[meteorite-list] Witnessed fall lunars?

[Ted Bunch]

Sterling - very well done, indeed.

Ted Bunch


On 9/8/10 11:39 AM, "Randy Korotev" <korotev at wustl.edu> wrote:

> Dear Sterling:
> 
> Thanks so much for that enlightening explanation!
> 
> Randy Korotev
> 
> 
> At 10:32 PM 2010-09-07 Tuesday, you wrote:
>> Hi, Lunar Gang, and List,
>> 
>> We have a situation here that needs straightening
>> out.
>> 
>> Escaping from the Moon is one thing. Getting
>> to the Earth is another. Here's how it starts.
>> 
>> An object is propelled off the lunar surface
>> (doesn't matter how). As soon as it's no longer
>> in contact with the force that impelled it, its
>> speed can't increase.
>> 
>> It can decrease, though, and it does. Lunar
>> gravity will pull down on it, reducing its speed
>> at the same rate it would gain if it fell. It goes
>> slower and slower. Eventually, its speed will fall
>> to zero and it will reverse course and start to
>> fall back.
>> 
>> UNLESS its starting velocity is above or at the
>> Moon's escape velocity. It takes 2380 meters/sec
>> to escape to the point 38,000 miles from the Moon's
>> center to where the gravitation pull of the Earth
>> and the Moon are equal. If the rock started with
>> 2381 m/sec, it will get there moving at 1 m/sec,
>> a crawl. After that, the important thing is: which
>> way was it headed?
>> 
>> Surrounding the Moon is a distorted spherical
>> (parabolic) envelope with its "pocket" pointing
>> directly at Earth that outlines that balancing
>> point between the Earth's and the Moon's "pull."
>> It's called the Hill Sphere (for any body). The Hill
>> Sphere, or equipotential point for the Moon, is
>> at a radius of about 38,000 miles, still over 200,000
>> miles from earth.
>> 
>> If a Lunar escapee has enough speed to reach the
>> Moon's Hill Sphere and cross over, it will be under
>> the control of the Earth's gravitational field. The
>> Moon has only 1/81.3 of the mass of the Earth, so
>> the balance point between them is much closer
>> to the Moon than the Earth.
>> 
>> Oh, if it was going very fast, it could escape the
>> Earth too, but the odds against that are great. No,
>> that rock is dam lucky to have made it to the
>> Translunar Gravitational Equipotential Point for
>> its flight.
>> 
>> In general, since Lunar escape velocity is low
>> compared to the Earth's, if a rock just barely escapes,
>> by the time it crosses the Border, it would be moving
>> very slowly, almost standing still. From the viewpoint
>> of the Earth, it's like someone carried a rock 'way out
>> there and while "standing still" far from Earth, dropped it.
>> 
>> Like so many borders, once you cross it, you're in
>> another jurisdiction. The Moon no longer has any
>> say in what happens to the rock that crosses the
>> Hill Sphere Border.
>> 
>> Slowly at first, it begins to fall toward Earth, but it moves
>> faster and faster, eventually acquiring (up to) 11,233
>> meters/sec, plus any starting speed, blah, blah...
>> Will it curve and swerve and head straight for the
>> Earth's central spot?
>> 
>> No, not often. There are a variety of outcomes and
>> few of them will get a rock to land on Earth. Many will
>> end up co-orbiting the Sun along with the Earth and
>> will eventually tangle with the Big Mother Planet again.
>> 
>> Some, that are headed more or less toward the Earth
>> to begin with will scream past in an asymptotic pass,
>> whipping around the Earth, changing direction and
>> picking up speed, in a home grown version of the
>> "gravity well" maneuver. They will tossed far and gone,
>> in a gentler version of what Jupiter does to anything
>> gets near it.
>> 
>> But only if they miss...
>> 
>> Some of those headed our way, a small percentage,
>> will actually "strike" the Earth, or come in at a steep
>> angle. They might survive to the ground... or they
>> might not.
>> 
>> A few, we lucky few, will graze the top of the Earth's
>> atmosphere tangentially, in a flat trajectory roughly
>> parallel to the surface of the planet, at about zero
>> degrees of altitude (relative to us). They will be moving
>> between 11,186 meters/sec and 13,466 meters/sec
>> and their chances of landing are As Good As It Gets.
>> 
>> That's the simple view from Physics 101. It turns out
>> to be more complicated, however.
>> 
>> NOW, we have to turn the question around and look
>> at it from the Moon's and the Rock's perspective. If you're
>> a rock looking to get the Earth, what's the best way to
>> leave home? That will determine what happens to you
>> in the long run.
>> 
>> So, imagine you're an indecisive rock staring at the
>> black Lunar sky... If you aim for where the Earth is
>> NOW, it won't be there when you arrive. so which way
>> do I go?! There are no signposts and no obvious solution...
>> 
>> Now, it's time to introduce you to Barbara E. Shute. Her
>> work can be found at the NASA Technical Reports Server:
>> http://ntrs.nasa.gov/search.jsp?No=10&Ne=35&N=4294963886&Ns=ArchiveName|0&as=
>> false
>> 
>> I suggest "Dynamical behavior of ejecta from the moon.
>> Part I - Initial conditions," a PDF of which can be found at:
>> http://hdl.handle.net/2060/19660021054
>> 
>> It's just what that rock is looking for --- a road map to
>> Earth! However, this is pretty heavy lifting if your orbital
>> mechanics are rusty, like mine, although no doubt Rob
>> Matson will eat it up and ask for please, another bowl, sir?
>> 
>> First, the Moon, OUR Moon, is odd. It's a long way from
>> the Earth and its orbital velocity (1022 m/sec) is much
>> slower than its escape velocity (2380 m/sec), so when
>> a rock does escape the Moon's gravity, it's in for a wild
>> ride, as it's often going too fast or too slow for where it is.
>> 
>> First, to actually escape the Moon, the rock's speed has to
>> be greater than mere escape velocity. Escape velocity will
>> only get you to the Hill Sphere Border. It seems that velocities
>> of 2600 to 2700 meters/sec are needed to actually escape the
>> gravitational environment beyond the Moon's Hill Sphere..
>> 
>> Second, given that you're going fast enough, the one
>> critical factor is the angle at which you leave the Moon's
>> surface. There is one critical angle for each spot on the
>> Moon's surface that guarantees you'll get to Earth if
>> your speed is right. That ideal angle for the minimum
>> possible velocity varies depending on where on the
>> Moon you are, but other angles will do the job if you
>> are going faster.
>> 
>> An intriguing conclusion that it is just as easy to get
>> to the Earth from the "back" side as it is from the "front"
>> (or facing) side. That means that all our breathless
>> speculation about whether a Lunar meteorite COULD
>> have come from the Backside is wasted. It makes
>> NO DIFFERENCE. Each side is an equally likely
>> source.
>> 
>> However, the Eastern Hemisphere is heavily favored, and
>> it seems likely that everything that makes it to the Earth
>> came from the Moon's "East Coast." When the rock leaves
>> the East Hemisphere, its velocity is added to the Moon's
>> orbital velocity. If it's pointed right, it's on a "fast return
>> trajectory" toward the Earth.
>> 
>> But if it pops out of the Moon's gravitational control from
>> the West Hemisphere, it's suddenly running too slowly
>> in a retrograde orbit that can't be sustained. It makes a
>> sharp right turn and crashes back into the Moon's surface
>> and makes a new (smaller) crater!
>> 
>> If Shute's math is too much for you (show of hands?), skip
>> to the charts and diagrams at the end. They make things
>> much clearer. Shute did numerical integrations to sample
>> impacts, ejecta-producing events, and concludes that as
>> much as 3.3% of the ejecta could get to Earth.
>> 
>> Surviving the landing is another matter. (Isn't it always?)
>> After reading this, it's my impression that the Moon likely
>> produces much more material that arrives at the Earth
>> than we usually think it does, and that the short supply
>> of Lunaites is a "collection selection" effect, as has been
>> suggested.
>> 
>> Another impression is that it may only be the more
>> powerful impacts that produce Lunaites. In that case,
>> deliveries to the Earth may only occur at intervals and
>> there may be a multitude of Lunaites delivered from
>> each impact (although they may be scattered), in contrast
>> to the steady rain of meteoroids from far beyond the Earth.
>> 
>> I'm too Googled out to check, but is there "clustering"
>> of the terrestrial ages of Lunaites at irregular intervals?
>> 
>> 
>> Sterling K. Webb
>> -----------------------------------------------------------------------------
>> ----
>> ----- Original Message ----- From: "Randy Korotev" <korotev at wustl.edu>
>> To: <meteorite-list at meteoritecentral.com>
>> Sent: Tuesday, September 07, 2010 4:06 PM
>> Subject: Re: [meteorite-list] Witnessed fall lunars?
>> 
>> 
>>> 
>>>> MikeG asks:
>>> 
>>>> "Is there a theory for why there have been no witnessed falls of lunar
>>>> meteorites?  It seems odd to me that we have 4 Martian witnessed falls
>>>> (Shergotty, Chassigny, Zagami, Nakhla, and almost Lafayette) and no
>>>> lunars."
>>> 
>>> One issue is that these 5 meteorites are 5 kg, 4 kg, 18 kg, 10 kg,
>>> and 0.8 kg in mass.  Only 3 lunars are >4 kg in mass.
>>> 
>>> Another issue (probably more important) is that lunar escape
>>> velocity is only 2.4 km/s and very little material ejected from the
>>> Moon is going much faster than that.  This velocity compares with
>>> 20-40 km/s for asteroidal meteorites.  Is a rock entering the
>>> atmosphere at 2.4 km/s going to noticeably incandesce?  I don't
>>> know.  I believe that the space shuttle hits the atmosphere at ~7.7 km/s.
>>> 
>>> Melanie asks:
>>> 
>>> "I asked this a while ago on Greg Catterton's forum, and I was told
>>> that rocks
>>> from the moon aren't as solid (tough) as Mars rocks, and therefore are less
>>> likely to survive entry... yet what about all these Howardites?"
>>> 
>>> Although breccias, most of the lunar meteorites are very tough
>>> rocks. Any rock that survives being blasted off the Moon isn't
>>> going to disintegrate in Earth's atmosphere any more than an
>>> asteroidal or martian meteorite.
>>> 
>>> Steve says:
>>> "The moon is close to the earth and material knocked off the moon
>>> has a relatively short time to reach the earth."
>>> 
>>> Compared to what?  Some lunar meteorites took a million years or
>>> more to reach Earth.
>>> 
>>> "Mars is farther away and not protected by a companion and its
>>> closer to the asteroid belt so it receives many more impacts than the moon."
>>> 
>>> Not "many more."  Only a factor of two greater for Mars, but the
>>> average velocity of the impactors is only 60% as great.
>>> 
>>> 
>>> 
>>> Randy Korotev
>>> Washington University in St. Louis
>>> 
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