Sterling - very well done, indeed. Ted Bunch
On 9/8/10 11:39 AM, "Randy Korotev" <koro...@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" <koro...@wustl.edu> >> To: <meteorite-list@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 >>> >>> ______________________________________________ >>> Visit the Archives at >>> http://www.meteoritecentral.com/mailing-list-archives.html >>> Meteorite-list mailing list >>> Meteorite-list@meteoritecentral.com >>> http://six.pairlist.net/mailman/listinfo/meteorite-list > > ______________________________________________ > Visit the Archives at > http://www.meteoritecentral.com/mailing-list-archives.html > Meteorite-list mailing list > Meteorite-list@meteoritecentral.com > http://six.pairlist.net/mailman/listinfo/meteorite-list ______________________________________________ Visit the Archives at http://www.meteoritecentral.com/mailing-list-archives.html Meteorite-list mailing list Meteorite-list@meteoritecentral.com http://six.pairlist.net/mailman/listinfo/meteorite-list