Changing the Risk Paradigm

As we continue to think about the implications of Planetary Resources and its plans for asteroid mining, I was interested to see exoplanet hunter Sara Seager (MIT) make a rousing case for the company’s ideas and for commercial space ventures in general. Seager, who works with Planetary Resources as a science advisor, tells The Atlantic‘s Ross Andersen in a May 14 interview that one reason for optimism is the progress we’re making with robotics. Mining operations currently being managed beneath the seas are being handled by robotics. Couple that with our ability to get to and orbit an asteroid as well as to scoop up surface materials and you have all the ingredients for a workable mining operation in a low-gravity environment.

Seager explains that asteroids are attractive mining targets because unlike fully formed planets like the Earth, their heavier elements have not largely sunk inside through planetary differentiation in the early days of the planet’s existence. Asteroids are either fragments of bigger objects or building blocks that were never fully formed, meaning that high-value platinum metals should be readily accessible on the right kind of object. Their low gravity and, in the case of NEA’s, proximity mean that they are attractive targets from which to return materials.

Image: All the technologies may be falling into place for asteroid mining. But is a move to commercial operations a story with even bigger implications? Credit: NASA.

Planetary Resources is intriguing not only because of potential mining returns but because it involves a different model of detail and risk than would be acceptable in a government-created program. Here Seager invokes the Mars Science Laboratory, a $2 billion mission that will land a rover on Mars this summer. MSL became a huge operation because it is a general science mission that demands the 10 different science instruments aboard the craft, making it a heavier rover and demanding a landing system far more complicated than the air-bag methods we’ve used successfully in our last several Mars landings. A private firm, on the other hand, can focus tightly on a specialized goal rather than aiming for a multi-purpose mission from the start.

But there’s a bigger difference, adds Seager:

In the private spaceflight world there are focused goals with profit and new capability as priorities. At NASA the motivation for space missions is different. In addition to big and general science goals, the main goal appears to be not to fail. In this sort of culture the bigger space companies and academia are taught that it, the mission, has to work.

Even the large space companies like Lockheed and Northrop Grumman can become trapped inside this paradigm, for they are not creating long-term, sustainable businesses with the work they perform for the government. Instead, they are operating within a culture riddled with bureaucracy and plagued with high costs. Seager likes the look of young and lean space companies:

…at small space companies, things can fail. Risk is part of developing new technology. Also, for the big space companies the whole competition is just getting the government contract. The competition is not about making something awesomely cool, first to market, and making a ton of money out of it. So in my opinion, the motivation factor and the risk aversion factor make it basically impossible for these larger companies to shift gears. The question that is on the minds of a lot of people is “Can America continue to be competitive in space with the current paradigm?” And the answer is no. That is the reason we have seen the rise of the commercial space flight world—they’re trying to start a new paradigm for spaceflight with a sustainable business that doesn’t just rely on government contracts.

The Seager interview is well worth your time as she discusses not only the Planetary Resources business model but the implications involved in getting a new generation of small and inexpensive technology into space. It’s no surprise that the Arkyd series of spacecraft should catch her eye, since Seager is also involved in a project called ExoplanetSat, a prototype ‘nanosatellite’ that can monitor a single, Sun-like star for two years. This gets seriously interesting when you start talking about producing a large number of such satellites, because while we have the Kepler mission monitoring planetary transits in a fixed field, we have no mission in the works to hunt for planets around the nearest and brightest stars.

So instead of a single space telescope fixated on tens of thousands of stars, most of them distant from the Sun, we invert the model to produce a fleet of tiny telescopes with a single target each, with the detailed properties of each star under observation programmed into each instrument. You can see why Planetary Resources’ plan to launch a large number of small space telescopes would appeal to Seager. The Arkyd series (based on the company’s original name) would allow small institutions to buy a space telescope for a price ranging from $1-10 million, opening space-based observations to universities or even wealthy individuals.

Image: ExoPlanetSat is just 10 centimeters tall, 10 cm wide and 30 cm long, and will complement existing planet-hunters like NASA’s Kepler space telescope and ground-based assets. It gives NASA the ability to dedicate relatively inexpensive assets to stare at a star for long periods of time to look for transits. Credit: MIT/Draper Laboratory.

Here again Seager sees Planetary Resources tweaking the basic model of how science gets done. A telescope specifically designed for a unique science goal can produce superb results, as we’ve learned from Hubble, CoRoT, Kepler and other missions. But bring a commercial interest into the mix and a new flexibility emerges. Planetary Resources can sell small space telescopes into a new market, while also using the product for its asteroid characterization work. The mix of motivations provided by commercial space drives the enterprise. Adds Seager, “If you’re part and parcel of the commercial space flight world, it appears you can get a lot of interesting things done. I think that in academia we could learn a lot from the business world.”

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A Near-Term Enterprise?

It’s too bad we don’t already have a workable Enterprise, that vast near-term rendition of the Star Trek vehicle that a systems engineer named ‘Dan’ has been talking about on BuildTheEnterprise.org (a site which has been so heavily trafficked in the last 48 hours that it has proven almost inaccessible). What Dan has in mind is the design, down to the smallest level of detail, of a ship powered by three ion propulsion engines that tap on-board nuclear reactors to remain operational. It may not be an antimatter-powered Enterprise, but it’s a faithful simulacrum, reflecting its creator’s long-lasting interest in the ship that William Shatner once commanded.

Dan thinks the new Enterprise could get us to Mars in 90 days, but getting nuclear reactors into low Earth orbit in the first place will be a challenge not only technically but politically, and shielding the crew will also involve a serious amount of mass that has to get lifted. One of the fascinations of this highly detailed site is that many of these objections are anticipated:

NASA is developing a heavy lifter, the Space Launch System (SLS), that will be able to carry a payload of 280,000 pounds, about the same as a Saturn 5 rocket. Unfortunately this is about a factor of four too low for what the Enterprise will optimally need. Because the Enterprise’s wet mass will be around 187 million pounds, a suitable heavy lifter should carry a payload of at least 1 million pounds to keep down the total number of launches needed. This is a payload similar to the Nova rocket designs from the 1960s that were never taken to production. So, in general, if the Enterprise program is someday funded, NASA will have to start a new heavy lifter rocket program that can carry much bigger payloads than their current plans.

And what about radiators to remove excess heat? Dan’s design better factor those in. An informal peer review of the concept is already beginning, as witness Adam Crowl’s take on the radiator problem on Crowlspace and back-channel discussions among aerospace engineers and designers in various places. If you want to track the new Enterprise beyond its own site, Dan’s Twitter handle is @BTE-Dan, and I’ll plan to have a report on some of the informal peer review in these pages before long.

Dan is a man with a long-term plan — he’s proposing not only building a huge ship but making it the first of a series, with three new ships per century, each keying on advances made during the intervals between construction. Early missions could involve the Moon, Mars, Venus and perhaps the moons of Jupiter, for while we’re a long way from Star Trek‘s warp drive, Dan claims the new Enterprise’s ion propulsion would allow a constant .002g acceleration for planetary exploration. A rotating wheel within the ship’s saucer section would provide an artificial 1g of gravity. The latter is one case of reworking the original Enterprise design to fit the requirements of a technology far less sophisticated than what was proposed in the TV series.

Image: A new Enterprise engineered around current and near-future technologies. Credit: BuildTheEnterprise.org.

The Daily Mail looks at the new Enterprise in a May 15 story, quoting its creator on his changes to the ship, one of which was made to keep the ship’s officers in workable conditions:

“Another example of a change is that the bridge is not at the top center of the saucer hull as it is shown in the figure above. If it was there in the Gen1 Enterprise then there would be no gravity on the bridge. Having the ship’s captain and crew floating around inside the bridge just makes no sense. Thus, in the Gen1 Enterprise the bridge is in a dedicated section of the gravity wheel so that they will work in 1g gravity.

“While things get moved around quite a bit inside the Gen1 Enterprise when compared to the ships from Star Trek, they are not moved around upon a whim. They are moved around because the Gen1 ship’s technological capabilities demand certain changes.”

The gung-ho spirit of Dan’s vision is engaging, especially his belief that all this can be achieved in 20 years, and the man who describes himself as a systems and electrical engineer in his day job tells the Daily Mail his BuildTheEnterprise site grew naturally out of the same kind of thinking he brings to bear at his high-tech firm, built on exploring new ideas and pushing technologies. I’m glad to see that he’s also hoping that young people find inspiration in his site, for it’s this kind of brainstorming, so often found in science fiction, that can motivate young minds into engineering or scientific careers. “…this may still be a long way from warp drives powered by anti-matter,” he tells the Daily Mail, “but it will be a respectable start.”

I love thinking big, but if we did have the technological means to build the first generation Enterprise in the short term, what about the needed economic and political environment? Is Congress likely to fund NASA to embark on a project of this magnitude — while continuing its funding for robotic missions to planets and elsewhere — given the size of the budget deficit and an environment of overwhelming debt? Surely that idea is more fantastic than the actual construction of a ship that can accommodate 1000 people within the next 20 years.

No, let’s take a longer perspective, with all due respect for energetic thinkers like Dan who want it done tomorrow. Ideas grow in their own time, and something along the lines of the new Enterprise design in terms of propulsion — i.e., large scale ion propulsion fed by nuclear reactors — may emerge as a working concept for our future Solar System-wide infrastructure, one that not a few scientists and engineers are now examining to weigh its merits and ponder its implications. In any case, Dan has a backup plan of his own in case his schedule is too optimistic. Once his site stabilizes under the current traffic load, have a look at it to see his proposed way forward.

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Remembering Dandridge Cole

I’ve been thinking all weekend about Dandridge Cole, the aerospace engineer and futurist whose death at age 44 deprived interstellar studies of one of its most insightful advocates. Cole died in 1965, just five years before a deadline he himself set (in 1953!) for a manned landing on the Moon. But then, the former paratrooper from Ohio thought a lot about the future and the need for a kind of ‘future studies’ that would look at current technological trends and project going forward just as conventional historical studies reconstruct what happened to us in centuries past.

The heart attack that struck Cole down in his office at General Electric’s Space Technology Center in Valley Forge, PA deprived us of much, but we do have the substantial legacy of a number of articles and monographs, along with three books, among which Islands in Space: The Challenge of the Planetoids, written with Donald Cox (Chilton Books, 1964) may stand out as the most influential. Andreas Hein, who is heading up the Project Hyperion worldship study for Icarus Interstellar, harks back to the inspiration of Cole in The Hollow Asteroid Starship: Dissemination of an Idea, published on the Icarus blog late last week.

Image: Dandridge Cole, who coined the term ‘macro-life’ to refer to human colonies in space and their evolution. Credit: Wikimedia Commons.

The idea is now a familiar one to science fiction fans, especially after its appropriation by George Zebrowski in his 1979 novel Macrolife, but in the mid-60s, the notion of hollowing out an asteroid to create an interstellar vehicle would hardly have been common currency. As Hein comments in his article, what Cole was doing was creating a bridge between the kind of space colonies that Gerard O’Neill would make famous and the worldships that might one day take a large human colony, a self-contained society, to a distant star.

The idea has resonance because star journeys may turn out to be multi-generational affairs that evolve naturally out of our eventually mastered skills at creating self-contained habitats in nearby space. If you can build a ship large enough and comfortable enough to re-create a planet-like environment within it, then living there might become so natural that future generations born aboard the craft would see no need for planetary living. A colony world like that might eventually disengage from the stellar system that created it and begin a voyage that would have no other aim than continuing exploration, taking ‘home’ with the crew wherever it went.

Artist and futurist Roy Scarfo provided the artwork in Cole’s 1965 book Beyond Tomorrow. On his site, Scarfo recalls going with Cole in the ambulance and being in the hospital at the time of his death. A futurist to the end, Cole had planned to have his body frozen and had made a serious study of cryogenics:

When we got to the hospital, the hospital personnel took him to a room. When they informed me that Dan was dead, and knowing that Dan wanted to be frozen, I called Ettinger, who I believe was in Chicago and who was the authority on cryogenics at the time. He knew Dan and instructed me to get in touch with a hospital and make arrangements for freezing. I believe it was the University of Pennsylvania hospital. I was racing against time as every second counted to preserve the body.

Personal and legal issues persuaded the family not to proceed with the arrangements, and Cole was buried conventionally, with Scarfo serving as one of the pallbearers.

Scarfo also wrote an appreciation of Cole on Alex Michael Bonnici’s Discovery Enterprise site in which he recalls working with Cole on Beyond Tomorrow in the evenings after work in Scarfo’s office at GE, where they would go over the chapters word by word. Says Scarfo:

Our work together gave us a handle as “the weird couple” because of the way-out material we were producing together. Today many of those concepts are as common as soap. The majority of our work together was done outside our regular responsibilities at GE, although sometimes they overlapped. We would meet almost daily for lunch at the cafeteria and afterward walk and talk during the rest of our lunch hour. This went on for years.

We’re surely due for a renewed look at Cole’s contribution and his ideas, especially as attention now turns to mining and the other possibilities the asteroids represent. Alex Michael Bonnici wrote his own tribute to Cole in 2007, one that encapsulates the asteroid-as-habitat idea:

In 1963, Cole wrote Exploring the Secrets of Space: Astronautics for the Layman with I. M. Levitt. In this book they suggested hollowing out an ellipsoidal asteroid about 30 km long, and rotating it about its major axis to simulate gravity. By reflecting sunlight inside with mirrors, and creating, on its inner surface, a pastoral setting an asteroid could be transformed into a permanent space colony. Cole and Cox also envisioned that asteroids would provide the raw materials to form the basis of a spacefaring civilization. And, that asteroidal materials would also serve terrestrial needs. In their view these materials could be transported using mass drivers or linear motors. Cole’s work largely presages that of Gerard K. O’Neill by more than a decade.

Extend the notion to an interstellar journey and you get what Cole would call a ‘nomadic pseudo-Earth’ that would be the seeding ground for so-called ‘macro-life.’ Cole’s view was that future human evolution inside such habitats, which includes synchrony between humans, their environment, and their technology, creates a ‘new large-scale life form.’ It was one he felt we must become, for in the years not long before his death, he had become extremely worried about our species not only in terms of population pressure but also weapons proliferation. Moving into space would be the chance to give humanity a progressing series of new and better starts.

Image: The populated asteroid from without and within. Credit: Roy Scarfo.

Here’s TIME‘s take on Cole’s macro-life views in a January 27, 1961 article:

Cole proposes the development of giant spaceships, each of which would contain at least 10,000 individual humans who would function rather like the cells of a multicelled animal; collectively, they would constitute what Cole calls a unit of “macrolife.” Stowed along with the humans in the vast body of the macroorganism would be domestic animals, plants, raw materials, machines and computers, as well as microfilms of all the books in the Library of Congress. A fully developed unit of macrolife would have rocket propulsion to enable it to move at will around the solar system. It would be able to live independently almost anywhere in space, but its normal habitat would be the asteroid belt between Mars and Jupiter where it could feed upon the mineral riches of the asteroids.

Macrolife in space would be self-adjusting, spinning off new units aboard new asteroids as necessary, but Cole freely acknowledged the difficulties in creating self-sustaining biospheres, urging that underwater bases or other sealed environments would need to become experimental testbeds for his ideas. A spacefaring species aboard a hollowed-out world, spun up for artificial gravity and provided with many of the amenities of planetary life, could well take to the stars one day. But in any case, Cole’s legacy of insightful probings of the human future will endure, the work of a man whose all too short life yielded much and has inspired interstellar theorists ever since.

For more on Cole, see Joseph Friedlander’s In Praise of Large Payloads for Space.

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Pushing Beyond Pluto

What would you do if you had a spacecraft pushing toward the edge of the Solar System with nothing much to do? The answer is to assign it an extended mission, as we found out with the two Voyagers and their continuing data return that is helping us understand the boundaries of the heliosphere. In the case of New Horizons, NASA’s probe to Pluto/Charon, two extended missions may be involved after Pluto, the first being a flyby of one or more Kuiper Belt targets, the second being a further look at what is actually going on where the solar wind meets the interstellar medium.

Alan Stern, principal investigator for New Horizons, comments on the possibility in his latest report on the mission, noting that a second extended mission isn’t out of the question, and adding that New Horizons won’t make it as far as the Voyagers before it runs out of power. But 90 to 100 AU seems a possibility, which would provide a useful supplement to Voyager data. Remember that New Horizons carries two instruments ideal for this part of the system. The first is the Solar Wind Around Pluto (SWAP) plasma instrument, the second the Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI). All this is in addition to what the spacecraft’s dust counter, its two imagers and its ultraviolet spectrometer may tell us.

Stern’s report on New Horizons comes at the same time we have word, from a new paper in Science, that the assumed ‘bow shock’ at the outer edge of the heliosphere may not actually exist. The bow shock is at the boundary between the solar wind pushing out from the Sun and the interstellar medium, an area of presumed turbulence that has been observed around other stars. The new paper from David McComas (SwRI) and colleagues presents findings from the Interstellar Boundary Explorer (IBEX) that show the Sun is moving more slowly in relation to the interstellar medium than previously thought, slow enough to prevent a bow shock from forming.

Image: IBEX has caught the interstellar wind that surrounds and compresses our heliosphere and has found that it travels more slowly and in a different direction than previously thought. This new understanding has important implications for the size and shape of the heliosphere and may inform the history and future of the solar system. Credit: SwRI.

Maybe New Horizons can help us clarify the situation with studies of the outer heliosphere, but we still lack a mission that could get us out as far as the bow shock region itself (the Voyagers have entered the heliosheath, but their signals will surely be lost before getting to the needed 200 AU or more from the Sun). All of this ties in with recent Cassini results suggesting that the heliosphere is more spherical than comet-shaped, so perhaps the interactions at system’s edge aren’t quite as fierce as has been thought. We need Innovative Interstellar Explorer to learn more, or a comparable mission specifically designed to penetrate into true interstellar space.

New Horizons in the Kuiper Belt

Meanwhile, our Pluto/Charon mission is, says Stern, doing just fine, having exited a period of hibernation on April 30 to begin a series of extensive systems checkouts. The spacecraft’s Pluto encounter occurs in the summer of 2015, but it should take a year to get all the encounter data back to Earth due to the slow data transmission rates at that distance. It’s after that that the first extended mission, subject to approval by NASA, would study objects in the Kuiper Belt. The spacecraft should have about 40 percent of its fuel still available, so a choice of KBOs should be possible, assuming the ongoing hunt for likely candidates turns up workable targets.

The New Horizons team has been using Earth-based telescopes to hunt for KBOs, but so far none has been identified that would be within range of New Horizons. It’s a tricky search, and one Stern assumes will succeed, but his recent report explains some of the problems:

First, the only KBOs within our reach are likely to be small, roughly 50 kilometers in diameter. Because they are small and far away, they will be faint as seen from Earth. In fact, calculations show that the KBOs we need to find are going to be about 25,000 times fainter than Pluto, which is itself about 10,000 times fainter than the eye can see. This means we have to search for objects with the largest telescopes and most sensitive astronomical cameras on Earth.

The second factor making the search tough is that our trajectory is pointed at the heart of the Milky Way’s densest star fields — those of the galactic center in the constellation Sagittarius. So our search is kind of a “needle in a haystack” hunt for very faint objects slowly moving against regions of the sky thick with stars!

All I could think of when I read that was an image of Clyde Tombaugh working the blink comparator at Lowell Observatory in 1930. I wonder what he would have thought then of the chances for tracking a target 25,000 times fainter than the dim planet (well, dwarf planet) he eventually found. The New Horizons effort should have at least one target defined by 2015, at which time an engine burn in the fall of that year would change the spacecraft’s trajectory to reach the first KBO, a journey that — if the team’s calculations are accurate — should last three or four years and perhaps longer. That could place the first KBO flyby as early as 2018 or as late as 2021.

What’s exciting about Stern’s report this time around is his statement that any target KBO will be approached at distances perhaps as close as the Pluto/Charon flyby, which means we should get images from the KBOs that are as detailed as those from Pluto. The down side: With no other Kuiper Belt mission in the works, we’ll need every bit of New Horizons’ observations on KBO surface composition and features, temperatures, moon or rings system and anything else the brief encounter can deliver, for as Stern puts it, “New Horizons is very likely to be the only spacecraft that will explore KBOs in the lifetime of most people alive today.”

Or maybe not. Let’s assume that first extended mission into the Kuiper Belt will be approved, which will yield not only close-up KBO images but also more distant observations of KBO satellites as well as dust particle distribution data. And while we get behind missions like Innovative Interstellar Explorer and push to see them implemented, let’s also cross our fingers for that second extended mission that would keep New Horizons active until it goes silent somewhere out around 100 AU. As the latest IBEX findings remind us, we know all too little about the boundary between our Solar System and the interstellar gulf beyond.

The new IBEX findings are in McComas et al., “The Heliosphere’s Interstellar Interaction: No Bow Shock,” published online in Science 10 May 2012 (abstract).

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KOI-872: Timing is Everything

It’s no surprise that the techniques we’re using to look for moons around exoplanets should start turning up new planets on their own. We’re still looking for that first exomoon, but a team of researchers working with the Hunt for Exomoons with Kepler (HEK) project has found transit variations that have revealed a second planet around a star already known to have one transiting planet. The star is the intriguing KOI-872 (KOI stands for Kepler Object of Interest), the data on which were recently released by the Kepler team and analyzed swiftly by HEK.

Kepler’s transit methods examine the change in starlight when an exoplanet passes in front of the star being observed. This lightcurve, however, can tell more than a single tale. David Kipping (Harvard-Smithsonian Center for Astrophysics) is head of HEK and second author of the paper on the new work, which was published online today in the journal Science:

“For a planet following a strictly Keplerian orbit around its host star, the spacing, timing and other properties of the observed transit light curve should be unchanging in time. Several effects, however, can produce deviations from the Keplerian case so that the spacing of the transits is not strictly periodic.”

Those effects are clear cut, changes in how long the transit takes (Transit Duration Variation, or TDV), and changes to when it actually occurs (Transit Timing Variation, or TTV). These deviations are sensitive to objects as small as 0.2 Earth masses, which shows their utility in hunting for large exomoons. In the case of the Sun-like star KOI-872, transits of the known planet show time variations of two hours. The TTVs are large and precise enough to allow scientists to calculate the orbit of the second planet. According to Kipping, both the transiting planet and the unseen planet perturbing its orbit are Saturn-class worlds. Moreover, they orbit close to a 5:3 mean motion resonance, accounting for the size of the timing variations.

Image: Using Kepler Telescope transit data of planet “b”, scientists predicted that a second planet “c” about the mass of Saturn orbits the distant star KOI-872. This research, led by Southwest Research Institute and the Harvard-Smithsonian Center for Astrophysics, is providing evidence of an orderly arrangement of planets orbiting KOI-872, not unlike our own solar system. Credit: Southwest Research Institute.

You may recall from last fall the story of Kepler-19b (discussed here in On Planets and What We Can See), a probable mini-Neptune some 650 light years away in the constellation of Lyra. Researchers at the Harvard-Smithsonian Center for Astrophysics were able to uncover a second world in the same system, Kepler-19c, by studying the transit timing variations of Kepler-19b. In this case, the timing variations were about five minutes long, but other than revealing the planet’s existence, they allowed no further deductions about its size or composition. In fact, the prospects — all consistent with the limited data available — ranged from a rocky planet on a circular five-day orbit to a gas giant on an oblong 100-day orbit.

But the new planet around KOI-872 is another matter entirely, and in Kipping’s words represents the transit timing variation model coming into full maturity, allowing us to measure the mass of the unseen planet and to determine the 5:3 orbital resonance. Moreover, we get tight constraints on the inclination, semi-major axis and eccentricity of both planets, which indicate they follow circular, co-planar orbits much like planets in our own Solar System. We now know that the unseen planet orbits its star every 57 days. Further Kepler observations will allow us to refine these details and tune up TTV and TDV methods for future planet and exomoon discoveries.

Image: Scientists analyzed Kepler Telescope data and identified KOI-872 as a stellar system where measured transits of a planet orbiting the star show large time variations (the shifting bumps in the data) indicative of a hidden companion. A team led by Southwest Research Institute and the Harvard-Smithsonian Center for Astrophysics determined that the observed variations can be best explained by an unseen planet about the mass of Saturn orbiting the host star every 57 days. Credit: Southwest Research Institute.

When the HEK team went to work on KOI-872, it was motivated in part by the fact that the transiting planet was large enough to hold on to a large moon of the size that current TTV techniques could uncover. The large TTVs yielded a planet rather than a moon in this case, but future finds of large moons around gas giants in the habitable zone will give us some idea as to whether single, rocky planets are the only likely venue for life. Are there as many habitable moons in the galaxy as habitable planets, or even more? HEK is the first step toward helping us find out.

The paper is Nesvorný, Kipping et al., “The Detection and Characterization of a Nontransiting Planet by Transit Timing Variations,” published online in Science May 10 2012 (abstract).

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