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@mailman.xmission.com <math-fun-request@mailman.xmission.com> wrote:

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Today's Topics:

1. meteorites (Bill Gosper) 2. Re: meteorites (rcs@xmission.com) 3. Re: Fwd: Re: generalized law of cosines (rcs@xmission.com) 4. Fwd: R.I.P. Tom Rodgers (rcs@xmission.com) 5. Re: Fwd: R.I.P. Tom Rodgers (Thane Plambeck) 6. Re: meteorites (Henry Baker)

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Message: 1 Date: Tue, 10 Apr 2012 13:11:22 -0700 From: Bill Gosper <billgosper@gmail.com> To: math-fun@mailman.xmission.com Subject: [math-fun] meteorites Message-ID: <CAA-4O0E8pzXOZG4wf5bGqhc1qV1xBKQcvpOe8HDTVCm95rEsHQ@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@xmission.com To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: Re: [math-fun] meteorites Message-ID: <20120410192251.tre0mjutjlwccoow@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@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@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Message: 3 Date: Tue, 10 Apr 2012 19:35:23 -0600 From: rcs@xmission.com To: math-fun@mailman.xmission.com Cc: Bill Gosper <billgosper@gmail.com>, rcs@xmission.com Subject: Re: [math-fun] Fwd: Re: generalized law of cosines Message-ID: <20120410193523.dkj0lmr9ico8c40o@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@gmail.com>:

...

Fred>On 4/7/12, rcs@xmission.com <http://gosper.org/webmail/src/compose.php?send_to=rcs%40xmission.com> <rcs@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-cyclic...

--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@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@xmission.com To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: [math-fun] Fwd: R.I.P. Tom Rodgers Message-ID: <20120410194355.5puzl1ldc04oo0k4@webmail.xmission.com> Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; format="flowed"

via Jeannine Mosely <j9mosely@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@gmail.com> To: math-fun <math-fun@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@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@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Cc: rcs@xmission.com Subject: Re: [math-fun] Fwd: R.I.P. Tom Rodgers Message-ID: <CAKr6Liso1B==0t1kS=ZoGJfE3saCB35OzAcEApc5Peb5=-V74A@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@xmission.com> wrote:

...

via Jeannine Mosely <j9mosely@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@gmail.com> To: math-fun <math-fun@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@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@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/

------------------------------

Message: 6 Date: Tue, 10 Apr 2012 21:12:00 -0700 From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] meteorites Message-ID: <E1SHp38-0003VE-Hi@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@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@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

------------------------------

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End of math-fun Digest, Vol 110, Issue 12 *****************************************

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