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ALH84001 is a famous meteorite found in Antarctica. Scientists have since claimed that (1) this meteorite came from Mars (along with several other meteorites), and (2) that it contained evidence of life.

The focus here is on the first claim, that the rock comes from Mars.

A game of cosmic pinball is involved. The rocks have to escape Mars gravity by some event, orbit around in space, and hit Earth before hitting something else.

The NASA website explanation seems to be, more or less, "gas bubbles":

How do we know the meteorite came from Mars?

Meteorite ALH84001 is a softball-sized igneous rock weighing 1.9 kilograms (4.2 pounds). It is one of twelve meteorites discovered on Earth which are thought to be from Mars. Most meteorites formed early in the history of the solar system, some 4.6 billion years ago. Eleven of the twelve martian meteorites have ages less than 1.3 billion years, ALH84001 at 4.5 billion years old being the only exception. All twelve are igneous rocks crystallized from molten magma in a way which suggests they formed in a planetary-sized body, not an asteroid. They have similar oxygen isotope characteristics to each other and higher concentrations of ferric iron, water, and other volatiles than other meteorites. All twelve also show evidence of shock heating, presumably as a result of the impact which ejected them into space. Gas bubbles trapped in one meteorite, EETA79001, have a composition which matches the current martian atmosphere as measured by the Viking Landers, compelling evidence that this meteorite and by association the others, including ALH84001, came from Mars

An article in Wired http://www.wired.com/wiredscience/2010/04/allan-hills-meteorite-age/ notes that the estimated age of the rock had to be adjusted in light of new evidence.

Why does it matter that the gas in the meteorite matches a modern Martian atmosphere if the rock was ejected from Mars in a cataclysm over a billion years ago? Would the atmosphere still be the same? Aren't there other solar system objects, such as comets, that contain gas whose composition we either haven't yet observed, or whose gas might otherwise mimic what scientists saw in the Mars probe observations? As a meteorite enters Earth's atmosphere, isn't it subject to thermal stresses that could produce or change gas bubbles?

Since we now have rovers on Mars whose primary job is to examine rocks, shouldn't there be more evidence when comparing the meteorites than "gas bubbles"?

As a number of meteorites are now classified as being from Mars, how does this number compare to what might have possibly landed on Earth? Has anyone estimated the probability that ejecta from Mars will occur, and eventually land on the Earth (as opposed to orbiting the sun, or again landing on Mars, exiting the solar system, or impacting another larger body such as Jupiter).

The doubt for me would be that there are few ejecta events that produce material that exits Martian orbit, whose trajectory subsequently crosses Earth's atmosphere before impacting some other body, whose material also is large enough to survive atmospheric entry, to finally rest on land and (probability 1/3 with 2/3 ocean), specifically land untouched in a desolate area like antarctica.

This seems doubtful because we keep having to multiply what would seem like small probabilities. Taking just the first item, how often do events on the Earth occur that launches rocks at escape velocity?

Should we believe the claims that these rocks can be traced to Mars?

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To understand how scientists came to the conclusion that these rocks came from Mars, you have to follow the timeline of meteorite classification. Meteorites are categorized by their contents, and fall into 3 broad categories (iron, stony, and stony-iron). Within these groups, there are dozens of sub-categories, depending on their exact mineral content and other factors.

In 1992 a meteorite now knows as "Allan Hills 81005" was analyzed and discovered to be significantly different from other known rocks, but was found to be remarkably similar in content to rocks returned from the moon by the Apollo astronauts. (Original journal abstract, wiki article on lunar meteorites)

Since the mineral evidence seemed persuasive (with lunar rocks available for direct comparison), there must have been some way for this meteorite to get to Earth. You've already discussed the proposed mechanism (an impact throwing rocks into space), and while that seems improbable, it must have happened (since the rocks are here).

As soon as we accept the possibility of that happening for lunar rocks, meteorites from other more distant bodies (Mars, asteroids, Mercury, etc.), while likely even more rare, don't seem entirely impossible.

Another set of meteorites (the "SNC group", 14 known at the time) had already been recognized as different than most other rocks, and were already suspected of being from Mars due to similarity of content to the rocks analyzed by the 1976 Viking landers (wiki article). In 1983, trapped gas in some of them were analyzed, showing similarity to the martian atmosphere. A 2000 publication (abstract) concluded that they either came from Mars or from another body "substantially identical" to Mars.

So it seems persuasive (at least to me) that these rocks are, in fact, from Mars.

If you want to talk about probabilities, I would say that its far more likely that they are from Mars as opposed to the chance of some random comet having both rocks with similar content to Martian rocks and gases similar to Mars' atmosphere.

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There is a more direct way to answer this question. The mars rover Curiosity is presently on Mars analyzing the planet. Apropos to this question they do a direct comparison of the martian atmosphere and a sample of martian meteorite found on earth.

The story is here.. Weighing Molecules on Mars

The plot on the left shows new results from the Sample Analysis at Mars, or SAM, instrument on NASA's Curiosity rover. The instrument measured levels of different gas isotopes in the atmosphere. Isotopes are variations of atoms weighing different amounts. As seen on the plot, SAM detected about 2,000 times as much argon-40 as argon-36, which weighs less. This result is the most precise measurement yet of argon isotope ratios on Mars, and confirms the connection between Mars and Martian meteorites found on Earth, an example of which is shown at the right. The dark blobs in the meteorite are areas where atmospheric gases were trapped when the meteorite was ejected from Mars, and they include argon with the same ratio of argon-40 to argon-36 as SAM has measured in Gale Crater

The bolding is my emphasis

enter image description here

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    This is an excellent example of the theory making a prediction and having it confirmed, but it is missing a piece to prove that meteorites came from Mars - the comparison with other potential meteor sources. Do comets, for example, have the same ratio? – Oddthinking Nov 6 '12 at 0:26
  • Good answer, +1. I'm curious about Oddthinking's question as well. – Paul Nov 6 '12 at 6:23
  • Looking back at my question, I have to ask: What was the Ar36/Ar40 ratio in the earth's atmosphere at the time (perhaps millions of years ago) when the rock was subjected to the thermal stresses of atmospheric entry that could have trapped Earth atmospheric gas (including gas high up in the atmosphere) when part of the rock was in some kind of partially melted or plastic state? – Paul Nov 6 '12 at 6:29

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