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Space Science

Transit Method Reveals Many Extrasolar Planets 174

Posted by ScuttleMonkey
from the through-the-looking-glass dept.
eldavojohn writes "You might recall not too long ago the first photo of an extra solar planet or, more recently, the mapping & speculation on these planets that lie outside our own solar system. Long since those first few spotted in the 90s, we're now starting to find them in droves due to the popularity of a method that relies on the planet passing directly between the viewer on earth and the star that it orbits. Be sure to check out Space.com's list of the most interesting extra-solar planets. Will we ever find Earth 2.0 candidates?"
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Transit Method Reveals Many Extrasolar Planets

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  • by It doesn't come easy (695416) * on Monday June 11, 2007 @02:03PM (#19467855) Journal
    Considering the statistically unlikely percentage of planetary orbits that would naturally line up so that the planet would transit its sun from our point of view, planets must be pretty much common as dust. Either that or God was nice enough to line them up so it's easy for us to find them (possible, I hear God is a very nice person)...
    • Re: (Score:2, Interesting)

      by rblancarte (213492)
      This is the whole argument that Stephen Hawkins uses to "believe in God." Basically that things like this don't just happen randomly.

      RonB
      • by Sciros (986030)
        Hey hey wait a second *I* get to decide what gets to happen randomly, not *you*!
      • by jobsagoodun (669748) on Monday June 11, 2007 @02:54PM (#19468415)
        This is the whole argument that Stephen Hawkins uses to "believe in God."

        Quite the opposite actually...

        "You cannot prove that I exist", says God, "For Proof denies faith, and without faith I am nothing!"
        "Ah", says man, "But the planets lining up nicely like that so that we can see them is a dead give away isn't it. It proves you exist, and therefore by your own logic you don't. QED"
        "Oh bugger I hadn't thought of that" says God and disappears in a puff of logic.


        Sorry Mr Adams.
      • Re: (Score:2, Insightful)

        by Anonymous Coward
        This is the whole argument that Stephen Hawkins uses to "believe in God." Basically that things like this don't just happen randomly.

        Which is pretty much the reason for the existence of all gods throughout history; to provide an explanation for something that was otherwise unfathomable. And of course once a thing becomes "fathomed" that particular god is no longer needed, and disappears.

        I also might preemptively mention that "this is different, and also he's a really really smart guy way smarter than you

      • Re: (Score:3, Insightful)

        by elrous0 (869638) *
        Yeah, now the only question is "Which God?"
      • I suppose that you are referring to Stephen Hawking? But perhaps you ought to refer to number 8 on the Crackpot Index [ucr.edu].
    • Re: (Score:2, Funny)

      by 2names (531755)
      "God was nice enough to line them up so it's easy for us to find them"

      Um, you do know that the Universe is flat, right? Just like Earth. :)

    • by goombah99 (560566) on Monday June 11, 2007 @02:15PM (#19467995)

      Considering the statistically unlikely percentage of planetary orbits that would naturally line up so that the planet would transit its sun from our point of view, planets must be pretty much common as dust. Either that or God was nice enough to line them up so it's easy for us to find them (possible, I hear God is a very nice person)...
      Maybe not so lucky. Most of the planets in our solar system (not all) have their rotational axes mostly parallel to their orbital axis. I assume there's some reason for that, perhaps simply if they are spun off of the sun then they acquire it's angular momentum. Or like the moon where tidal forces lock the orbit. In any case then, the next question is if the solar systems in our galaxy mainly orbit in the plane of the galaxies rotation. I'd assume so.

      Given all that then it's not too surprising that there be a preference for this favorable occultation geometry.

      Finally I note that we are not really interested in planets that don't rotate in their orbital plane since otherwise they'd be roastingly hot on one side and freezing on the other.

      • Re: (Score:3, Interesting)

        by Black Perl (12686)
        Finally I note that we are not really interested in planets that don't rotate in their orbital plane since otherwise they'd be roastingly hot on one side and freezing on the other.

        Yes, but wouldn't there be a certain ring that is exactly 70 degrees? Also, you'd have an endless supply of geothermal energy. The hot-as-lava side could double as an incinerator--no trash problems. Obviously terraforming would be impossible but I'd think you could establish a permanent colony there.
        • by Chris Burke (6130) on Monday June 11, 2007 @03:02PM (#19468515) Homepage
          Yes, but wouldn't there be a certain ring that is exactly 70 degrees?

          I'm no expert, but I'd be willing to bet that what you'd really get is a ring that fluctuates violently between the hot and cold extremes of the two sides of the planet and is constantly bombarded by gigantic storms. I mean we're basically talking about a permanent clash between hot and cold weather fronts.

          Huge temperature deltas do not result in nice smooth gradients between them.
        • by escay (923320)
          Exactly what I was thinking, but in a different context. The (#6 on the list) exoplanet Upsilon Andromeda B [space.com] is tidally locked with its sun - so, one side is burning hot while the other is freezing cold. There must exist a ring zone that is temperate, since the temperature gradient cannot be discretely sharp. Couple that with unlimited supply of geothermal energy, and we got one cheap earth.
      • by jae471 (1102461) on Monday June 11, 2007 @03:26PM (#19468739) Journal
        It should be noted that out the Sun's axis of rotation (and that of the major planets) is NOT with the galactic plane. We can see them, but they can't see us...
      • by mp3phish (747341) on Monday June 11, 2007 @04:09PM (#19469459)
        Your statement seems misleading but it may just be incomplete (IMO).

        "Finally I note that we are not really interested in planets that don't rotate in their orbital plane since otherwise they'd be roastingly hot on one side and freezing on the other."

        The rotation of the planet has nothing to do with the detection of planets in this method, only the orbit determines the ability to detect it. So while some planets may or may not be rotating on the correct axis to support multiple seasons, it isn't accounted for in this type of study because they can't detect this with the transient method.

        Also, there are actually a large variation of planes that can be detected with this method. Imagine our solar system as a disk. Then imaging looking at it from the top view. This view does not allow the planet detection using the transient method. However, angle your view down until you can see just one of the planets cross over the sun. From this angle on, and twisted up to 360 degrees, is where this transient method works. So actually, there are many planes of orbit which can be used to detect planets with this method. And assuming that a percentage of these planets are within the habitable distance from their star, and that a percentage of these rotate on a reasonable axis, then they could contain life. But nothing in these studies is determining that any of this is the case. Right now they are just looking for ANY planets. so we can detect extrasolar planets even if their orbital planes are perpendicular to the galactic disk, so long as they are close to parallel to our viewing line of site. With this in mind, you can imagine that if you can view stars in our galaxy from 360 degrees around our planet, that we would be able to detect every orbital plane angle available in the galaxy, depending on which direction we are looking from the earth. So while we can't see all of them, we can see a very large subset of them with this method.

        Also, the reason that all the planets in the solar system follow close to same typical plane of orbit is because of the way solar systems form. They start as a gaseous body collapsing. As the rotation of the gas nears closer and closer to the center of the nebula, the rotational inertia causes the forming of a disk due to inertia. The same thing happens to drag car tires when they spin fast (they turn more disk-like). From this disk-like nebula the planets form. The center typically ends up with something larger than a gas giant (the sun, or a couple of suns) and the other planets turn into gas giants (Jupiter) or solid planets (i forgot the name, but they gain gravitational pull and pull in particles from the nebular disk)

        So this is why the planets are all in one plane of orbit. If all star systems are formed in this general method (something that is assumed) then it is fairly easy to say that they should all be in a single plane. But each system does not necessarily have to be in the same plane relative to each other just because they are in the same galaxy. Each nebula forms independently and collapses typically from an outside force, but not necessarily on the same rotational plane.

        Also, the planets have their own disks associated with them. The moons and rings of Uranus and Saturn and Jupiter follow different planes. They don't necessarily need to follow the same plane as the solar system. This is because each of those planets also formed independently of each other. The spin of those depends on the angular momentum of the local mass as it formed, which would be different than the parent nebular disk especially when you take into account collisions of forming bodies. The same could be said to happen on the galaxy level, if you compare the galaxy formation to solar system formation.

        These are just my points of view of what I have studied. Many people will have different points of view formed from the same observations.
      • by Hays (409837) on Monday June 11, 2007 @04:23PM (#19469651)
        In any case then, the next question is if the solar systems in our galaxy mainly orbit in the plane of the galaxies rotation. I'd assume so.

        They don't. See http://curious.astro.cornell.edu/question.php?numb er=633 [cornell.edu]

        Our own Solar system is not at all aligned with the galaxy. If it were, the milky way would appear more east-west in the night sky, especially during the equinox.
        • by HiThere (15173)
          Sorry, you're arguing from a single case. True, it's the only one we're real certain of, but it's still just a single case.

          I think that the presumption is that solar systems do generally basically orbit in the plane of the galaxy. OTOH, there are LOTS of "captive star streams" that one would expect to have different orbital inclinations. (Also, lots of things can perturb an orbit.)

          OTOH, look at how thick the "plane of rotation of the galaxy" is. It's not a plane, but rather a wobble. And it's dubious t
          • by Hays (409837)
            Sorry, you're arguing from a single case. True, it's the only one we're real certain of, but it's still just a single case. ...

            Think about it your self, do a bit of reading, and make up your own mind.


            But... but... I referenced an answer from professional astronomers. And while I gave the example of our own solar system, their answer says "They're oriented in all different directions. The size of a solar system is so much smaller than the size of the Galaxy, that the Galaxy's structure has no impact on the
      • by argStyopa (232550)
        I'm not sure I follow you. Oh sure, I agree that at observable scales from planetary on up to the galaxy itself (I believe it fails thereafter), there seems to be a planar bias which make a sort of logical sense - kind of an astronomic "ontogeny recapitulates phylogeny"?

        However, in the previous poster's comments, he's right too - even conceding a tendency to form solar systems on a plane (and I would guess this is only a TENDENCY, not a majority), even then the odds that a planet would pass directly betwee
      • Re: (Score:3, Interesting)

        by The_Wilschon (782534)
        Not so. The plane of the ecliptic and the galactic equator are offset from one another by about 62 degrees. [1] So it would appear that there is probably wide variation in the tilt of the ecliptic planes of other stellar systems.

        Or, a naive argument from astrophysics (IANA astrophysicist, although I am a physicist): Perhaps the disk of a new-formed star is typically rather thin (in the direction perpendicular to the ecliptic). Then material undergoing gravitational accretion to form planets would all c
      • Being serious for a moment, there may be a simpler explanation to the reason we see so many planets crossing the star's disk...

        Generally, almost everything that spins also wobbles around the axis of spin at least a little bit. All other things being equal, I assume solar systems as a single gravitational whole also wobble (over an extended time frame, no doubt). If so, at any given instant there will be some small percentage of systems where their orbital plane lines up with our line-of-sight in relatio
      • in any case then, the next question is if the solar systems in our galaxy mainly orbit in the plane of the galaxies rotation. I'd assume so.

        The galactic plane is inclined at 123 degrees from the ecliptic. Its only a single example but your hypothesis has no basis. The torque that would bring the oblate, rotating sun and galactic core into the same plane are vanishingly small.

      • by HiThere (15173)
        Well....sort of.

        I'm no cosmologist or astrophysicist, so take this with a grain of salt, but here goes.

        A solar system condenses from a rotating gas cloud. Becuase of this the axii of rotation of the condensates (suns, planets, etc.) tend to line up.

        But also the Galaxy (spiral galaxies only!) condensed from a gas cloud. Because of this the nebulae (thicker gas clouds within it) have rotational axii that tend to line up.

        So stars within a spiral galaxy will tend to have aligned axii of rotation. And their p
    • Re: (Score:3, Informative)

      by Stephan202 (1003355)
      Aren't you referring to the Drake equation [wikipedia.org]?
    • Re: (Score:3, Funny)

      by Rei (128717)
      possible, I hear God is a very nice person

      Really? Then why'd he go and bury all of those dinosaur bones and radioisotopes to test our faith?
    • by jafiwam (310805)
      Yeah, that sort of depends on whether you think the galactic plane and solar (stellar) plane have a tendency to coincide or not.

      Our solar system is off galactic plane by around 63 degrees or so. The solar (stellar) plane is a function of the angular momentum of the dust cloud (assuming the solar system creation model we have is correct). The galactic plane, is the same thing, only on much larger scale of the galaxy (duh).

      One would think that the total aggregate angular momentum of the galaxy would strongl
      • by mcvos (645701)

        One would think that the total aggregate angular momentum of the galaxy would strongly suggest the same bias toward stellar planes more or less lining up.

        One would think wrong. Stars move in all sorts of weird directions in our galaxy, and they definitely spin in just about any direction you can imagine.

        Basically if you look at a star it's probability of having the stellar plane line up with us is a bell curve where the center is 0 degrees out of galactic plane, and the higher you go the fewer do.

  • by 2names (531755) on Monday June 11, 2007 @02:05PM (#19467871)
    Yes, as long as we don't kill ourselves first.
    • by ls -la (937805) on Monday June 11, 2007 @02:13PM (#19467979) Journal

      Yes, as long as we don't kill ourselves first.
      Better hurry up and colonize other planets.
    • by omeomi (675045) on Monday June 11, 2007 @02:15PM (#19467991) Homepage
      Will we ever find Earth 2.0 candidates?"

      I certainly hope it contains the same easy-to use ergonomic AJAX functionality as Web 2.0...I hate having to reload an entire Earth page every time I want to do something...
    • It is mars. It is not 100%, but close enough. And there is increasing data to indicate that it does have life (bacterial, but still life).
    • by s4m7 (519684)

      Yes, as long as we don't kill ourselves first.

      Yeah, except we already have found a good Earth 2.0 candidate and it's called Mars. Using roughly apollo-era technology, we can get there in a mere 9 months. Without the discovery of some loophole in physics that allows us to travel significantly faster than we are currently capable of, any other candidate will take more than a lifetime to get to. Using existing or near-term feasible technology we could slap multiple bases on Mars within a decade, and begin a terraforming process that could very well be

  • by cybrpnk2 (579066) on Monday June 11, 2007 @02:06PM (#19467887) Homepage
    Read the article. Discovering planets via the transit method (eclipse dimming of the star) is rare. Around 80% are instead discovered using the so called wobble method, which measures changes in starlight doppler shift.
    • Wow! An uninhabited planet where we can rape all the resources, pollute as much as we want, and no one can complain!

      ROCK ON!

      2 cents,

      QueenB.
    • The great thing about the occultation method is that it can be used to determine a planet's volume. Add that to the wobble method, which determines a planet's mass, and you now have enough data to calculate the planet's density
  • Who wants to deal with stupid grendlers [wikipedia.org]? Let's just skip to 3.
    • Let's just skip to 3.

      Third Earth? Well, if that's your choice of destination I suppose you're free to go there, but I'd suggest you avoid going anywhere near the Onyx Pyramid. Just a helpful safety tip.

  • Yes (Score:4, Interesting)

    by nizo (81281) * on Monday June 11, 2007 @02:11PM (#19467945) Homepage Journal
    Will we ever find Earth 2.0 candidates?


    Of course; space is big and there are bound to be tons of great planets out there. I just hope there is no one already living on our soon to be discovered new colony planet so we can move in quicker.

    • by jez9999 (618189)
      I just hope there is no one already living on our soon to be discovered new colony planet so we can move in quicker.

      Yep. And every second of extra speed counts, with Alpha Centauri being a mere 42 trillion km away.
    • Re: (Score:3, Funny)

      by StikyPad (445176)
      I just hope there is no one already living on our soon to be discovered new colony planet so we can move in quicker.

      Barring that, hopefully we can develop some kickass motherships and tripod walkers.
    • I heard that it's at the 2.0b stage, so it should be released any century now!

      Seriously, unless you're planning on making a minor revision on a planet, you could just call it Earth 2 and not sound geeky :(
    • But if there's *nothing* there, how could we live on it in an independant, sustainable way?

      Can we really expect to find a place that will enable us to plant crops and raise animals for food, yet has no indigenous life forms?

      Nah...
  • So, by this did you mean...other planets to rape and pillage?
  • Bowman 2.0 (Score:5, Funny)

    by Rob T Firefly (844560) on Monday June 11, 2007 @02:12PM (#19467963) Homepage Journal
    All these World 2.0s are yours except Europa 2.0. Attempt no landings there.
  • by jhouserizer (616566) on Monday June 11, 2007 @02:13PM (#19467967) Homepage
    Will we ever find Earth 2.0 candidates? I'm sure we will. And when we do, I have a number of candidates for who should be sent there.
    • by john83 (923470)

      I'm sure we will. And when we do, I have a number of candidates for who should be sent there.
      Hairdressers, tired TV producers, insurance salesmen, personnel officers, security guards, public relations executives, management consultants, the middlemen you see.
  • I realize the existing crop of candidates leaves much to be desired, but is looking outside the solar system for our next president really a solution? How would you square that with the Constitutional requirement that the President be born in the US? Isn't that why Schwarzenegger can never really fulfill his political ambitions?
    • by elrous0 (869638) *
      I think we should make an exception for any aliens capable of destroying us on a whim. I for one don't want to anger anyone capable of kidnapping me and shoving an anal probe up my ass.
  • Version (Score:3, Funny)

    by Bromskloss (750445) <auxiliary DOT ad ... privacy AT gmail> on Monday June 11, 2007 @02:16PM (#19468011)

    Will we ever find Earth 2.0 candidates?

    How about making the current one stable first?

  • Extra Solar (Score:2, Funny)

    by Punko (784684)
    Every time I see "Extra solar planet" I envision a planet with more than one sun.
    I mean "extra salt" = more salt, right ?
  • by polar red (215081) on Monday June 11, 2007 @02:21PM (#19468079)

    Will we ever find Earth 2.0 candidates?
    so we can ...
    • continue to wreck this one?
    • declare them part of the axis of evil?
    • export our garbage there ?
    • ... ?
    • by Himring (646324)
      This is just a starter planet anyhow....
  • by niloroth (462586) on Monday June 11, 2007 @02:30PM (#19468179) Homepage
    What are we going to do about getting there? Unless we can figure out some way to travel faster than the speed of light, i doubt any human will ever step foot on a planet outside our solar system. I think it far more likely that we will have to terraform one of the ones near us, and even then, we seem to messing this one up way faster than we could even start that process. I think hawkins may be right, 1000 years at most left for us. Although that really may have been a bit optimistic.
    • by cdrguru (88047)
      There are lots of ways of getting there that we already know about. The first thing is to get a probe launched to some system with something that appears to have strong possibilities for life. This would be potential water signatures, right distance from the star, etc. The first probe will be a difficult and long-term project but will spur many activities.

      If you've read stuff by Larry Niven, what started everything was probes. And then hibernation ships that caught up to and passed some probes by.

      How lo
    • Re: (Score:3, Interesting)

      by jshriverWVU (810740)
      Your view seems 1/2 true. No person in a single lifetime can make the journey. The goal would be to create a ship large enough to sustain many families, and the resulting offspring of a couple generations would make it.
      • Re: (Score:3, Interesting)

        by StikyPad (445176)
        the resulting offspring of a couple generations would make it.

        Aside from the lifetimes of "Are we there yet?", you know the offspring would just take the fact that they're on an interstellar voyage for granted, and they wouldn't even appreciate the arrival. "This is the planet my great grandfather wanted to visit," they'd say. "Let's check out Earth."
      • by aldheorte (162967)
        You may not need a generation ship. You could use a cryogenic ship. There are several species on earth that can go into indefinite freeze and reanimate (frogs being one). It's likely that human cryogenics will become a reality long before the technology for sending a self-sufficient colony to another solar system becomes a reality and therefore the colonists who leave Earth will be the ones who arrive, even if they are very old in real time when they do, but not much older in biological time.
    • Standard SF options (Score:2, Interesting)

      by geek2k5 (882748)

      While we don't have the tech in place to make the trip now, we do have ideas of what could be done. We just need to get some cheap Earth to Orbit launch facilities in place so we can start research and development of the tech needed. (Rutan's SpaceShipX ships. Space elevators. Catapult launch from high altitude sites.)

      Once we have a lot of people and equipment in space, we could do such things as build generation ships and take the slow route. Whether powered by Sol base lasers, atomic bombs (Orion), i

    • by mcvos (645701)

      Not all extrasolar planets are hundreds of lightyears away. The closest known so far is only 10 lightyears away. At .5 c that's 20 years. Give the colonists a free World of Warcraft subscription and off you go.

  • by blindd0t (855876) on Monday June 11, 2007 @02:32PM (#19468215)

    ...when I say if it is actually called "Earth 2.0" that I would seek Kevorkian's "assistance." (Joking, of course.) The moniker is used way too much! Instead, I feel we should call the planet "Godzilla" so it would be entertaining to hear people scream its name in excitement upon viewing it for the first time.

  • Updated stats (Score:2, Interesting)

    by EvilGrin5000 (951851)
    The link to Space.com for the 'most interesting extra-solar planets' has a top 10 list with all the new updated data. The article from the summary said that the fastest planet's orbit around its sun is 1.2 days, where instead the top-10 list shows a recently discovered planet with an orbit of just 10 hours! There is a link that leads to this page http://www.space.com/scienceastronomy/061004_fast_ planets.html [space.com] that talks about 'fast planets' and shows the new data.

    I recommend going to the top-10 list found
  • What the heck are you smoking?

    How about "earth-like planets"? Or "planets like ours"?

    Honestly... phrases like "earth 2.0" and "web 2.0" (not to mention WiFi, which really ought to be pronounced "whiffy") make me wonder about the collective intelligence of the technically inclined.
    • Re: (Score:2, Informative)

      by Loke the Dog (1054294)
      Its a joke based on the hype around "web 2.0", which everyone knows sounds stupid. Now, laugh.
    • by cnettel (836611)
      I for one, am waiting for Earth 3.1. I'm just not sure if it will be like MS-DOS 3.1 or Windows 3.1.
  • by sean.peters (568334) on Monday June 11, 2007 @03:36PM (#19468903) Homepage

    God, what a mess the "Top 10 Exoplanets" site is! Bright orange background that is absolutely physically painful to look at, requires 10 click-throughs to read the whole article (when each page has about a paragraph of text), the text itself is in little iframes that require you to scroll to get past the first few sentences - and don't get me started about the content (what little there is). If you haven't visited it... don't.

  • by clovis (4684) * on Monday June 11, 2007 @04:17PM (#19469587)
    Why do you assume that we are not already on Earth 2.0?
  • Well... (Score:3, Insightful)

    by Greyfox (87712) on Monday June 11, 2007 @04:23PM (#19469653) Homepage Journal
    We'd have to work around that nasty speed of light thing first. I seem to recall that it'd take about 450,000 years to reach the one we found that has water, which is 20 light years from here. If that proves impossible then those planets will be forever out of our reach.
    • Re: (Score:2, Insightful)

      by cswiger (63672)

      We'd have to work around that nasty speed of light thing first.

      True, that's a big problem compared with the popular "space opera" notion we've gotten from Star Wars, Star Trek, and so forth. But if we could get a vessel up to 10% of light speed, we could get to Epsilon Eridani in about 107 years, which isn't an impossibly long timeframe.

      Of course, the fastest we've gotten any space craft going is about 0.02% of light speed (Helios 2 @ 241,350 km/h), if I've done my math right, but that took advantage of the solar gravity well to accelerate into a tighter orbit, rat

    • by master_p (608214)
      It's not that impossible to travel to another planet within a radius of 500 light years, provided that we built an autonomous spaceship which can host many generations of people...the most likely candidate is a big rotating cylinder which offers 'gravity' by rotation. If it can achieve the 1/2 of speed of light, then it can reach the other planet in 10-15 generations. Achieving 1/2 of the speed of light is not that impossible, provided that the spacecraft can accelerate for a long time.
       
    • by mcvos (645701)

      We'd have to work around that nasty speed of light thing first. I seem to recall that it'd take about 450,000 years to reach the one we found that has water, which is 20 light years from here.

      Light actually travels slightly faster than you think it does. 20 light years means that at lightspeed, you'd need 20 years to get there. Ofcourse we can't reach lightspeed, but at half lightspeed, we'd need 40 years, and at 10% of lightspeed, it's 200 years. A long time, but a lot less than 450,000 years.

      • We don't HAVE a spaceship that can go 10% of light speed right now...
        • by mcvos (645701)

          We don't HAVE a spaceship that can go 10% of light speed right now...

          We also don't have a spaceship that can go there in 450,000 years. Not one that can carry people, anyway. When you want to go beyond Earth's orbit, I'm afraid you're going to have to build a custom vehicle to get you there. And we can build one that can go 10% of light speed. We're just not willing to spend that kind of money.

  • The IAU recently cemented the definition of planet, carefully avoiding a useful classification that generalizes to objects outside the solar system. Suffice to say, under the current definition, no extrasolar body is a planet, even if it's a sub-molecular copy of Earth squarely in the habitable zone of a star which purely by coincidence happens to be a spectral twin of Sol.

In any formula, constants (especially those obtained from handbooks) are to be treated as variables.

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