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Moving (and Saving) the Planet

The ever reliable Dennis Overbye gives us a look at the Earth’s fate in his most recent story for the New York Times. Citing the work of Klaus-Peter Schroeder (University of Guanajuato, Mexico) and Robert Connon Smith (University of Sussex), Overbye describes our planet’s eventual engulfment by a red giant Sun. Earlier studies had questioned whether the Earth might survive this phase, but Smith and Schroeder say no. Their calculations show a red giant Sun 256 times as wide as today’s star, and fully 2730 times more luminous. And it will swallow the Earth.

I was interested to see Overbye’s reference to a 2001 paper that, in the spirit of speculative jeu d’esprit familiar in good science fiction, looks at a way to save the planet. But first, let’s run through where our star is heading. Burning through its hydrogen on the main sequence, the Sun should keep getting hotter and larger. Figure 1.1 billion years until you reach the point where it is 11 percent brighter than today, creating a greenhouse effect that devastates the biosphere. By the time you’re 3.5 billion years out, the Sun is forty percent more luminous than today and any surviving vestiges of life as we know it should be gone.

But ponder this: We are at present less than halfway through the main sequence life of the Sun. In six billion years, even though the Sun’s luminosity should be a factor of 2.2 greater than its current value, a planet just 1.5 AU out would receive about the same amount of solar energy that Earth now receives. Thus the notion of increasing the radius of the Earth’s orbit, which Don Korycansky and our friend Greg Laughlin (both at UC-Santa Cruz), working with Fred Adams (University of Michigan), describe. Do this right and the lifespan of the surface biosphere gets a five billlion year reprieve. Here’s the basic idea, as drawn from the paper:

An attractive scenario for gradually increasing the Earth’s orbital radius is to successively deflect a large object or objects from the outer regions of the solar system (the Oort Cloud or the Kuiper Belt) onto trajectories which pass close to the Earth. By analogy to the gravity-assisted flight paths employed by spacecraft directed to outer solar-system targets… the close passage of such an object to the Earth can result in a decrease in the orbital energy of the object and a concomitant increase of the Earth’s orbital energy.

Sins of the Fathers magazine cover

A science fiction scenario par excellence! And one that recalls Stanley Schmidt’s Sins of the Fathers, which I read long ago (1973-74) when it ran as an Analog serial. There the idea was to move a threatened Earth (the galactic core has exploded) with the help of ingenious alien technologies to a new and safer home. A more recent example of world moving is Robert Metzger’s Cusp (2005), where mysterious alien technologies are activated, the Singularity arrives and stars and planets fly (not to mention ideas galore). I had the good fortune to discuss Cusp with Metzger over lunch in Chapel Hill a couple of years back — if you’re into hard SF that doesn’t let up, be sure to read him.

But back to the paper under discussion. Just how would we move the Earth? The authors work out a typical mass for large Edgeworth/Kuiper Belt objects (1022 grams) and calculate that some 106 passages involving a ‘cumulative flyby mass’ of about 1.5 Earth masses would do the trick, moving the Earth to 1.5 AU. An average of one pass every 6000 years over the remaining lifetime of the Sun ought to do the job, which doesn’t sound as onerous as one might have expected.

And, of course, we have an Edgeworth/Kuiper Belt stuffed with objects larger than 100 kilometers in diameter. Here we’re on speculative ground, but the authors figure the belt should hold as many as 105 such bodies, with a total of perhaps 10 percent of the Earth’s mass. And then there’s the Oort Cloud, thought to hold 1011 objects totaling thirty or more Earth masses. Small trajectory changes would bring many an Oort object into an Earth crossing orbit (Laughlin makes sure that Overbye understands, in the Times article, that he’s not advocating such a dangerous move — one mistake takes out our planet — but simply sketching out the boundaries of the possible).

What’s happening in the rescue scheme is that repeated gravity assists in effect transfer orbital energy from Jupiter to the Earth. A close pass by the Earth by an object in a highly elliptical orbit transfers energy from the object to the Earth. Outbound, the object crosses Jupiter’s orbit, timed to encounter the planet and pick up the energy lost to Earth. The paper spells out the procedure in details that point to a long-term and ‘almost alarmingly feasible’ scenario, one that would use technologies that, although beyond our current capabilities, are by no means beyond the powers of a more advanced civilization. The long-term result seems promising:

Due to the acceleration of the Sun’s luminosity increase, the encounters must be more frequent as the Sun approaches the end of its main-sequence life. In order to use the same secondary body for many encounters, modest adjustments in its orbit are necessary. However, by scheduling the secondary body to encounter additional planets (e.g., Jupiter and/or Saturn) in addition to the primary Earth encounter, the energy requirements for orbital adjustment at the object’s aphelion can be substantially reduced. In particular, the energy consumed by such course corrections is not likely to dominate the energy budget.

And note this interesting fact: The energy required to move the Earth is modest compared to that needed for interstellar travel. Working out the numbers, the team finds that the scheme is actually highly efficient when compared to interstellar migration and compares favorably with various terraforming projects that have been examined in the past. Usefully for more contemporary concerns, the basic methods might also be utilised to move hazardous asteroids, or to set up delivery mechanisms for useful Edgeworth/Kuiper Belt materials whose resources could be exploited.

The paper is Korycansky, Laughlin and Adams, “Astronomical engineering: a strategy for modifying planetary orbits,” Astrophysics and Space Science 275 (2001), pp. 349-366 (abstract). It’s one you don’t want to miss.

Comments on this entry are closed.

  • Jim Baerg March 12, 2008, 10:38

    Given a technological civilization that lasts for billions of years & continues to advance, some means of removing material from the sun so it dims & lasts longer, might be a better option.

    This is definitely something to be tried on a star with no habitable planets, but there’s plenty of time to travel to a nearby star & experiment.

  • Ronald March 12, 2008, 11:11

    I am surprised by the (apparently) relatively low energy requirements to knock the Kuiper belt and Oort Cloud objects out of their orbit into an earthbound trajectory. Originally, I would have thought this to have been too prohibitive in terms of energy requirements to ever become a feasible option. I must admit I am still not quite convinced that it would be competitive with interstellar colonization, in energy terms, not with terraforming Mars.

    In this case then, it might also become an equally feasible option to use this approach to move Venus out to a more agreeable orbit (i.e. inside the sun’s CHZ).

    However, (at least) one great objection remains to this approach in comparison with stellar travel and Mars terraforming: the immensely long time-frame.

    Stellar travel may become doable within one or two centuries, terraforming Mars might take on the order of a millennium.

    In my view, the galactic future of humankind is much (MUCH) more likely to be one of interstellar leaps in combination with terraforming suitable (i.e. biocompatible but not yet inhabited) planets.

  • donald wilkins March 12, 2008, 11:34

    Good morning,

    You shouldn’t forget A World Out of Time by Larry Niven. http://en.wikipedia.org/wiki/A_World_Out_of_Time If I remember correctly, Mr. Niven, who never goes for the small answer, has our descendants drop a very large fusion engine into Jupiter and use it to tug Earth into a safer orbit.

    When much of the news seems to gloat that we will die tomorrow it it bracing when others look at gigayear problems and believe that we will be there to solve them.

    THanks,
    Don

  • Tim March 12, 2008, 12:41

    Unfortunately, I do not have access to the paper mentioned in your article so I cannot check their math. However, it seems to me that such a substantial change in earths orbit could substantially effect the stability of the entire system. E.g. what happens to Mars orbit, and to Jupiters orbit and what are the ‘feedback’ effects on the earth?

  • andy March 12, 2008, 12:52

    …and while you’re at it, you can stick Mars in one of the Trojan points, to keep it out of the way and put it at a more convenient distance for terraforming ;)

  • Administrator March 12, 2008, 13:01

    Tim, the paper is downloadable through the link I provided; click to get the abstract and then you’ll see you can download the PDF. And yes, the authors address this point — that the stability of the system would be affected by these moves — explicitly. As you say, it’s clearly a factor in the potential outcome. The authors look in particular at effects on both Jupiter and Saturn, as well as the Moon and Mars. Here’s a snip from the Mars discussion:

    “The fate of Mars in this scenario remains unresolved. By the time this migration question becomes urgent, Mars (and perhaps other bodies in the solar system) may have been altered for habitability, or at least become valuable as natural resources. Certainly, the dynamical consequences of significantly re-arranging the Solar System must be evaluated. For example, recent work by Innanen et al. (1998) has shown that if the Earth were removed from the Solar System, then Venus and Mercury would be destabilized within a relatively short time. In addition, the Earth will traverse various secular and mean-motion resonances with the other planets as it moves gradually outward. A larger flux of encounters might be needed to escort the Earth rapidly through these potential trouble spots. In this case, additional solar system objects may require their own migration schemes.”

  • Administrator March 12, 2008, 13:02

    Right you are, Don, and thank you for the memory jog. A World Out of Time is certainly worth re-visiting!

  • ljk March 12, 2008, 13:31

    I thought we were going to turn the entire Sol system into
    a Dyson Shell and keep our star fusing far longer than it
    would naturally, making this whole issue moot?

    Or we all just hop aboard gigantic multigeneration ships
    and roam deep space, stopping at star systems along the
    way for fresh supplies, so that we are never stuck with just
    one star that will eventually go bad.

  • david March 12, 2008, 13:57

    I’m not so sure that an increase of 11 percent in the sun’s output would be devastating to the earth’s biosphere.

    Fossils of cyanobacteria have been found that are 3.4 billions years old. Quoted from (http://phoenix.lpl.arizona.edu/mars144.php) “If ancient stromatolites formed the same way that microbial mats do today, then photosynthetic life could have already evolved significantly by 3.5 billion years ago.”

    Also we know that the sun today should be around 40 percent brighter than it was 4.6 billion years ago. If that was a straight line increase then the sun over the last 3.5 billion years has increased in its luminosity by around 27-28 percent. Despite that increase life has flourished.

    One can imagine ways that the earth’s biosphere might adapt to allow another 11 percent increase.

    Anywhere from increased flows within the ocean that heats up the northern and southern parts of the planet more while cooling the equator regions. This might occur naturally since with more energy to drive them such energy flows might increase, which would lead to a faster distribution of the increased energy.

    To plants changing their color so that more energy is reflected back into space. Dark plants could more easily be devastated by forest fires while regions of lightly colored plants absorbing less energy, hence less heat, might be subjected less to such devastations.

    ==========

    I wonder if another way to move the earth might be by magnetic bubbles. One of the proposed methods for spacecraft propulsion described here (http://science.nasa.gov/newhome/headlines/prop08apr99_1.htm).

    If 3kw of power and 3(kg?/ib?) of helium can have such an affect then what might happen if that 30-60km bubble was expanded to 30-60 million kilometers. It would have a propulsive force a trillion times greater. Applied a few thousand years every couple of million years I wonder if it could do the trick. What would be the affect on the earth’s atmosphere and biosphere of such an extreme magnetic field?

    Also, if the plate tectonics ceasing in a few hundred million years is going to kill the planet might moving the planet cause enough stress to reactivate them?

    (also been wondering if this method might be used to move mercury in order to give mars a moon)

  • Damien R. S. March 12, 2008, 17:41

    Other option for dealing with a more luminous Sun: reflective sunshades blocking some of the light.

    Paul Birch has written about moving planets via dynamic mass streams as well; his ideas were not large intermittent comets but a near-continuous stream of pellets sent around other planets and the Sun, to transfer momentum that way. Also usable for improving Venus’s rotation rate.

    http://www.paulbirch.net/
    “terraforming venus quickly” and “how to spin a planet”, in a bizarre format of ZIPped collections of scanned pages.

  • andy March 12, 2008, 18:20

    IIRC, in Beyond the Fall of Night, the solar system had been rearranged to have most of the habitable planets (including a depleted Saturn) around Jupiter, with the Earth and maybe Venus as independent worlds. However there is no way you will persuade me to reread the novel to check this.

  • dad2059 March 12, 2008, 19:29

    The mighty influence of science fiction firing the imaginations of inquisitive minds here.

    I love it!

    I noticed no Church of the Singularity solutions. How about posthumans/AI entities converting the Sun and the Solar System into a computronium Dyson Shell and moving the whole shebang to the edge of the Galaxy where it’s cold so the VR upload computations run nice and cool. 8)

  • ljk March 12, 2008, 22:16

    dad2059, I guessed you missed my earlier comment on
    turning the Sol system into a Dyson Shell. I guess my
    other comment on multigenerational starships isn’t quite
    a Singularity technology.

    Having reread the article, I now conclude that it is incredibly
    short-sighted, although I am sure the authors think they are
    being very advanced, perhaps even “out there” with such an
    “audacious” idea as moving the planets around to avoid being
    friend by Sol.

    If anything to me it sounds like the old ideas of travelling to
    the Moon using flocks of birds or balloons. The idea is a
    wild one for the time, but the methods are primitive, to say
    nothing of impractical.

    Unless we go extinct and no other life forms take our place
    on this planet, or if no one in the galaxy ever comes to visit
    the Sol system, I doubt our star and its attending worlds will
    remain untouched in the coming ages. Why would you want
    to save one rather small planet when you could turn the whole
    place into a structure that would give us more room than we
    can almost imagine (a solid Dyson Shell would have the
    equivalent of 5 billion Earths).

    In just 50 years the human population will reach 10 billion.
    Think Earth will be enough room (to say nothing of having
    enough resources) a few billion years from now? A swelling
    sun will not be our first concern.

    Long before then I expect us to be spread out across the
    galaxy in one form or another – or we will be extinct. Carl
    Sagan himself said our choice is spaceflight or extinction.

    Long before 5 billion CE happens, no one will be recalling
    Earth, Sol, or humanity. 5 billion years ago, Earth was a
    molten mass just starting to form, and life did not evolve
    beyond microbes and algae until about 600 million years ago.

    By the way, this segment from Cosmos has a bit on “the
    last perfect day”, showing how Earth and Sol will come to
    an end assuming no one interferes with them beforehand
    (towards the end of this clip):

    http://youtube.com/watch?v=KG-CfVjRr74

  • ljk March 13, 2008, 9:29

    I want to clarify my earlier comments on the idea of moving
    Earth around to save it from being fried by Sol billions of
    years from now. I may have come across as harsher than
    I intended.

    I am not criticizing the idea or methods employed by the
    folks who came up with the concept of moving Earth. That
    such a thing isn’t entirely stuck in the realm of science fiction
    is wonderful and exciting. It hold many possibilities for our
    future existence and indicates what an already advanced
    ETI might do with other worlds.

    What I was really commenting on is the idea that our planet
    will still be around in a few billion years time, or that whoever
    is living then is going to be concerned about saving Earth or
    even be aware of its existence.

    I do not see our planet or our species being left as is by then.
    We will either be long gone or spread out into the galaxy and
    beyond. Earth may be lucky if it is recalled as anything other
    than a distant memory. It won’t be healthy for us to maintain
    our population and technology growth rate and assume we can
    remain on Earth without consequences. We will have to move
    off and/or change our planet some day, or face extinction. Our
    descendants will not call Earth home – and that will be a good
    thing for our species.

  • dad2059 March 13, 2008, 13:06

    ljk: I did see your comment about the Dyson Shell and yes the generation ship idea did distract me from that, I apologize.

    Personally, I love the generation ship/ark/spome idea. It was the first interstellar concept I read about many years ago, so it will forever be stuck in my mind.

    Although the Technological Singularity has a religious overtone to it that I suspect many people of science find a little ‘unsettling’, it can really happen given the right conditions. You are quite correct when you state that when human beings leave the comfort of the Solar System, most won’t be recognizable as human anymore.

    My theory is that there won’t be any one method that will be ‘the method’ of interstellar travel, or mega-engineering. The interstellar ark/spome method might be used by semi-baseline humans/asteroid belters who are political dissidents, persecuted by religion or to flee posthumans converting the Solar System into a computronium shell/matrioshka brain. Human history is full of Diasporas, I don’t think the future will be any different.

  • Ron S March 13, 2008, 13:10

    By and large I agree with ljk’s comment. However I won’t criticize speculations or closely worked out methods for moving large bodies, including Earth. I think it’s a good thing to think big and try to come with novel solutions to novel problems that test our ingenuity, in much the same way I might solve a puzzle as a means of mental exercise. And who knows, we may learn something useful in the process, even if it’s far removed from the original topic of discussion. We just need to understand why we work on these problems and not lose perspective. I see generational starships and von Neumann probes among the same class of topics.

    Regarding sci-fi novels in this vein, there’s the aptly named “Moving Mars” by Greg Bear.

  • Jason Brady March 13, 2008, 16:38

    Speaking of sci-fi novels in this vein, don’t forget the “Cities In Flight” series by James Blish. In one of the installments (the fourth and final, “The Triumph of Time”) in which an entire planet is on the move through the galaxy, out of control until the inhabitants learn to control the “spindizzy” anti-gravity device.

    Personally, I do not see why it is so difficult to build a Dillon-Wagoner Graviton Polarity Generator, or spindizzy, machine. I built one last year, and it’s sitting next to the table saw in my garage. ;-)

  • Administrator March 13, 2008, 18:31

    Cities in Flight! What a great memory…

  • ljk March 13, 2008, 21:58

    How about Larry Niven’s Ringworld series. Not only do we
    get a Dyson Belt, we also have the Puppeteers moving their
    entire solar system out of the Milky Way galaxy to escape
    the explosion at the galactic core.

  • Ronald March 14, 2008, 4:23

    @ljk: I did not find your earlier comments harsh at all, just sharp and to the point, and I largely agree, as I stated before: not everything we can do will be done, because there will be other, more feasible options.
    We can probably make bricks fly, but we don’t because aluminum airplanes work better.

    Likewise, terraforming Mars and going to the stars will most likely be a much better option for the survival of humankind (especially with regard to time-frame) than moving our planet. Like the difference between emigrating to another country, settling there, or moving the whole house.

    On to the stars!

  • Doug M. March 14, 2008, 13:47

    A few years back on Usenet, I proposed a variant of this idea. As far as I know it’s original to me.

    “Disassemble a biggish asteroid into several trillion one
    kilogram chunks. Each chunk has a solar sail and a stupid little chip
    brain with a few simple instructions: 1) gain delta-vee 2) find an
    orbit that will transfer delta-vee to Earth 3) repeat forever 4) oh,
    and don’t bump into anything.

    “All these little guys do is sail around the solar system using their
    light sails to accelerate into higher and more elliptical orbits. Then
    they do a momentum-transferring flyby with Earth. They drop back
    into a lower orbit and Earth is lifted into a micro-fractionally
    higher one. Repeat endlessly.

    “The chunks are programmed to avoid collisions; and even if something
    goes wrong, a collision with Earth will do no harm…”

    [later post]

    “BOTE calculation here.

    “MEarth = 6×10^24 kg

    “Let us say we need a delta-V of 10 km/s to move it to the safer orbit.

    “Say further that every time a 1 kg swarm-bot passes, it drops 10 km/s
    of delta-V. Earth, in turn, gains that much energy. We need only make
    6×10^24 passes, and our work is done! We have 500 million years to
    work with, so a mere 1.2 x 10^18 passes per year will do it.

    “…hmmm. Assume 1% of our swarm can make a pass in any given year; the
    other 99 years are spent solar-sailing back to a higher orbit,
    regaining those lost 10 km/s of delta V. This means a constant
    acceleration of about one one-millionth of a gee, which doesn’t seem
    unreasonable.

    “So, the total number of swarm-bots will be 1.2 x 10^20. This gives the
    swarm the total mass of a biggish asteroid… it’s about half the mass
    of Pallas.

    “To my mild surprise, this seems remotely plausible.”

    Doug M.

  • david March 14, 2008, 17:38

    If we do decide to colonize the stars in a large way we could use a method that as a side affect would give the earth a larger orbit.

    Should we decide on solar sails or magsails as a method for the colonization we could build massive lasers or particle accelerators on the moon. Used to drive the spacecraft it would also impart some momentum to the moon, which would also affect the earth. One could imagine a billion ton colony ship accelerated to 1/10th light speed at a constant 1g using lasers based on the moon. With some down time 10 such ships could be launched per year with a single laser, with more lasers for more launches always an option. With a couple hundred billion stars to colonize ….

    If fuel becomes a problem for the lasers then just crash a few small comets into the moon and mine the ice. I imagine they could be impacted in such a way that they also give the moon, and thus the earth, some momentum in the right direction.

  • Adam March 14, 2008, 19:02

    Hi Doug

    Nice one! Sounds almost doable in that light. Though the upper-mass limit can probably be boosted for objects with solar-sails – they’d re-enter the atmosphere of Earth pretty harmlessly with such low areal densities. I do wonder how many would be needed to replace swarm-bots taken out by collisions per year.

    If we want to get Earth out to 1.5 AU by 5.5 billion AD then the acceleration can be very low. A continuous thrust of just 190 giganewtons is enough to move the Earth-Moon system. A soletta 256,000 km across could do it. A big fusion engine burning ~ 12 tons of D-He3 every second could do it too. Both would need to be parked on a big mass to use as a gravity tractor – perhaps the Moon could be juggled into the right position.

    Swarm-bots sound more elegant, and less hair-raising than a Life-Terminator sized planetoid swinging by every 6 millennia.

  • James M. Essig March 15, 2008, 1:14

    Hi Folks;

    Another method of potentially tugging the Earth further out to say 1.5 AU to 5.0 AU might be to build huge space elevator like bean stalks wherein very large solar energy collection systems would be attached or otherwise within energy transmission communication with the bean stalk. The bean stalk could scoup up reaction mass from Earth or collect it from reaction mass harvested from other regions of the solar system such as asteriods, moons, planets, etc., wherein the reaction mass would be accellerated very rapidly to ultra-relativistic velocities in batch mode in either solid or plasma form or continuosly in small pellet form or plasma beam form in order to provide the 190 GigaNewtons of thrust to propell the Earth further out. The solar energy required to power the system could be obtained from huge solar reflectors such as inflatable dish type reflectors beyond the orbit of Earth so as not to interfere with the Earth’s reception of solar energy. Inflatable collectors in the form of a single inflatable unit or a thin array or matrix of small units with a collection area of 1 million kilometers by 1 million kilomters or the equivalent or about 1 trillion square kilometers could capture 10 EXP 21 Watts of solar energy or 10 EXP 21 Joules/Second. Larger sails could do even better with power collection rates proportional to the collection area.

    This power example is 10 EXP 21 Newton-Meters/Second or 10 trillion Newtons excerted over a distance of 100 million meters every second. Using the Newtonian approximation, this would entail accelerating a 10,000 kilogram mass over a distance of 100 million meters in one second. This could be done with an accellerative force of 20 million Gs or an acceleration of about 2 x (10 EXP 8) meters per second squared according to the Newtonian formula Distance = D = (1/2) a (t EXP 2) where a is accelleration and t is elapsed time and d is distance travel with starting velocity equal to zero. Essentially, an efficient thruster could produce 10 TeraNewtons of thrust with a reaction mass of 10,000 kilograms leaving an accellerator or mass driver at a muzzle velocity of mildy relativistic velocity every second in either continuous plasma beam form, or small pellet stream form or in the form of large solid reaction masses.

    Since the mass of a projectile increases with velocity according to the formula Mrel = Mrest/{[ 1 – [(v exp 2)/(c exp 2)]] EXP (1/2)}, the distance that the projectile of 10,000 kilograms under an accelleration of 20 million Gs would have to travel would actually be significantly but not greatly less that that provided by the Newtonian Formula for the example given above.

    The special relativistic formula for force is F = (gamma)m(a hat) + {((gamma) EXP 3) m {[(v hat) dot (a hat)]/(c exp 2)]}}(v hat) where gamma = 1/{[1 – [(v exp 2)/(c exp 2)]] EXP (1/2)}, a hat is the accelleration vector, v hat is the velocity vector, dot represents the dot product operation. When the velocity vector and the acceleration vector are paralell:

    F = (gamma)ma + [(gamma) EXP 3] m [[(v) (a)]/(c exp 2)](v).

    Relativistic mechanics thus would give a more accurate solution than my crude Newtonian calculation but at the expense of much greater complexity.

    Note that if the mass beam accelleration rate was much higher, much higher muzzle gamma factors could be reached thus resulting in much lower rest mass requirements for the ejected matter in order to achieve the 10 EXP 13 Newtons of thrust. Also note that the beam would have to be aimed in directions such that it would not impinge on the Earth and also so that it would effectively gradually pull the Earth further away from the sun and/or accellerate the Earth in a direction that is approximately tangential and paralell to its orbital motion without causing the bean stalk to become de-orbited or collapsed.

    Thanks;

    Jim

  • James M. Essig March 15, 2008, 1:32

    Hi Folks;

    I have a correction to make. The value of the reaction mass used in the Newtonian calculations should be 100,000 Kilograms instead of 10,000 kilograms.

    Thanks;

    Jim

  • James M. Essig March 15, 2008, 1:55

    Hi Folks;

    Please do not be upset by yet another error. The actual rest mass would be 50,000 kilograms instead of 100,000 kilograms as falsely reported above. For the equation Work = Force x distance = (10 EXP 13 Newtons )x (10 EXP 8 meters) = 10 EXP 21 Joules. 10 EXP 13 Newtons = (50,000)(20,000,000)(10) Newtons. The relation F = ma yields F = 10 EXP 13 Newtons ~ (50,000 Kg)(20,000,000 Gs) ~ (50,000 Kg)(200,000,000 meter/(Sec exp 2).

    Now I finally got it right.

    Thanks;

    Jim

  • Doug M. March 15, 2008, 18:20

    Hi Adam,

    The swarm-bot system does (IMHO) have several advantages.

    1) Safety. If an object of 10^19 kg hits the Earth by accident, kiss Earth goodbye. It will vaporize most of the biosphere and kill anything bigger than a bacterium. Other hand, if a swarm of 1 kg rocks hits the atmosphere, you get nothing worse than a rather spectacular meteor shower.

    2) Tunability. Instead of one big orbit-altering momentum transfer every 6,000 years, we have continuous flow. If we allow overrides to modify the rocks’ basic programming, then the momentum transfer can be sped up, slowed down, or even thrown into reverse for a while (say, to put off an inconvenient ice age).

    3) Autonomy. The 6,000-year asteroid flybys must be set up individually. I suppose you could put a long-lived AI in charge, but can you trust it over millions of years? So, this requires a civilization that maintains high technology and continuity of purpose over millions of years.

    The swarm-rocks, on the other hand, are run by simple chips executing a handful of basic commands. Civilizations can rise and fall — hell, humanity can evolve into something else, or leave Earth for somewhere else, or go extinct. Left to their own devices, the trillions of little rocks will continue faithfully carrying out their mission.

    As to collisions, ideally the answer should be “none”. Remember, avoiding impacts is one of the Three Basic Laws. Obviously there will be attrition over time, but it should be pretty tiny.

    Doug M.

  • Adam March 15, 2008, 22:30

    Hi All

    Very low acceleration orbits have a delta-vee of the difference in orbital velocities – so travelling from 1 AU to 1.5 AU is equivalent to travelling from 1.5 AU to 2.5 AU. Problem is that when we get to that stage the Sun is climbing the Red Giant Branch very rapidly – in a billion years it climbs in luminosity from ~2.5 times present day to over 2700 times… then undergoes the Helium Flash (the core explodes, but the burst is expended in heaving the core onto the Helium Main Sequence at a luminosity of ~50 times present day.)

    At the same time the Sun’s solar wind is blowing away about 27.5% of its mass, making the Earth moving job slightly easier. Roughly speaking the Earth needs to be accelerated about 4 times quicker than during the slow expansion from the present day – a not inconsiderable rise in difficulty, but with so many billions of years to prepare it should be pretty straightforward. The enhanced solar wind might be a boon, allowing a plasma sail to provide sufficient thrust at a size of just 7000 km radius…

  • ljk March 18, 2008, 0:18

    Impact cratering and the Oort cloud

    Authors: J.T. Wickramasinghe, W.M. Napier

    (Submitted on 17 Mar 2008)

    Abstract: We calculate the expected flux profile of comets into the planetary system from the Oort cloud arising from Galactic tides and encounters with molecular clouds. We find that both periodic and sporadic bombardment episodes, with amplitudes an order of magnitude above background, occur on characteristic timescales ~25-35 Myr.

    Bombardment episodes occurring preferentially during spiral arm crossings may be responsible both for mass extinctions of life and the transfer of viable microorganisms from the bombarded Earth into the disturbing nebulae. Good agreement is found between the theoretical expectations and the age distribution of large, well-dated terrestrial impact craters of the past 250 million years.

    A weak periodicity of ~36 Myr in the cratering record is consistent with the Sun’s recent passage through the Galactic plane, and implies a central plane density ~0.15 M_Sun pc^(-3). This leaves little room for a significant dark matter component in the disc.

    Subjects: Astrophysics (astro-ph)

    Cite as: arXiv:0803.2492v1 [astro-ph]

    Submission history

    From: Janaki Wickramasinghe [view email]

    [v1] Mon, 17 Mar 2008 17:51:18 GMT (54kb)

    http://arxiv.org/abs/0803.2492

  • ljk September 1, 2009, 21:59

    Engineering the climate

    Geoengineering has so far been something of a taboo topic for climate scientists. Peter Cox and Hazel Jeffery explain why it is now time to take it seriously

    http://physicsworld.com/cws/article/print/40222