[meteorite-list] "Gravitational focusing"

From: Matson, Robert <ROBERT.D.MATSON_at_meteoritecentral.com>
Date: Thu Apr 22 09:37:32 2004
Message-ID: <AF564D2B9D91D411B9FE00508BF1C8692C5D41_at_US-Torrance.mail.saic.com>

Hi Darryl and list,

On the tektite origin subject, Darryl replied to Jarmo's post:

"A tektite strewnfield is not found scattered all over the earth, due to the
> powerful effect of the earth's gravitional focusing. See page 6332 of :
> Chapman, D. R., 1971, Australasian tektite geographic pattern, crater, and
> ray of origin, and theory of tektite events. J. of Geophys. Res. 76, #26,
> 6309-6338."
Let me start off by saying that I am not an expert on tektites,
so do not yet have a strong opinion as to their likely origin
(though I would say I'm leaning toward an earthly one). But
I *do* have an extensive background in celestial mechanics,
particularly the orbital mechanics associated with the earth's
gravitational field, and I have to say that this statement is
not supported by Keplerian motion laws. Without consulting
the reference, I cannot say whether the journal paper's
conclusions are erroneous, or Darryl's interpretation of them.

Whatever the case, the earth's gravitational field is very nearly
spherically symmetric. If a lunar volcano was to fire ejecta at
or beyond lunar escape velocity in the general direction of the
earth, it is far more likely that these rocks would end up in a
highly elliptical earth orbit (HEO) than on a direct intercept
path. The inclinations of these orbits would be random: some
prograde, some retrograde. The closer the initial trajectory
was to a direct intercept, the lower the perigee height and the
greater the initial eccentricity.

For very low perigee heights, the orbit may decay in a matter
of only weeks or months. For larger perigees, the orbit may
not decay for decades, centuries or even millennia. The point
I'm trying to make is that the ultimate reentry point would
be completely random in longitude, and nearly so in latitude.
(Latitudes closer to the equator are slightly favored over ones
closer to the poles due to the earth's oblateness). So there
are no special locations on the earth that would have a greater
chance of a tektite reentry -- assuming a lunar origin.

What about lunar eruptions directed far enough away from the
earth that they are not captured by earth's gravity? (Such
eruptions would far outnumber those in earth's direction).
These would go into heliocentric orbit, essentially becoming
NEOs. Over time, some of these could eventually get captured by
the earth's gravitational field, while others could be perturbed
into the sun, Venus or Mercury.

In conclusion, I find it very difficult for the Moon to be the
source of tektites given the extremely limited locations in which
they are found. An additional related point: what are the sizes
and geographical shapes of tektite "strewn fields"? Unless they
are highly elliptical, covering hundreds of kilometers in the
long-axis, I would have to pretty much rule out a lunar origin
just from an orbital dynamics standpoint.

I look forward to any comments, corrections or counter-arguments
from our esteemed group. The subject is certainly an interesting

Rob Matson
Received on Tue 05 Dec 2000 09:44:05 PM PST

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