflight beyond the Van Allen radiation belt requires significantly more shielding than Apollo style short term missions.
To break the stalemate, many have suggested the use of autonomous or teleoperated spacecraft to develop a soon-to-be Earth Hill-sphere crossing NEO into a life sustaining capable radiation bunker. As many appropriately sized NEOs cross within 2 or 3 lunar distances (LD) of the Earth, it's clear that only a short term mission is required to "jump on board" and bunker down. With adequate prediction of the NEOs orbit, resupply could be successfully staged ahead of time on slower, more energy efficient, trajectories.

When considering the risk involved in such an adventure, and the market opportunities of any such settlement, Earth or Moon orbiting alternatives start to sound a lot more attractive. So let's consider an orbital habitat that is closer to home.

To get mass from the surface of the Moon into an appropriate orbit, it is suggested, one can use a solar powered mass driver. The immense cost of building a lunar mass driver is quickly amortized over every kg of steel and regolith launched and the sheer quantities of mass required - 150,000 kg for the torus designs, 42,300,000 kg for the cylindrical designs, and that's just the structural mass (steel), for shielding it's 9.9 and 23.3 million tons of regolith - mass drivers beat rockets hands down. But building a mass driver of that scale, and all the infrastructure required to supply it with regolith and power is another roadblock. When people talk about it, I suggest that by the time those quantities of regolith are available from lunar industry there will be tract housing available there anyway.

Do we have to rule out NEOs for shielding of Earth or Moon orbiting space settlements?

Recently, the asteroid 2010 AL30 flew by Earth, closer than the Moon's orbit, traveling at a relative velocity of 9855 m/s. Approximately 10-15 meters in size, it is estimated to be one of nearly 2 million such objects in near-Earth space. On average, an asteroid of this size passes within a lunar distance once a week. Asteroids come in a variety of different types and densities, but on the lower end of the spectrum (2.6g/cm^3), 2010 AL30 would have a mass of at least 2,600,000 kg.

Capturing small asteroids like this in Earth or, better yet, the Moon's gravity is a difficult proposition. For the altitude that 2010 AL30 was traveling at, it would have to lose 8139 m/s of velocity to enter a circular orbit. Suppose we were to send a spacecraft to hit it head-on. The most recent example of an impactor in near-Earth space was the LCROSS mission, impacting a crater at the lunar south pole, it delivered a 2305 kg Centaur stage at 2700 m/s. If we take that velocity as representative, we would require our spacecraft to have a mass of 7,929,037 kg.. unsurprisingly, we require a bigger rock to slow down the smaller rock.

A better question might be, how big of an asteroid can we capture by head-on impact with a Centaur stage? Again using 2700 m/s as a reference, you'll find the asteroid can be no more than 756 kg in mass, which converts to an asteroid 66 cm on a side using the same density as before.

LCROSS was launched as a secondary payload on an Atlas V 401. The Centaur provided the entire burn, although there was a small amount of gravity assist provided by the Moon. The shepherding spacecraft followed the Centaur into Cabeus crater as the Moon is quite a hard target to miss at that range, but I can imagine a similar spacecraft avoiding the brunt of the impact of intercepting an asteroid. If the
spacecraft is equipped with a solar powered propulsion system, be it Hall-effect thruster or an electrostatic ion thruster (as used on the Deep Space 1 spacecraft that did a flyby of a comet) or even a mass driver, it is conceivable it could rendezvous with the various fragments, assemble them into a whole and shepherd them to another intercept.

As the shepherded mass grows, larger asteroids can be intercepted.

Such a spacecraft could also find purpose cleaning up more traditional
orbital debris.

Note: I wrote this a while ago, but forgot to post it, I'm not terribly sure of the math anymore. It seems about right, but I know now there are lower delta-v asteroids that wiz by the Earth within a lunar distance. But it has some good references.

Prospector's Skymap

There have been over 535,000 asteroids discovered to date and they're all different. Some 7,121 of them are known to cross the orbit of the Earth and so are referred to as the near-Earth asteroids. If you're interested in flying a robotic mission to an asteroid, you need some idea of how much delta-v your spacecraft is going to need. I've written on this before. However, if you're interested in flying humans to an asteroid, you also need to know how long the round trip is likely to be.

To answer this, one needs to know both how far away the asteroid is at closest approach to Earth, and for how many days it will remain that close. To the interested public, finding this information out using the available NASA tools is a slow process, and understanding what you've discovered is difficult without good visualization.

click for interactive skymap

Introducing the Prospector's Skymap, a tool for visualizing Earth-centric plots of asteroid trajectories over the next 20 years, in 3d. Included is ~500 asteroids that have low delta-v rendezvous. The blue part of the trajectory is "within range" of an average human mission duration of 6 months, which can be configured by setting the maximum lunar distance in the range box. See the online help.

In addition to visualization I've been doing some offline data processing. Probably the most interesting result is a list of targets that have low delta-v rendezvous requirements, close approach within 20 lunar distances, sorted by year, for the next 20 years. Here's the csv file.

* under 20 LD
AsteroidClose approachDistance (LD)#days*
(2009 SH2)2010 SEP 307.12333537
(2005 UN)2010 OCT 2411.01831426
(2006 JY26)2010 NOV 0414.30419131
(2010 JW34)2010 NOV 2119.35112616
(2008 KT)2010 NOV 235.56063661
(2009 BS5)2011 JAN 113.39771261
(2009 UK20)2011 MAY 028.56922830
(2009 BD)2011 JUN 020.900437127
(2007 RQ17)2011 JUL 2213.23054356
(2007 DD)2011 JUL 239.29576344
(2009 TM8)2011 OCT 171.10182922
(2009 WN6)2011 NOV 056.32427124
(2008 UR)2011 NOV 1317.55155519
(2008 EL68)2012 JAN 058.29607746
(2008 EJ85)2012 MAR 069.22909625
(2010 FR9)2012 MAR 2218.4059868
(2001 CQ36)2012 MAY 3010.00337228
(2009 BW2)2012 AUG 0913.12194325
(2010 JK1)2012 NOV 259.30796028
(2008 ON10)2013 AUG 1619.01999813
(2007 CN26)2013 AUG 2811.86088421
(2008 PW4)2013 AUG 3013.84872319
(2005 TG50)2013 NOV 1215.92644738
(2001 AV43)2013 NOV 182.889049103
(2004 FJ31)2014 APR 1011.56957118
(2007 HB15)2014 APR 287.40614228
(2010 KV7)2014 AUG 1517.87178217
(2006 WZ184)2014 NOV 0919.8203364
(2010 GH7)2015 MAR 207.38268635
(2006 HX30)2015 MAY 1611.01162832
(2007 BB)2016 JAN 1611.16409139
(1994 UG)2016 MAR 2517.27587312
(2008 HU4)2016 APR 164.882098136
(2009 DL46)2016 MAY 245.95465826
(2005 OH3)2016 AUG 046.46712048
(2007 RU19)2016 AUG 1113.42974322
(2004 KG17)2017 MAY 1610.74741430
(2006 SR131)2017 SEP 2712.11301815
(2001 WH49)2017 OCT 2615.11413823
(2006 XY)2017 DEC 206.14696635
(2008 WM61)2017 DEC 023.59290338
(1991 VG)2018 FEB 1118.36795347
(2010 AG3)2018 MAR 0415.75370025
(1999 FN19)2018 MAY 079.64622628
(2008 HS3)2019 MAY 1014.44907123
(2001 KW18)2019 MAY 2117.54578318
(2006 QV89)2019 SEP 2114.49611228
(2008 UD95)2019 OCT 0816.75618826
(2008 EA9)2019 NOV 2311.24244671
(2007 UN12)2020 JUL 0416.82181637
(2009 OS5)2020 JUL 1417.84387832
(2001 GP2)2020 OCT 033.12459267
(2008 TY9)2020 OCT 1017.51670915
(2007 TA23)2020 OCT 1216.49788921
(2008 GM2)2020 OCT 2515.82038030
(2005 AZ28)2020 NOV 1013.80427926
(1993 BX3)2021 JAN 1718.42055419
(2004 RW2)2021 SEP 0515.73470515
(1982 DB)2021 DEC 1110.23523523
(2009 BF58)2022 JAN 256.08112523
(2008 JP24)2022 JAN 2619.2299329
(2007 UY1)2022 FEB 0813.88990819
(2009 FX4)2022 AUG 059.98926435
(2003 YS70)2022 DEC 1310.01710938
(2004 XD51)2022 DEC 2711.59694325
(2006 EW)2023 FEB 1214.57483420
(2004 OW10)2023 MAR 2512.79139124
(2009 QR)2023 AUG 212.68601633
(2001 QQ142)2023 DEC 0614.37718919
(2005 FG)2024 APR 0715.85655919
(2009 FK)2024 MAY 2117.90962013
(1998 KY26)2024 JUN 0111.98590627
(2005 ND63)2024 JUL 1414.22454014
(2002 NV16)2024 OCT 2411.75661158
(2006 HU50)2025 MAY 029.26089223
(2008 ST)2025 MAY 2014.25303651
(2008 DG5)2025 JUN 069.08584125
(2008 CM74)2025 JUN 254.86452343
(1999 SF10)2025 DEC 187.27896964
(1999 AO10)2026 FEB 1310.43336156
(2000 SZ162)2026 OCT 1614.38559324
(2006 SF281)2026 OCT 186.03932842
(2009 SH1)2026 SEP 1710.78361319
(2009 HC)2027 APR 106.02300480
(2008 VC)2027 NOV 025.11435633
(2004 AD)2028 JAN 0618.2709469
(2005 ER95)2028 MAR 2313.02533046
(2009 FQ32)2028 MAR 313.80321238
(2009 WC106)2028 MAY 0216.25007621
(2000 SG344)2028 MAY 077.636435212
(2009 WR52)2028 MAY 202.46465131
(2006 RH120)2028 AUG 0811.213795188
(2008 EY84)2028 SEP 0911.88311431
(2007 DC)2028 NOV 055.71717550
(2006 SU49)2029 JAN 283.18766637
(2006 UQ216)2029 FEB 1913.49571745
(2009 CV)2029 MAR 038.61242277
(2007 WA)2029 MAY 136.03633634
(2000 SL10)2029 MAY 166.76024021
(2010 NN)2029 JUN 1412.25846121
(2009 DC12)2029 JUL 0618.68069815
(2008 TN9)2029 SEP 2918.17875710
(2006 HE2)2029 SEP 302.02912734
(2008 UA202)2029 OCT 205.29932660

From this data you can determine which target is most favorable in any given year. If you're after really low delta-v requirements, as well as short transit times, then the list gets smaller.

AsteroidClose approachDistance (LD)#days*delta-v
(2010 JW34)2010 NOV 2119.351126164.839129
(2008 KT)2010 NOV 235.560636615.800001
(2009 BD)2011 JUN 020.9004371274.793479
(2005 TG50)2013 NOV 1215.926447386.153250
(2008 HU4)2016 APR 164.8820981364.577387
(1991 VG)2018 FEB 1118.367953475.238135
(2008 EA9)2019 NOV 2311.242446715.392948
(2007 UN12)2020 JUL 0416.821816376.080512
(2009 OS5)2020 JUL 1417.843878325.764455
(2001 GP2)2020 OCT 033.124592675.595356
(2008 ST)2025 MAY 2014.253036515.637181
(1999 AO10)2026 FEB 1310.433361565.858708
(2005 ER95)2028 MAR 2313.025330465.814350
(2000 SG344)2028 MAY 077.6364352125.197308
(2006 RH120)2028 AUG 0811.2137951883.385696
(2006 UQ216)2029 FEB 1913.495717456.081869
(2008 UA202)2029 OCT 205.299326605.953219

And the list of known near-Earth asteroids keeps growing.

Saturday, August 14, 2010

Mission To Asteroid Using SpaceX Hardware - NASA's Target

As a target of study, NASA has identified the asteroid 1999AO10 as the 2025 destination for human exploration. We've heard that NASA plans to build a giant heavy lift vehicle to make the trip, but is it really necessary?

I previously described a human asteroid mission, but I assumed the logical choice of asteroid with the lowest known delta-v (and included analysis for the second lowest too), but for some reason this isn't as interesting to NASA, so let's consider how one might do the trip to their preferred target, using existing SpaceX hardware.

The reference numbers are: Earth departure stage 3291m/s, and storable propellant 3939m/s of total delta-v. We could improve this by carefully measuring the boiloff of LOX in Falcon 9 upper stages and analyzing the required insulation to do the arrival rendezvous using non-storable propellants, but I don't really have that information handy, so I'll just go with the storables.

Like last time, we'll use the Dragon spacecraft as our crew vehicle. Unlike last time we'll actually have a look at the thrusters, it uses 18 Draco thrusters which are similar to the Aerojet 445 in performance with 309s of ISP. The Dragon is carried to orbit on a Falcon 9 with 3000kg of payload in the "trunk", 3000kg of payload pressurized (that includes the astronauts), and 1290kg of storable propellant, giving a dry mass of around 1710kg. To provide 4710kg (dry mass + pressurized payload) with a total of 3939m/s of delta-v requires a gross mass of 19544kg, which means the external tank will be 13544kg when filled.

The Earth departure stage will be the Falcon 9 upper stage, with the Merlin 1C vacuum performance of 342s ISP. The total initial mass in low Earth orbit is therefore 56710kg. Meaning 37166kg of that is LOX/RP-1. With a mixture ratio of 2.56, that means 10440kg of RP-1 and 26726kg of LOX. (btw, if we had a Raptor stage the IMLEO would be 46328kg, and presumably mass-to-LEO of each flight would be bigger, but the boil-off analysis would be completely different, as you'll see).

Ok, so we have all the numbers we need, now we just have to decide what order to launch it all in to reduce the total mission risk. Storable propellants are called that because they can sit without being used for long periods of time and be ready to go when needed. Also, they don't suffer from boil-off when stored on-orbit, or at least not so much as we need to care in this kind of analysis when compared to cryogenics like LOX. As such, I'm of the opinion that the best strategy is to launch the storable propellants in the external tank, and the RP-1, first.

This is a total of 23984kg and includes some of the mass for the tanks to contain the propellants. So we're looking at two Falcon-9 flights with a shortfall of 3084kg. If an initial parking orbit is chosen well, these first two flights can be spread out over as long a time period as desired, limited only by orbital decay.

We now need to deliver 26726kg of LOX, along with the remaining 3084kg of non-cryogenic propellants, for a total of 29810kg. These three Falcon-9 flights will deliver 1540kg of excess LOX which should account for boil-off if the flights are launched without delays. At 0.1% per day boiloff, the launch campaign must be complete in 50 days. But we have an ace up our sleeve.

The final flight of the launch campaign is the manned Dragon. It will be carrying the crew, with all their provisions, on-board propellant, some of which will be used for rendezvous and orbital assembly activities, and 3000kg of LOX in the trunk. Carrying cryogenics in the trunk may seem risky, but it has such an awesome payoff on cryogenic boil-off that it's worth it.

As described in the NASA concept, the mission departs the low Earth parking orbit, and arrives at the asteroid 3.5 months later. The astronauts stay on the rock for 2 weeks, then return to Earth a month later. The entire trip is 5 months. Radiation exposure is similar to a year long stay on the ISS, about half of an astronaut's lifetime limit.

Because of the suboptimal choice of destination, the new mission has five tanking flights at $56M each, and the manned Dragon flight which I estimate at $150M, for a grand total of $430M. This is about 100 times less than what I expect NASA will spend trying to do the same thing.