systemic

Of course, there are still 7 hours and 13 days left until the close of 2009, but I’ve got every confidence that the discovery of the decade has landed on the ground. The Mearth project has found a transiting 6.55 Earth-mass planet in orbit around the nearby red dwarf star GJ 1214. The parent star is bright enough, and the planet-star area ratio is large enough so that direct atmospheric characterization will be possible not just with JWST, but with HST. Incredible. I’m inspired, invigorated, envious. This discovery is a game changer.

The GJ1214 discovery is all over the news today. The coverage is deservedly laudatory, but interestingly, the most dramatic aspect of the detection received rather short schrift. This is easily the most valuable planet yet found by any technique, and the discovery, start to finish, required an investment of ~500K (along with the equivalent of 1-2 nights of HARPS time to do the follow-up confirmation and to measure the planet’s mass). By contrast, well over a billion dollars has been spent on the search for planets.

I’m milking that contrast for drama, of course. It’s true that GJ1214b is low-hanging fruit. The team with the foresight to arrive on the scene first gets to pick it. And the last thing I’m suggesting is a cut in the resources devoted to exoplanet research — it’s my whole world, so to speak. I do think, though, that Mearth epitomizes the approach that will ultimately yield the planets that will give us the answers we want. You search for transits among the brightest stars at given spectral type, and you design your strategy from the outset to avoid the impedance mismatches that produce bottlenecks at the RV-confirmation stage.

There’s a factor-of-fourteen mass gap in our solar system between the terrestrial planets and the ice giants, and so with the discovery of Gl 1214b (and the bizzare CoRoT-7b) we’re getting the “last first look” at a fundamentally new type of planet. CoRoT-7b is clearly a dense iron-silicate dominated object, but it likely didn’t form that way. Gliese 1214b’s radius indicates that it probably contains a lot of water. I think this is going to turn out to be the rule as more transiting objects in the Earth-to-Neptune mass range are detected.

So what next? With a modest increase in capability, Mearth is capable of going after truly habitable planets orbiting the very nearest stars. I think it’s time to put some money down…

I’m nostalgic for ’97, when the discovery of a new extrasolar planet was literally front-page news. What’s now cliche was then fully viable poetic sweep. Epicurus and his multitude of worlds. Bruno burning at the stake. In that frame of mind, it’s fascinating to go back and read John Noble Wilford’s extended New York Times piece, written at the moment when the number of known extrasolar planets equaled the number of planets in our own solar system.

Some of the hyperbole still seems fresh, especially with regard to the frequency and diversity of planetary systems:

And the discoveries may be only beginning. One recent study suggested that planets might be lurking around half the Milky Way’s stars. Astronomers have already seen enough to suspect that their definition of planets may have to be broadened considerably to encompass the new reality. As soon as they can detect several planets around a single star, they are almost resigned to finding that the Sun’s family, previously their only example, is anything but typical among planetary systems.

At the recent Porto conference, the Geneva team not only reiterated their claims regarding the frequency of low-mass planets, but actually upped their yield predictions. According to a contact who heard Stephane Udry’s talk, the latest indication from HARPS is that between 38% (at the low end) and 58% (at the high end) of nearby solar-type stars harbor at least one readily detectable M<50 Earth-mass planet. This is quite extraordinary, especially given the fact that were the HARPS GTO survey located 10 parsecs away and observing the Sun, our own solar system (largely in the guise of Jupiter’s decade-long 12-m/s wobble)  would not yet be eliciting any particular cause for remark.

It also looks like planets beyond the snowline are quite common. In yesterday’s astro-ph listing, there’s a nice microlensing detection of a cold Neptune-like planet orbiting a ~0.65 solar mass star with a semi-major axis of at least 3 AU. The microlensing detections to date indicate that Neptune-mass objects are at least three times as common as Jupiter mass objects when orbital periods are greater than five years or so. Microlensing detections are an extremely cost-effective way to build up the statistics of the galactic planetary census during belt-tightening times. Much of the work is done for free by small telescope observers.

Yet another dispatch pointing toward a profusion of planets comes from an article posted last week on astro-ph by Brendan Bowler of the IfA in Hawaii. Work that he’s done with John Johnson and collaborators indicates that the frequency of true gas giant planets orbiting intermediate-mass stars (former A-type stars like Sirius that are now in the process of crossing the Hertzsprung gap) is a hefty 26% within ~3 AU.

An embarrassment of riches? Certainly, the outsize planetary frequency means that the cutting-edge of the planet-detection effort will be shifting toward the Sun’s nearest stellar neighbors, as these are the stars that offer by far the best opportunities for follow-up with space-based assets such as HST, Spitzer, JWST et al.

As competition for ground-based large-telescope RV confirmation of run-of-the-mill planet transit candidates orbiting dim stars heats up, the threshold magnitude (at a given bandpass) at which stars become largely too faint to bother with will grow increasingly bright. We’re talking twelve. Maybe nine. Pont et al., in their discovery paper for OGLE-TR-182b refer to this threshold as the “Twilight Zone” of transit surveys:

The confirmation follow-up process for OGLE-TR-182 necessitated more than ten hours of FLAMES/VLT time for the radial velocity orbit, plus a comparable amount of FORS/VLT time for the transit lightcurve. In addition, several unsuccessful attempts were made to recover the transit timing in 2007 with the OGLE telescope, and 7 hours of UVES/VLT were devoted to measuring the spectroscopic parameters of the primary. This represents a very large amount of observational resources, and can be considered near the upper limit of what can reasonably be invested to identify a transiting planet.

Earth occulting the Sun, seen from Apollo 12 (source).

The year 1995 fades into increasingly ancient history, but I vividly remember the excitement surrounding Mayor and Queloz’s Nature article describing the discovery of 51 Peg b. Back in the day, the idea of a Jovian planet roasting in a 4.2-day orbit was outlandish to the edge of credibility.

In the five years following the Mayor-Queloz paper, four additional Doppler-wobble planets with periods less than a week (Ups And b, Tau Boo b, HD 187123b, and HD 75289b) were announced. Each one orbited close enough to its parent star to have a significant a-priori probability of transiting, and by mid-1999, the summed expectation for the number of transiting planets grew to N=0.68. Each new planet-bearing star was monitored for transits, and each star came up flat. Non-planet explanations for the radial velocity variations gained credence. The “planets” were due to stellar oscillations. The “planets” were actually mostly brown dwarfs or low-mass stars on orbits lying almost in the plane of the sky.

The discovery of HD 209458b, the first transiting extrasolar planets was therefore a huge deal. Instantly, the hot Jupiters gained true planetary status. There’s a huge leap from a mass-times-a-sine-of-an-inclination to density, temperature, composition, weather. 209458 was the moment when the study of alien solar systems kicked into high gear.

At the moment, we’re within a year of getting news of the first Earth-mass planet orbiting a solar-type star. It’s effectively a coin flip whether the announcement will come from Kepler or from the radial velocity surveys. In either case, the first Earth will likely be too hot for habitability, but within a few years we’ll be seeing genuinely habitable, multi-million dollar worlds. Kepler, for one, will deliver them in bulk.

Enter the TESS mission.

Here’s the scoop: The TESS satellite consists of six wide-field cameras placed on a satellite in low-Earth orbit. If it’s selected, then during its two-year mission, it will monitor the 2.5 million brightest stars with a per-point accuracy of 0.1 millimagnitude (one part in ten thousand) for the brightest, most interesting stars. It will find all of the transiting Jovian and Neptune-mass planets with orbital periods of less than 36 days, and it can make fully characterized detections of transiting planets with periods up to 72 days. Where transits are concerned, brighter stars are better stars. TESS will locate all the bright star transits for Neptune-mass planets and up, and equally important, it will find the best examples of large transiting terrestrial planets that exist.

TESS also provides an eminently workable path to the actual characterization of a potentially habitable planet. Included in the 2.5 million brightest stars are a substantial number of M dwarfs. Detailed Monte-Carlo simulations indicate that there’s a 98% probability that TESS will locate a potentially habitable transiting terrestrial planet orbiting a red dwarf lying closer than 50 parsecs. When this planet is found, JWST (which will launch near the end of TESS’s two year mission) can take its spectrum and obtain resolved measurements of molecular absorption in the atmosphere.

If TESS is selected for flight, we’re literally just five years away from probing the atmospheres of transiting planets in the habitable zone.

There have been a number of recent developments on the Alpha Centauri front.

Several weeks ago, Lee Billings wrote an article for Seed Magazine that delves at length into the hunt for terrestrial planets orbiting Alpha Cen. It hits a really inspiring tone. (I suggest pairing it with Nick Paumgarten’s equally well-written The Death of Kings to get a sense of how we’re living in what is effectively a bizarre superposition of worlds of varying habitability.) In keeping with the zeitgeist, the Alpha Cen story was also picked up last Monday with an article by Joel Achenbach in the Washington Post.

Billings’ article is entitled “The Long Shot”, with the reference being to Project Longshot, the far-out 1988 mission design for an unmanned 100-year nuclear pulse propelled mission to the Proxima/Alpha Centauri system. I, for one, definitely hope to be counted present when such a mission begins phase E.

Interestingly, the Seed article divulges an important clue to the extent of the Geneva Team’s current data set for Alpha Cen B, with the source apparently being a telephone interview with Michel Mayor:

Since 2003, Mayor and his team have used HARPS to search for planets around Alpha Centauri B. Last August, they began observing the star every available night in a strategy similar to Fischer’s.

The italics are mine, and for Alpha Cen fans, this is great news. Recent developments have made it abundantly clear that when HARPS is working full bore on a bright quiet star, it can drill right down into the habitable zone. If we assume that the statement in the above excerpt is accurate, we can put very interesting current limits on habitable planets in the Alpha Cen B system.

The star HD69830 (which harbors three-Neptune mass planets, see e.g. here and here) is a good proxy for Alpha Cen. The data set published in conjunction with the Lovis et al. article in Nature on HD 69830 contains 74 velocities taken over an 826 day period from Oct. 26 2003 through Jan 30 2006. That works out to 0.09 velocities per day, with each velocity having a reported instrumental error of ~0.8 m/s. This means that if Alpha Cen B received similar attention to that paid to HD 69830, then the Alpha Cen B data set as of last August would have contained ~160 velocities, each with ~0.8 m/s instrumental error.

If we look at the time series for HD 69830, however, we see that 160 Alpha Cen B velocities as of a year ago is likely an overestimate. It’s clear that the HD 69830 planets were starting to show after the first six months of observations, and as a result, the cadence on the star was increased by more than a factor of two. Based on the initial cadence on the star, it’s reasonable to expect that Alpha Cen B has been accumulating ~15 velocities per year, which works out to ~75 velocities in August 08 when the cadence was increased.

It seems reasonable to expect that when firing on all cylinders, HARPS can pull in 100 velocities per year for Alpha Cen B. This means that by the end of this summer, the Geneva team could quite reasonable be in possession of an N=175 point time series. Alpha Cen has near year-round observability from La Silla, so we can create a synthetic data sets which spread 75 velocities randomly across five years, followed by a year with 100 randomly spaced velocities. The data that the Geneva team currently have in hand probably look something like this:

The habitable zone for Alpha Cen B is at P~250d. Let’s assume that a planet with this period has an orbit of eccentricity e~0.05, and look at representative Lomb-Scargle periodograms of Monte-Carlo data sets created for different values of the planet mass. In keeping with the results for Gliese 581 and HD 69830, let’s also assume a 1 m/s normally distributed radial velocity jitter produced by the star.

An Msin(i)=4.6 Earth-mass planet in an optimally habitable orbit around Alpha Cen B is worth USD 100K (which seems like a remarkably good deal). Three periodograms for different Monte-Carlo realizations indicate that such a planet would be right on the verge of current “announceability”:

If the mass is reduced to Msin(i)=2.3 Earth masses (which jacks the value to a cool USD 227 million) the data sets (three of which are shown just below) are not quite seeing the planet yet. Another year and a half or so will be required.

During the coming 18 months or so, we’ll therefore be in an interesting situation in which no news on Alpha Cen is very good news. Perhaps any Wall Street types who read this blog might try their hand at pricing an option on Alpha Cen Bb.

And finally, the theoretical objections to the formation of terrestrial planets orbiting Alpha Cen B are dissipating rapidly. I’ll pick up that story in an upcoming post…

Georges-Louis Leclerc, Comte de Buffon is well known to givers of planet talks as one of the original proponents of physical cosmogony. Further fame accrues to his long-distance tangle with Thomas Jefferson over the size and the valor of the North American fauna. Buffon also made interesting contributions to probability theory, including the very sensible proposition that 1/10,000th is the smallest practical probability [source].

I think it’s reasonable to apply Buffon’s rule of thumb in discussing scenarios for the detection of the first potentially habitable extrasolar planet. If a scenario has a less than 10^-4 chance of unfolding, then it’s not worth expounding on in a web log post.

There’s no getting around the fact that the extrasolar planets are a long way away. Traveling at just under the speed of light, one reaches Alpha Cen Bb during Obama’s second term, and Gliese 581c, the extrasolar planet with the highest current value on the habitable planet valuation scale, lies 20 light years away. For practically-minded types such as myself, it’s depressing to think of the realistic prospects (or lack thereof) of actually reaching these worlds in a lifetime. And why spend trillions of dollars to visit Gliese 581 c when Venus is basically right next door?

It’s imperative to know the addresses of the nearest potentially habitable planets, though, and this is a goal that should be reached within roughly a decade or two. Barring a strike with some household name like Alpha Centauri or Tau Ceti, it’s a reasonable bet that the closest million-dollar world is orbiting a red dwarf.

The general suitability of red dwarf planets is often viewed with suspicion. Atmosphere-eroding flares, tidally spin-synchronized orbits, and gloomy formation-by-accretion scenarios provide ample material for space-age Jeremiahs. But first things first. With what frequency are Earth-sized T_eff~300K planets actually to be found in orbit around red dwarfs?

If planets form from analogs of the so-called Minimum Mass Solar Nebula, then the answer is quite well established: almost never.

If, however, instead of scaling down from the Minimum Mass Solar Nebula, we scale up from the proto-Jovian, proto-Saturnian and proto-Uranian disks, then the prospects are quite good. Ryan Montgomery and I have an Icarus preprint out which looks in detail at the consequences of an optimistic planet formation scenario for red dwarfs. Perhaps the most redeeming aspect of our theory is that it will be put to the test over the next decade. If hefty terrestrial planets are common around red dwarfs, then the currently operating ground-based MEarth survey will have an excellent chance of finding several examples of million-dollar wolds during the next several years, and the forthcoming TESS Mission will quite literally clean up.

In the spirit of Buffon, though, for the exact specifics of scenario three, it’s fun to probe right down to the limit of practical odds. Consider: An Earth orbiting a star at the bottom of the Main Sequence produces a transit depth that can approach 1%. If Barnard’s Star harbors an optimally sized and placed planet, then its value is a cool 400 million dollars. Such a planet would have an orbital period of about 13 days, and an a-priori transit probability of roughly 2%. I estimate a 1% chance that such a planet actually exists, which leads to a 1 in 5000 chance that it’s sitting there waiting for a skilled small-telescope observer to haul it in. In expectation, it’s worth $87,200, more than the equivalent of a Keck night, to monitor Barnard’s star at several milli-magnitude precision for a full-phase 13 days. That’s $280 dollars per hour. There are few better uses to which a high-quality amateur telescope could be put during those warm and clear early-summer nights.

Last weekend, I got e-mail from an A-list planet hunter who wrote in support of the little guys:

Why punish beloved M-dwarfs?

The last factor, currently written in terms of V, might be rewritten in terms of a less pejorative magnitude, like I or Z. Most stars in the Galaxy put their best (and brightest) foot forward at 1um!

Hard-working red dwarfs, like Barnard’s star or Proxima Centauri get the short end of the stick in the Oklo terrestrial planet valuation formula. Red dwarfs put out the bulk of their radiation in the near-infrared, rather than the optical, but dollar value is pegged to apparent magnitude in the V-band.

This leaves me in a position similar to that of a company spokesman trying to justify Wall Street bonuses.

“The fact of the matter, is that as a society, our planet-hunting values and priorities have been traditionally tied to the optical range of the spectrum. If we examine the resources that have been deployed to date, over a billion dollars have been spent on satellite-based planet-hunting programs that monitor stellar output in visible light. In the same way that an executive’s compensation is tied to the value that he or she brings to shareholders, a terrestrial planet’s value should therefore be tied to V-band magnitude.”

Flimsy, I admit. Therefore, in the interest of fairness, the first planet-hunting group or individual that discovers a planet worth USD 1M with Z-band apparent magnitude replacing V-band will receive an oklo.org T-shirt.

Several readers pointed out that the terrestrial planet valuation formula breaks down dramatically for Venus. Point taken! I’m not sure though, that a top-dollar Venus necessarily points to a flaw. The valuations are a quantitative measure of potential for a planet to be habitable, given only bulk physical properties currently measurable across light years of space. One is still faced with the quandry of whether to invest in to finding out whether a given planet measures up. If Venus were sheathed in water clouds rather than sulfur dioxide clouds, it would quite possibly achieve its potential as a quadrillion-dollar world.

At any rate, given its sky-high atmospheric D/H ratio, it’s not inconceivable that Venus was both habitable and inhabited, at least by microbes, in the distant past. Under the constraint of a zero-sum budget for solar system exploration, I would agitate for spending more exploring Venus and less exploring Mars.

It’s admittedly gauche to price planets like baseball cards. But it’s also true that taxpayer money, big money, well over a billion dollars of real money, is being spent to find planets, and astronomy has long since departed the ivory tower. We know from direct observation that an excitable media is more than eager to paint habitability-lottery losers in neon shades of blue and green. A middling $158.32 best-yet on a scale that will soon be registering million-dollar worlds underscores the importance of keeping the powder dry.

Which brings up scenario number two for how the first million-dollar detection (and indeed the first hundred-million dollar detection) could arise. It’s extremely likely that the first planets with genuine potential habitability will be detected from the ground. It’s also a good bet that these planets will arise from the same technique that’s produced the overwhelming majority of the big-ticket planet detections to date: Doppler radial velocity. If I were pressed to guess the particular star, I’d choose HD 40307. And if I were pressed to guess the time frame? Sometime within the next year.

The Mayor et al. (2009) HD 40307 paper rewards careful study, and indeed, may end up being as illuminating for what it reveals as for what it doesn’t reveal. In the paper, the evidence for the now-famous planets “b” (Msin(i)=4.2 M_Earth, P=4.3d), “c” (Msin(i)=6.8 M_Earth, P=9.6d), and “d” (Msin(i)=9.2 M_Earth, P=20.5d) is presented in the form of phase-folded plots of the radial velocities, and a periodogram of the velocities prior to any fitting. That all three planets are clearly visible in the raw periodogram is in itself quite remarkable. The orbits are close to circular, the system has been observed for many periods, and the signals (despite the small half-amplitudes) are unambiguous:

The actual radial velocities, however, are not included in the paper, and would-be Dexterers are thwarted by the fact that the only plots showing the full data set are phase-folded. The journal version of the paper reports that the velocities are available at: http://cdsarc.u-strasbg.fr/cgi-bin/qcat?J/A+A/493/639 , but the link is still empty…

In lieu of access to the actual data, we have carte blanche to engage in irresponsible (yet technically accurate) speculations to get a sense for what further secrets the HD 40307 system might harbor. Let’s construct a Monte-Carlo data set. An optimally habitable ten million-dollar planet in the HD 40307 system has a mass of ~2.3 Earth masses, an orbital period of 141 days, and induces a K=0.35 m/s radial velocity half-amplitude. We can make a model system that includes such a planet along with the three known planets (noting that the Mayor et al. 2009 paper contains an error for K_d in Table 2). We can generate a synthetic radial velocity data set by perturbing the four-planet model with the reported 0.32 m/s instrumental measurement error and 0.75 m/s of Gaussian stellar jitter, and observing at 135 randomly spaced times within a span of 1628 days.

We can put the resulting data set into the Systemic Console. Removing the 20-day planet gives a residuals periodogram that clearly shows the 9.6d and 4.3d planets, along with an alias peak at ~2 days. As with the actual periodogram in the Mayor paper, there’s nothing particularly interesting at 141 days. That is, there’s no sign of the ten million-dollar world that was baked into the data.

Remarkably, however, when the 9.6d and 4.3d planets are fitted and removed, the periodogram peak for the 141d planet is quite prominent. It’ll be very interesting to see if anything like this is present in the actual data set when it goes online:

It’s straightforward to recover the 141d planet in the orbital fit. Removing the three known inner planets and phase-folding the data at the period of the 141d planet shows what its current (as of last June) signature would look like:

A real planet with these properties would thus be right on the edge of announceability. HD 40307, furthermore, is by no means the only quiet Mv~7 K dwarf in the local galactic neighborhood…

Without regard to order of likelihood, I thought it’d be interesting to lay out a few very specific scenarios by which the first extrasolar world with a 1 million+ habitability valuation could be discovered.

A favorite space-art trope is the habitable moon orbiting the giant planet (which is generally well-endowed with an impressive ring system). Smoggy frigid Titan is the best our solar system can do along these lines, but there’s nothing preventing better opportunities for habitability lying further afield.

I’ve always been intrigued by the fact that the regular satellite systems of the solar system giants each contain of order 2 parts in 10,000 of the mass of the parent planet. At present, there’s no reason to expect that this scaling is any different for extrasolar planets, and given the example of Titan, there doesn’t seem to be anything to prevent the bulk of a given planet’s satellite mass from being tied up in a single large body. Furthermore, since it’s my weblog, I’ll take the liberty of assuming that the satellite mass fraction scales with stellar metallicity.

Image source.

It’s perfectly reasonable to imagine, then, that HD 28185b is accompanied by a 0.63 M_earth, 0.86 R_earth satellite with an orbital radius of a million kilometers. HD 28185b itself has Msin(i)=5.7 Mjup, and the metallicity of HD 28185 is [Fe/H]=+0.24.

Now, for a long shot: let’s assume that on July 11th, 2009, a cadre of small telescope observers in Australia, South Africa and South America discover that HD 28185b transits its parent star. The geometric a-priori odds of the transit are ~0.5%. The expected transit depth is an eminently detectable 1%. A transit of moderate impact parameter lasts about 12 hours.

If a detection is made on July 11th, 2009, it’s a sure thing that the following transit (July 29th, 2010) will be the subject of great scrutiny. The current ground-based state of the art using orthogonal transfer arrays is demonstrating 0.4 mmag photometry with 80 second cadence. At this level, with spot filters and several observatory-class telescopes participating, the piggyback detection of the satellite transit is a many-sigma detection.The cake would be iced on Aug 16th, 2011, when the ~25 second difference in midpoint-to-midpoint intervals would be detected. We’d then be in possession of a potentially habitable terrestrial world warmed by an admirably bright and nearby parent star. Accurate mass and radius determinations would be fully forthcoming. All from the ground, and all at a total cost measured in thousands of dollars of amortized telescope time on existing facilities.

Admittedly, the odds of this specific scenario are slim. I estimate one in two thousand. The payoff, however, is massive. HD 28185bb (with the properties given above) is worth a staggering 100 million dollars. In expectation, then, that’s 50,000 dollars for fully covering the transit window this July…

I’m completely invigorated by the Kepler Mission. This is, of course, because of the fantastic discoveries it’ll make, but also (I’ll admit) because it establishes a crystal clear and present challenge to competitively-minded planet hunters everywhere. If you want to discover the first truly potentially habitable world orbiting another star, then you’ve got, in all likelihood, 3.5 years to do it.

A coveted oklo baseball cap (from a limited edition of five) will be sent to the first person or team that detects an extrasolar planet worth one million dollars or more as defined by the terrestrial planet valuation formula set out in Thursday’s post:

For purposes of definiteness, (1) terrestrial planet densities are assumed to be 5 gm/cm^3. (2) A measurement of Msin(i) is counted as a measurement of M. (3) Teff is computed assuming that the planet is a spherical blackbody radiator. (4) The parent star needs to be on the Main Sequence. (5) If the stellar age can’t be accurately determined, then it can be assumed to be half the Main Sequence lifetime or 5Gyr, whichever is shorter.

Gliese 581 c (see here for more details).

The formula is pretty stringent, and is not kind to planets of dubious habitability. Gliese 581c, which I believe is the extrasolar planet with the highest value found to date, clocks in at $158.32. Mars, taking outsize advantage of the Sun’s V=-26.7 apparent magnitude, is worth almost 100 times as much, at $13,988.

In upcoming posts, I’ll put forth some scenarios (spanning a wide range of likelihood) that could produce high-dollar detections during the next three and a half years.

In 1803, the fledgling United States purchased the Louisiana Territory from France, and thereby entered into what has wound up being one of history’s better real estate deals. Napoleon, as the principle on the sell side, remarked at the time, “This accession of territory affirms forever the power of the United States, and I have given England a maritime rival who sooner or later will humble her pride.” In somewhat typical fashion, the US House of Representatives was slower to grasp the stupendous advantage of the bargain, with Majority Leader John Randolph standing firmly against the purchase. Fortunately, a measure to axe the deal wound up failing by two votes, 59-57.

The Louisiana Purchase price was a (suspiciously spam-like) USD 15 million. For a payment of gold bullion and bonds, the United States obtained the entire western drainage of the Mississippi River. This constitutes ~2 million square miles, or roughly 1% of Earth’s ~200 million square mile total surface. Using the price of gold as a measure of inflation (Gold was USD 19.39 per oz. in 1803) the purchase in today’s currency was thus a mere USD 750 million.

Fast-forwarding two hundred years to the present, similarly good land deals are still to be had — not on Earth, but on potentially habitable terrestrial planets orbiting nearby stars! I think it’s fair to say that the successful launch of the Kepler Mission last weekend can be viewed as the first large-scale extraterrestrial land rush.

Oklo readers are doubtless familiar with the Kepler mission specs. The spacecraft will reside in an Earth-trailing orbit, and, during the 3.5-year mission will monitor ~100,000 main sequence stars with a photometric precision of 20ppm at 6.5h cadence. In all likelihood, it’ll detect of order 100 terrestrial planets. The total mission cost will be of order USD 600 million, remarkably close to the cost of the Louisiana purchase in 2009 dollars.

The advent of Kepler allows us to put meaningful prices on terrestrial extrasolar planets. I think the following valuation formula provides a reasonable start:

where $\tau_{\star}$ is the age of the planet-bearing star, and V is the apparent visual magnitude. Kepler’s best planets are likely going to come in with valuations of order 30 million dollars.

Applying the formula to an exact Earth-analog orbiting Alpha Cen B, the value is boosted to 6.4 billion dollars, which seems to be the right order of magnitude.

And applying the formula to Earth (using the Sun’s apparent visual magnitude) one arrives at a figure close to 5 quadrillion dollars, which is roughly the economic value of Earth (~100x the Earth’s current yearly GDP)…