April 2012 - mathfun@mailman.xmission.com

Re: [math-fun] Disk polyominoes
by Allan Wechsler 13 Apr '12

13 Apr '12

A funster who might or might not wish to remain anonymous has corrected me in private. A3 does not equal 2; it equals 1. The corrected sequence is: 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3 ... As before, I'm not entirely confident of the last couple of values. Thank you for the correction.

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Re: [math-fun] [EXTERNAL] Interplanetary microbes?
by Henry Baker 13 Apr '12

13 Apr '12

Superballs hitting one another? At 08:05 AM 4/13/2012, Torgerson, Mark D wrote: >What about multiple roughly simultaneous impacts? > >If the two debris clouds interact violently enough, then there may be lots of collisions at altitude. >Big thing smacks smaller thing(s), momentum transfer, and -bonk- out into space goes something that would never make it on its own. > >None of the colliding bodies would even have to achieve groundside escape velocity.

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[math-fun] interplanetary microbes: strength of ice, rock
by Warren Smith 13 Apr '12

13 Apr '12

Ice: http://www.agu.org/pubs/crossref/1983/JB088iB02p01197.shtml says ice has tensile strength of 17 MPa and frozen mud 21 MPa. "Pykrete" which is frozen ice where the water was mixed with 14% wood pulp or sawdust, is over 4X stronger than plain ice and also less brittle, and if you use newspapers you can make it stronger still ("super pykrete"). Rock tensile strengths http://www.finesoftware.eu/geotechnical-software/help/rock-stability/tensil… for 10 kinds of rock range from 2 to 23 MPa. Typical steel tensile strength is 250 MPa and for high strength steels can be over 1 GPa. So again, the question of whether the Tunguska object was ice or rock seems pretty irrelevant to the fracture question -- and steel is over 10X tougher than either.

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[math-fun] Interplanetary microbes?
by Warren Smith 13 Apr '12

13 Apr '12

Whether the Tunguska object was made mainly of rock, ice, dry ice, frozen mud, or whatever is essentially irrelevant to my questions. Who cares? Either way the temperatures involved at the surface are far larger than the vaporization point and ditto the total energies... The only way in which the composition is relevant is the materials strength and toughness issue. I happen to think a 1000 ton body COULD be ejected from earth in 1 piece if it were made of some very tough stuff like solid steel coated with ablative heat shielding --I think that could survive the initial blast without fragmenting. But 1000 ton chunks of steel are not available naturally on Earth. Whether typical rocks, permafrost, etc could survive it without fragmenting, is the question. They often have low tensile strength and are brittle. I can easily break even tough rocks using only my bare hands to provide the power, and with the aid of huge explosive blasts and for much larger rocks, it should be a lot easier than with my hands and a small rock... The larger the rock, the harder it is to keep it in 1 piece, because the stresses at a given acceleration grow with the size. That is why microbes (small) have no difficulty surviving huge accelerations even though from the materials point of view they are weak. But it is very hard for large objects to survive high accelerations. For example, a microbe easily survives inside a rifle bullet hitting a sandbag, 10^5 to 10^6 g. A human (much larger) usually dies if subjected to a mere 50g. I claim (without evidence) an elephant would usually die if subjected to a mere 10g. Beached whales die (slowly) with only 1g and large whales should die quickly at 3g. Andrei Yu. Ol'khovatov's "tectonic" "explanation" of Tunguska: http://olkhov.narod.ru/tunguska/tunguska.htm sounds to me like utter garbage for a vast number of obvious reasons. The wikipedia page's evidence clearly proves it was large and extraterrestrial and airburst (and it was not an "antimatter bullet" or mini black hole either).

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[math-fun] Interplanetary microbes?
by Warren Smith 13 Apr '12

13 Apr '12

> http://science.slashdot.org/story/12/04/12/0336211/scientists-study-traject… > > Posted by <mailto:samzenpus@slashdot.org>samzenpus on Thursday April > 12, @08:07AM > from the we-come-from-earth dept. > <http://honorewmarland.com/>Hugh Pickens writes "About 65 million > years ago, Earth was struck by an asteroid some 10 km in diameter > with a mass of well over a trillion tonnes that created megatsunamis, > global wildfires ignited by giant clouds of superheated ash, and the > mass extinction of land-based life on Earth. Now astrobiologists have > begun to study a less well known consequence: the ejection of > billions of tons of life-bearing rocks and water into space that has > made its way not just to other planets but other solar systems as > well. Calculations by Tetsuya Hara and his colleagues at Kyoto Sangyo > University in Japan show that a surprisingly large amount of > life-bearing material ended up not on the Moon and Mars, as might be > expected, but the > <http://www.technologyreview.com/blog/arxiv/27720/>Jovian moon Europa > and the Saturnian moon Enceladus also received tons of life-bearing > rock from earth. Even more amazingly, calculations suggest that most > Earth ejecta ended up in interstellar space and some has probably > already arrived at Earth-like exoplanets orbiting other stars. Hara > estimates that about a thousand Earth-rocks from this event would > have made the trip to Gliese 581, a red dwarf some 20 light years > away that is thought to > <http://www.time.com/time/health/article/0,8599,2022489,00.html>have > a super-Earth orbiting at the edge of the habitable zone, taking > about a million years to reach its destination. Of course, nobody > knows if microbes can survive that kind of journey or even the > shorter trips to Europa and Enceladus. But Hara says that if microbes > can survive that kind of journey, they > <http://journalofcosmology.com/PanspermiaHara.pdf>ought to flourish > on a super-Earth in the habitable zone (PDF). ... --this all sounds like total garbage to me. There is no way the simulators could know a lot of important input info which would have completely changed their results.

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[math-fun] Scientists Study Trajectories of Life-Bearing Earth Meteorites
by Ray Tayek 12 Apr '12

12 Apr '12

http://science.slashdot.org/story/12/04/12/0336211/scientists-study-traject… Posted by <mailto:samzenpus@slashdot.org>samzenpus on Thursday April 12, @08:07AM from the we-come-from-earth dept. <http://honorewmarland.com/>Hugh Pickens writes "About 65 million years ago, Earth was struck by an asteroid some 10 km in diameter with a mass of well over a trillion tonnes that created megatsunamis, global wildfires ignited by giant clouds of superheated ash, and the mass extinction of land-based life on Earth. Now astrobiologists have begun to study a less well known consequence: the ejection of billions of tons of life-bearing rocks and water into space that has made its way not just to other planets but other solar systems as well. Calculations by Tetsuya Hara and his colleagues at Kyoto Sangyo University in Japan show that a surprisingly large amount of life-bearing material ended up not on the Moon and Mars, as might be expected, but the <http://www.technologyreview.com/blog/arxiv/27720/>Jovian moon Europa and the Saturnian moon Enceladus also received tons of life-bearing rock from earth. Even more amazingly, calculations suggest that most Earth ejecta ended up in interstellar space and some has probably already arrived at Earth-like exoplanets orbiting other stars. Hara estimates that about a thousand Earth-rocks from this event would have made the trip to Gliese 581, a red dwarf some 20 light years away that is thought to <http://www.time.com/time/health/article/0,8599,2022489,00.html>have a super-Earth orbiting at the edge of the habitable zone, taking about a million years to reach its destination. Of course, nobody knows if microbes can survive that kind of journey or even the shorter trips to Europa and Enceladus. But Hara says that if microbes can survive that kind of journey, they <http://journalofcosmology.com/PanspermiaHara.pdf>ought to flourish on a super-Earth in the habitable zone (PDF). 'If we consider the possibility that the fragmented ejecta (smaller than 1cm) are accreted to comets and other icy bodies, then buried fertile material could make the interstellar journey throughout the Galaxy,' writes Hara. 'Under these circumstances fragments could continue the interstellar journey and Earth origin meteorites could be transferred to Gl 581 system. If we take it as viable, we should consider the <https://en.wikipedia.org/wiki/Panspermia>panspermia theories more seriously.'" --- co-chair http://ocjug.org/

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[math-fun] interplanetary microbes
by Warren Smith 11 Apr '12

11 Apr '12

Another problem is the following. As we saw, to get ejected from Earth, a rock needs to be at least 8 tons, probably 1000 tons, and it has to be tough to survive initial acceleration blast without fragmenting below this size. OK, so say we succeed in ejecting a rock that big and tough. Its misison is now to spread life to Mars. But a rock big and tough enough to traverse Earth atmosphere without losing much speed & staying in 1 piece, is easily big & tough enough to do same to the puny Martian atmosphere. Hence it will hit Mars surface at at least Martian escape velocity 5 km/sec. A 30-dalton atom at 5 km/sec has temperature 30,000 Kelvin from (3/2)*kB*T = m*v^2/2, where m=mass, v=veloc, kB=Boltzmann const, T=temp.. Hence the rock would be heated on impact enough to vaporize, or at least enough to sterilize. Failure. So the only way to get Earth-->Mars panspermia is for a big tough rock to get ejected from Earth (improbable?) then while in transit in interplanetary space it needs to get hit by another rock (improbable) thus splitting off smaller chunks. Those chuinsk need to be small enough to get slowed down by Mars atmosphere, but not so small that Mars atmosphere will destroy the chunk -- then THOSE chunks need to land on Mars. This mechanism is way more improbable than what Melosh talked about. So, I think Melosh had not thought it through enough, sorry. On 4/11/12, math-fun-request(a)mailman.xmission.com <math-fun-request(a)mailman.xmission.com> wrote: > Send math-fun mailing list submissions to > math-fun(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > or, via email, send a message with subject or body 'help' to > math-fun-request(a)mailman.xmission.com > > You can reach the person managing the list at > math-fun-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of math-fun digest..." > > > Today's Topics: > > 1. meteorites (Bill Gosper) > 2. Re: meteorites (rcs(a)xmission.com) > 3. Re: Fwd: Re: generalized law of cosines (rcs(a)xmission.com) > 4. Fwd: R.I.P. Tom Rodgers (rcs(a)xmission.com) > 5. Re: Fwd: R.I.P. Tom Rodgers (Thane Plambeck) > 6. Re: meteorites (Henry Baker) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Tue, 10 Apr 2012 13:11:22 -0700 > From: Bill Gosper <billgosper(a)gmail.com> > To: math-fun(a)mailman.xmission.com > Subject: [math-fun] meteorites > Message-ID: > <CAA-4O0E8pzXOZG4wf5bGqhc1qV1xBKQcvpOe8HDTVCm95rEsHQ(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > Warren>Here is the situation: A. meteor falls in at somewhat more than > escape velocity, perhaps as much as 1.5X escape. > > > This was Barringer's delusion. Stuff is falling in toward the *Sun*, > 42.1km/s =rt2*Earth orbital speed, vs 11.2km/s Earth escape speed. > > So his impactor was (42.1/11.2)^2 ~ 14 times less massive than he > thought, and was largely vaporized on impact. > Then he had the great misfortune to discover that angled impacts make > round craters, and drilled fruitlessly on. > > --rwg > > > ------------------------------ > > Message: 2 > Date: Tue, 10 Apr 2012 19:22:51 -0600 > From: rcs(a)xmission.com > To: math-fun(a)mailman.xmission.com > Cc: rcs(a)xmission.com > Subject: Re: [math-fun] meteorites > Message-ID: <20120410192251.tre0mjutjlwccoow(a)webmail.xmission.com> > Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; > format="flowed" > > Something coming in headon would enter at 25+18 = 43 mi/sec. > > Warren, in your guestimate of the sphere thickness required to > escape Venus: the thickness should vary linearly with the surface > atmospheric pressure. IIRC, Venus's is ~90 atmospheres. > > The Earth's surface pressure is about 30 inches of mercury, so a > skybound 4" thick steel plate will be facing quite a headwind. > > I think the most interesting thing about this is that a good fraction > of stuff that escapes into interplanetary space will eventually be > ejected into interstellar space. So we're broadcasting a wake of > bacterial DNA, and should expect some amount of incoming material. > I may be out of date, but my impression is that no confirmed extra-solar > meteorite has been found. > > Rich > > ------ > Quoting Bill Gosper <billgosper(a)gmail.com>: > >> Warren>Here is the situation: A. meteor falls in at somewhat more than >> escape velocity, perhaps as much as 1.5X escape. >> >> >> This was Barringer's delusion. Stuff is falling in toward the *Sun*, >> 42.1km/s =rt2*Earth orbital speed, vs 11.2km/s Earth escape speed. >> >> So his impactor was (42.1/11.2)^2 ~ 14 times less massive than he >> thought, and was largely vaporized on impact. >> Then he had the great misfortune to discover that angled impacts make >> round craters, and drilled fruitlessly on. >> >> --rwg >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> > > > > > > ------------------------------ > > Message: 3 > Date: Tue, 10 Apr 2012 19:35:23 -0600 > From: rcs(a)xmission.com > To: math-fun(a)mailman.xmission.com > Cc: Bill Gosper <billgosper(a)gmail.com>, rcs(a)xmission.com > Subject: Re: [math-fun] Fwd: Re: generalized law of cosines > Message-ID: <20120410193523.dkj0lmr9ico8c40o(a)webmail.xmission.com> > Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; > format="flowed" > > Gosper, re your Brama-tangent remark below: > > looking at it another way, both triangles & quads satisfy > sum of tans = sum of products of 3 tans. > > This looks like it could generalize further, to something like > sum of tans > - sum of products of 3 tans > + sum of products of 5 tans -+ ... = 0 > Of course, the LHS is the numerator of the tangent addition formula. > And the sum of the interior angles of a polygon is ... > > Rich > > ------ > Quoting Bill Gosper <billgosper(a)gmail.com>: > >> Fred>On 4/7/12, rcs(a)xmission.com >> <http://gosper.org/webmail/src/compose.php?send_to=rcs%40xmission.com> >> <rcs(a)xmission.com >> <http://gosper.org/webmail/src/compose.php?send_to=rcs%40xmission.com>> >> wrote:> ...> The final comment about splitting up the sides other >> than> 1 vs N-1 should give a very simple 2-2 formula for >> quadrilaterals,> and could lead to an angle-free formula relating the >> lengths> of the sides and the diagonals. Presumably this would give> >> the 2nd diagonal as a quadratic in the 4 sides and the first> >> diagonal. And there's likely something pretty involving the> sides of >> a pentagon and the "inscribed star".>> Rich> >> >> The relation between the sides and diagonals of a plane quadrilateral >> is that the volume of the tetrahedron with those edge-lengths vanishes. >> The volume is given by the Cayley-Menger determinant for 3-space, >> a cubic in the squares of the edge-lengths. See eg. >> >> http://en.wikipedia.org/wiki/Distance_geometry >> >> [I know most of you have heard all this before several times --- >> Rich obviously wasn't paying attention.] >> >> WFL >> >> See also: >> http://en.wikipedia.org/wiki/Brahmagupta%27s_formula#Extension_to_non-cycli… >> >> --rwg >> >> Something is wrong with either my math-fun archive or Apple's >> Finder|Spotlight. I can't find >> >> any references to "Brahmag" despite, e.g., my (2008?) >> >> subj: any noun can be verbed >> "Everybody" knows that, given any triangle, the sum of the angle tangents >> equals >> their product. This "Brahmagupts" into >> Given any quadrilateral, the sum of the angle tangents equals their >> product times the sum of the cotangents. Can't be new. But probably >> newer >> than Brahmagupta, since, even for trapezoids, it just says 0=0. >> --rwg >> >> which I found in a scratch file. >> >> "extremely ingenious" erratum: I miscopied more modern values for Euler's >> Bessel roots, >> >> which were considerably less accurate. Simply manually evaluating Bessel >> functions must >> >> have been so tedious as to discourage Newton's method. >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> > > > > > > ------------------------------ > > Message: 4 > Date: Tue, 10 Apr 2012 19:43:55 -0600 > From: rcs(a)xmission.com > To: math-fun(a)mailman.xmission.com > Cc: rcs(a)xmission.com > Subject: [math-fun] Fwd: R.I.P. Tom Rodgers > Message-ID: <20120410194355.5puzl1ldc04oo0k4(a)webmail.xmission.com> > Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; > format="flowed" > > via Jeannine Mosely <j9mosely(a)gmail.com>. > I've dropped the picture, to respect our 40KB size limit. > Contact me or Jeannine for an individual copy. --Rich > > ------- > Date: Tue, 10 Apr 2012 21:25:22 -0400 > Subject: Fwd: R.I.P. Tom Rodgers > From: Jeannine Mosely <j9mosely(a)gmail.com> > To: math-fun <math-fun(a)mailman.xmission.com> > > Many of you will have received this message already. For those who > don't know, Tom was the principal organizer of the bi-annual > Gatherings for Gardner. He will be missed. > > -- Jeannine Mosely > > > ---------- Forwarded message ---------- > From: tom rodgers <thomasmrodgers(a)gmail.com> > Date: Tue, Apr 10, 2012 at 6:59 PM > Subject: R.I.P. Tom Rodgers > To: > > > Dearest Friends and Family, > > Today at 6:12pm , Thomas Malin Rodgers Jr. passed away after a valiant > struggle with cancer. He fought like a bear till the very end. We, > the family, would like to thank everyone for their thoughts, prayers, > and help during his last days. > > Per Tom's request there will be no funeral service or burial. He is > to be cremated with his ashes distributed amongst his family. Please > feel free to celebrate Tom's life in your own way as no formal event > will occur. > > In lieu of flowers please consider donating to Tom's passion, The > Gathering 4 Gardner foundation. Please send checks payable to > "Gathering 4 Gardner, Inc" to the address below. > > Gathering 4 Gardner > C/O Scott Hudson, Secretary-Treasurer > 5475 Fulton Industrial Blvd. > Atlanta, GA 30336 > > Please forward this message along as you see fit. Tom had a diversity > of friends and interests. If we missed someone we apologize. > > Thank You, > The Rodgers > > P.S. For your enjoyment we have attached his rarely seen Senior > Yearbook photo from 1961. > > > > > > ------------------------------ > > Message: 5 > Date: Tue, 10 Apr 2012 18:46:25 -0700 > From: Thane Plambeck <tplambeck(a)gmail.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Cc: rcs(a)xmission.com > Subject: Re: [math-fun] Fwd: R.I.P. Tom Rodgers > Message-ID: > <CAKr6Liso1B==0t1kS=ZoGJfE3saCB35OzAcEApc5Peb5=-V74A(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > I've reposted the email and photo of Tom Rodgers (from his 1961 high > school yearbook) here > > http://www.flickr.com/photos/thane/6920012754/in/photostream > > On Tue, Apr 10, 2012 at 6:43 PM, <rcs(a)xmission.com> wrote: >> via Jeannine Mosely <j9mosely(a)gmail.com>. >> I've dropped the picture, to respect our 40KB size limit. >> Contact me or Jeannine for an individual copy. ?--Rich >> >> ------- >> Date: Tue, 10 Apr 2012 21:25:22 -0400 >> Subject: Fwd: R.I.P. Tom Rodgers >> From: Jeannine Mosely <j9mosely(a)gmail.com> >> To: math-fun <math-fun(a)mailman.xmission.com> >> >> Many of you will have received this message already. ?For those who >> don't know, Tom was the principal organizer of the bi-annual >> Gatherings for Gardner. ?He will be missed. >> >> -- Jeannine Mosely >> >> >> ---------- Forwarded message ---------- >> From: tom rodgers <thomasmrodgers(a)gmail.com> >> Date: Tue, Apr 10, 2012 at 6:59 PM >> Subject: R.I.P. Tom Rodgers >> To: >> >> >> Dearest Friends and Family, >> >> Today at 6:12pm , Thomas Malin Rodgers Jr. passed away after a valiant >> struggle with cancer. ?He fought like a bear till the very end. ?We, >> the family, would like to thank everyone for their thoughts, prayers, >> and help during his last days. >> >> Per Tom's request there will be no funeral service or burial. ?He is >> to be cremated with his ashes distributed amongst his family. ?Please >> feel free to celebrate Tom's life in your own way as no formal event >> will occur. >> >> In lieu of flowers please consider donating to Tom's passion, The >> Gathering 4 Gardner foundation. ?Please send checks payable to >> "Gathering 4 Gardner, Inc" to the address below. >> >> Gathering 4 Gardner >> C/O Scott Hudson, Secretary-Treasurer >> 5475 Fulton Industrial Blvd. >> Atlanta, GA 30336 >> >> Please forward this message along as you see fit. Tom had a diversity >> of friends and interests. ?If we missed someone we apologize. >> >> Thank You, >> The Rodgers >> >> P.S. ?For your enjoyment we have attached his rarely seen Senior >> Yearbook photo from 1961. >> >> >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > -- > Thane Plambeck > tplambeck(a)gmail.com > http://counterwave.com/ > > > > ------------------------------ > > Message: 6 > Date: Tue, 10 Apr 2012 21:12:00 -0700 > From: Henry Baker <hbaker1(a)pipeline.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] meteorites > Message-ID: <E1SHp38-0003VE-Hi(a)elasmtp-spurfowl.atl.sa.earthlink.net> > Content-Type: text/plain; charset="us-ascii" > > The Earth's atmospheric density falls off roughly exponentially, with > the 1/2 point around 19,000'. So if a body going upwards makes it to > this altitude, it has a much better chance of making it out. > > It isn't very likely, but if a meteor hit the top of a high mountain, > the atmosphere wouldn't be nearly the same problem for ejected material. > > I don't know the details of an impact explosion, but I would expect that > the radiation pulse travelling at some fraction of the vacuum speed of light > would heat up the atmosphere well ahead of any solid body being ejected, > so that the density encountered would be far less than normal. This is > analogous to the "Russian torpedo" effect I referred to previously. > > For example, on hot, humid summer days, it is much harder for airplanes > to fly, because the air is significantly less dense. What if the > temperature > were several thousand degrees instead of 100F ? > > At 06:22 PM 4/10/2012, rcs(a)xmission.com wrote: >>Something coming in headon would enter at 25+18 = 43 mi/sec. >> >>Warren, in your guestimate of the sphere thickness required to >>escape Venus: the thickness should vary linearly with the surface >>atmospheric pressure. IIRC, Venus's is ~90 atmospheres. >> >>The Earth's surface pressure is about 30 inches of mercury, so a >>skybound 4" thick steel plate will be facing quite a headwind. >> >>I think the most interesting thing about this is that a good fraction >>of stuff that escapes into interplanetary space will eventually be >>ejected into interstellar space. So we're broadcasting a wake of >>bacterial DNA, and should expect some amount of incoming material. >>I may be out of date, but my impression is that no confirmed extra-solar >>meteorite has been found. >> >>Rich >> >>------ >>Quoting Bill Gosper <billgosper(a)gmail.com>: >> >>>Warren>Here is the situation: A. meteor falls in at somewhat more than >>>escape velocity, perhaps as much as 1.5X escape. >>> >>>This was Barringer's delusion. Stuff is falling in toward the *Sun*, >>>42.1km/s =rt2*Earth orbital speed, vs 11.2km/s Earth escape speed. >>> >>>So his impactor was (42.1/11.2)^2 ~ 14 times less massive than he >>>thought, and was largely vaporized on impact. >>>Then he had the great misfortune to discover that angled impacts make >>>round craters, and drilled fruitlessly on. >>> >>>--rwg > > > > > ------------------------------ > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > End of math-fun Digest, Vol 110, Issue 12 > ***************************************** > -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html

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Re: [math-fun] Interplanetary microbes?
by Henry Baker 11 Apr '12

11 Apr '12

I already sent Warren a paper that Melosh sent me that addresses this issue to some extent. This is the basis of Melosh's conclusion that a significant % of such ejecta may eventually make it into interstellar space. There has been a huge amount of work on the early orbital evolution of the solar system. These simulations seem to indicate that the evolution of many of the planet types -- including a "Jupiter", an asteroid belt, Earth-size rocky planets like Venus & Earth, isn't such a rare thing. You are right; close encounters with Jupiter & the Sun send a lot of early planet wannabes packing into interstellar space. Some end up in extremely elliptical orbits, with periods in the hundreds and possibly thousands of years. There are now many, many simulations of the first 150 million years of our solar system because -- among other reasons -- it apparently took that long for the Earth's Moon to get into position and for most things to settle down into more-or-less the current configuration. Michele Trenti has done a lot of work on gravitational simulations: http://casa.colorado.edu/~trenti/home/highz.html http://www.ast.cam.ac.uk/~trenti/ At 08:50 AM 4/11/2012, Warren Smith wrote: >To eject stuff from not just earth, but in fact whole solar system, you'd >probably need help from "slingshot" effects around planets like Jupiter. >Is it really true system ejection is common? How do you know it is, if it is? > >There are observation-based claims that there are a ton of "rogue >planets" (more than the number of stars) wandering round the galaxy, >which were ejected from their systems by such effects. So it seems >plausible 10% of stuff inserted into the solar system in a "random >orbit" is ultimately ejected. But trying to justify such an estimate >mathematically or computationally might be very difficult, since the >ejection process could take 100M years.

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[math-fun] Computational complexity of physics
by Warren Smith 11 Apr '12

11 Apr '12

> But trying to justify such an estimate [10% solar system ejection rate?] > mathematically or computationally might be very difficult, since the > ejection process could take 100M years. --To put it another way, it is somewhat like the Turing halting problem. If your computer simulates some orbit for a few Myears, how does it know whether body will be ejected? If ejected, it knows. If not, then computer still does not know whether will be ejected later. Perhaps it can prove a theorem some orbit is stable? A paper by me of a related topic is Church's Thesis Meets the N-body Problem #21 here http://rangevoting.org/WarrenSmithPages/homepage/works.html in which I showed more strongly that Newton's laws of motion+gravity for point particles are UNSIMULABLE in the sense that if you have a Turing machine and it has input tapes giving the initial velocities, positions, masses of N bodies to infinite # decimal places, then if you ask machine "will body 5 enter the following spherical region xxxx in the next hour, or will it never enter the concentric 2X larger sphere even in 2 hours (I promise it will do one of these 2 things and there will never be a collision)?" then it is IMPOSSIBLE for any algorithm to answer question no matter how much simulation time. Furthermore, the trajectories of the bodies in the next hour can have "infinite descriptive complexity" and resemble/encode an arbitrary Turing machine infinite computation. This was part of a research program by me if trying to assess computational complexity of different physics theories; I succeeded in the case of Newton laws. Amazingly, quantum mechanics was found in a sense to be EASIER to simulate than classical mechanics... see paper #49, also a success... and for a partial success see paper #58 on hydrodynamics. The simulability of more advanced theories such as general relativity remains completely open.

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[math-fun] Interplanetary microbes?
by Warren Smith 11 Apr '12

11 Apr '12

Re meteors, sorry, I used the wrong number for Venus atm. pressure, it should have been 90 atm, not 600 atm. Anyhow, same conclusion: I think it is going to be extremely difficult to eject anything from Venus. > Warren>Here is the situation: A. meteor falls in at somewhat more than > escape velocity, perhaps as much as 1.5X escape. > > > This was Barringer's delusion. Stuff is falling in toward the *Sun*, > 42.1km/s =rt2*Earth orbital speed, vs 11.2km/s Earth escape speed. > > So his impactor was (42.1/11.2)^2 ~ 14 times less massive than he > thought, and was largely vaporized on impact. > Then he had the great misfortune to discover that angled impacts make > round craters, and drilled fruitlessly on. --Aha. OK, good, that corrects another error by me. So a large body hitting earth (1000 tons or more) could so so at sqrt(42.1^2 + 11.2^2) = 43.6 km/sec if it came in from cometary regions. If interstellar even faster speed possible under pessimal circumstances, as large as 73km/sec. I However, I think most things that hit us are co-orbiting the sun in orbits not hugely dissimilar to the Earth's orbit, hence would hit at more like 15 km/sec. --Another error (or rather omission) I made -- which might rescue Melosh to some extent, is this. I argued that if large stuff (8-1000 tons) was unable to be ejected without first being fractured into smaller stuff, then it would be unable to be ejected, period. However, an "escape clause" could be this. Suppose something huge like a mountain is accelerated roughly upward at 100000gs to 150% escape velocity and also at the same time fractured into gravel. Then the atmosphere might not NOTICE that it was gravel until it got 20 km up since not separated enough. This "swarm effect" might be enough, anyhow it is not obvious to me how much help it provides. (The whole slowdown effect is exponential and whence will exhibit a fairly sharp size threshhold...) > The Earth's surface pressure is about 30 inches of mercury, so a > skybound 4" thick steel plate will be facing quite a headwind. --exactly. > On a mountain, lower atmospheric pressure. --true, not a very big help though. > I think the most interesting thing about this is that a good fraction > of stuff that escapes into interplanetary space will eventually be > ejected into interstellar space. So we're broadcasting a wake of > bacterial DNA, and should expect some amount of incoming material. > I may be out of date, but my impression is that no confirmed extra-solar > meteorite has been found. --here is a 1996 paper http://articles.adsabs.harvard.edu/full/1997JRASC..91...68H which says interstellars are rare and maybe nonexistent. To eject stuff from not just earth, but in fact whole solar system, you'd probably need help from "slingshot" effects around planets like Jupiter. Is it really true system ejection is common? How do you know it is, if it is? There are observation-based claims that there are a ton of "rogue planets" (more than the number of stars) wandering round the galaxy, which were ejected from their systems by such effects. So it seems plausible 10% of stuff inserted into the solar system in a "random orbit" is ultimately ejected. But trying to justify such an estimate mathematically or computationally might be very difficult, since the ejection process could take 100M years.

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