[meteorite-list] FW: Lunar origin of tektites

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Sat Mar 26 11:04:12 2005
Message-ID: <42458785.F1957544_at_bhil.com>

Hi, Rob, List,

    I haven't crunched a number in nearly forty years, which is why I
unhesitatingly accept Rob's million simulations (as saving a lot of work).

but the logic of the situation alone shows why it's unlikely that tektites

could not have come from the Moon.
    Picture the moon in a paraboloidal pocket stuck nose-first into the
earth's gravity field. The center point of the paraboloid is where the
lunar and terrestrial gravity fields are equal and opposite, also known
as the L1 LaGrange point. The surface of the paraboloid is the null
sheet defined by all the points where the two fields balance, except
that all the other points except the central one have a small vector
directed toward the central point.
    If an object reached the null sheet with almost no residual
velocity, it would fall toward the earth, depending on the direction of
its vector, accelerating toward the local escape velocity, which is just
a hair less than the complete escape velocity of 11,200 m/sec, because
while 320,000 km away is a long way, it isn't infinity. The hair less is
maybe 20-25 m/sec (ok, I didn't stop to calculate it, but it's like less
than highway speeds).
    But if the object arrives at the null sheet with a small excess
velocity, say 50 m/sec, which is nevertheless greater than that "hair
less" velocity, then when it's accelerated toward the earth, it will
achieve more than earth's escape velocity (the square root of the sum of
the squares of the excess velocity and the local escape velocity).
    If that object missed the earth (and its atmosphere), it would leave
the earth-moon system on a "no-return trajectory." (These are the last
words you want to hear if the object is a capsule with you in it!)
    So, if objects are ejected from the moon's surface with less than
lunar escape velocity, they will fall back. If objects are ejected from
the moon's surface with more than a tiny excess velocity, they're gone.
Only a very, very small percentage of objects, with a small range of
low excess velocities will remain gravitationally bound to the
earth-moon system. All of these will eventually get to the earth (or its
atmosphere) because any object orbiting the earth with a semi-major axis
less than the moon's will be perturbed in eccentricity until its apogee
is lowered into the earth's atmosphere.
    I know, the moon is just hanging there over the earth. Common
"sense" (earthbound human inituition) says things just ought to fall
down. But the truth is it's not the easiest thing to jump off the moon
and land on the earth. I would estimate that <1% of lunar ejecta would
make it to the earth through the mechanism of a gravitationally bound
orbit.
    What about the rock that got away? That lucky rock, off on its own
heliocentric orbit, is in for a nasty surprise. Its orbit is virtually
the same as the earth's orbit. One lousy little rock sharing a nearly
identical orbit with a planet; it's like sleeping in the same bed with a
12,000 pound bear. Chances are good the bear will roll over in its
sleep. Most "escapees" (more than 50%) will be swept up by the earth
sooner or later, 10,000 years or more. Some (15%) will end up at the
Venus station. The fastest escapees will be the hardest to catch.
    The survivors will get their own heliocentric orbit, however whacky,
most by achieving an orbit close enough to a very minor resonance with
Jupiter to get nudged out of the way, but Jupiter is likely to toss them
anywhere. A really tiny percentage (<0.1%) will end up on Mars (with a
transit time of up to 50,000,000 years), where they will, in the future,
be auctioned off on mBay by dealers who bought them in the bazaars on
the edge of the Vastitas Borealis.

Sterling Webb
--------------------------------------------
"Matson, Robert" wrote:

> Hi Doug and List,
>
> Some of you (most of you?) are probably already aware of my position
> on the lunar origin of tektites, but for those who don't I'll throw
> in my two cents from the dynamics standpoint. Short answer: no dice.
>
> Years ago I didn't have an opinion or a vested interest one way or
> the other -- I was honestly curious if the lunar origin could be
> dynamically supported. So I modeled it and ran millions of Monte
> Carlo simulations to see where either volcanic or lunar impact
> ejecta material would end up. The answer is: if an intercept is
> possible, it rains down on more than a hemisphere of the earth (as
> well as significant portions either back on the Moon or in solar
> orbit). There is no natural way to favor a geographic region on
> the earth when the Keplerian trajectory origin is on the Moon. The
> angular tolerances are just too tight.
>
> Lunar volcanism is an even more restrictive case since it requires
> the initial velocity vector to not only deviate significantly from
> the local lunar zenith direction, but in exactly the correct direction
> for an earth intercept. Anything other than a direct intercept
> path on a pencil-thin beam results in tektites scattered over more
> than a hemisphere.
>
> > I am eating up Norm's comment that some bona fide Indochinite
> > researcher out there (an endangered species), is mulling over the
> > possibility of Lunar origin for Indochinites as this is EXACTLY
> > what I was implying in my last post about all glass not being
> > equal and a certain tektite not-so-hypothetically being proven
> > to be of Lunar origin.
>
> Not one researcher has offered a scenario by which a lunar impact
> results in tektites scattered on the earth in not only a limited
> geographic area, but with a non-elliptical pattern. The earth is
> a tiny enough target from the Moon's distance; to generate the
> limited (and non-elliptical) distribution of tektite finds requires
> a reasonable dynamic mechanism. None has been offered that can
> be mathematically reproduced.
>
> Norm wrote:
>
> > ... Dean Chapman's 1971 article in the Journal of Geophysical
> > Research ... looked at australasian distribution patterns and
> > demonstrated that they are consistent with theoretical
> > distributions of ejecta from a particular ray of crater Tycho
> > is more than a statement of opinion.
>
> I studied the special case of Tycho precisely because of Chapman's
> paper. Ignoring for the moment that the Tycho crater is believed
> to be about 100 million years old, I found the results irreproduce-
> able. Would love to see Chapman's source code to see what assumptions
> he made, but based on the lunar latitude and longitude of Tycho,
> and the azimuth angle of the Rosse ray, I do not come up with a
> direct intercept solution for the earth, no matter what one chooses
> for the local lunar elevation angle and initial velocity of the
> tektite precursor fragments.
>
> --Rob
>
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Received on Sat 26 Mar 2005 11:02:13 AM PST