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A meteoroid in orbit around the Sun has a heliocentric velocity in the vicinity of Earth of about 42.1 km/s. So if a meteoroid has a heliocentric velocity exceeding that, it will have an open (hyperbolic) orbit and would not have originated in the solar system. As a meteoroid encounters Earth's atmosphere it encounters atmospheric atoms and molecules, generating heat that causes atoms to boil off and collide with those in the atmosphere. This produces ionized particles which surround the meteoroid with a glowing envelope leaving a column of plasma. The meteoroid is now seen as a meteor.

Meteor velocities measured by radar and optical means have indicated the detection of many hyperbolic meteoroid orbits (heliocentric velocities exceeding 42.1 km/s), but velocity measurement errors which occur in the 10% range have cast doubt on their interstellar meteoroid status. However, it's clear that the solar system must be embedded in dusts and gasses originating from nearby star systems, so the existence of hyperbolic meteoroids should not be in doubt.

What is the technical difficulty in obtaining sufficiently accurate velocity measurements to prove or disprove the existence of interstellar meteors?

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Microlensing MACHO searches make it very clear that there are many sub-stellar heavy bodies out between the stars, and I don't know of anyone who doubts that there are light objects out there too, it just that Douglas Adams was going down the right road with his "Space is big..." line. –  dmckee Jun 13 '12 at 1:41
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This NEO page briefly discusses the uncertainties in the calculation of orbits. More detail will be on nasa.gov somewhere, though I must admit the page I linked is all I've found from a few minutes Googling.

As far as I know, all the objects on hyperbolic orbits are believed to have come from the Solar System. It's not hard for interactions in the Kuiper belt or Oort cloud to put objects into a hyperbolic orbits. Orbital velocities are pretty low that far out, so an accidental slingshot could easily send an object inwards with enough velocity to put it on a hyperbolic orbit.

If an object on a hyperbolic orbit does come from the Solar System you'd expect the velocity to be only just big enough to eject it from the Solar System. Presumably that's why even a relatively small error can make it hard to tell if the orbit is hyperbolic or not. Likewise, if an object came from outside the Solar System (and therefore at least 4.2 light years!) you'd expect it to have a velocity much greater than the Solar System escape velocity, so there would be no doubts about it's origin.

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I want to pick a nit with "(and therefore at least 4.2 light years!)". It's more-or-less true in this case, but it makes it sound like every interstellar object should be associated with a developed star system, which seems dubious to me. Presumably there are quite a few objects in interstellar space that were ejected from formation neublas or from other structure that underwent a bit of local gravitational collapse without having even the potential to form a full star. These cold objects could be drifting around with low relative velocities for enormous time periods. –  dmckee Jun 13 '12 at 15:42
    
I'll certainly concede your point. However I think it's still true that an extrasolar object detected in the Solar System would be extremely unlikely to have a velocity within 10% of the escape velocity, because that meant it was essentially stationary wrt the Earth before it entered the Sun's gravity well. –  John Rennie Jun 13 '12 at 16:31
    
Sure. If only because the mean time between encounters goes by $1/v$ most of the extrasolar material will be coming in pretty fast. –  dmckee Jun 13 '12 at 16:43
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In the "SETI Talks" series (available on YouTube) there is a talk (from 2011?) by Sigrid Close titled "Meteoroid Threats to Spacecraft". In the talk she outlines her search for ionization signal of meteoroids in the atmosphere.

In her talk, she briefly mentions a tentative signal that is consistent with interstellar meteoroids (after 36:45 in the talk) – at the time of the talk the paper was unpublished. I don't know what else happened on that topic, but searching for her work should be a good starter.

[Update]

Link: https://www.youtube.com/watch?v=LTeILRPG16Y

The relevant part starts here: http://youtu.be/LTeILRPG16Y?t=36m44s

Basically, with radar they see trajectory and velocity of incoming meteoroids, and with both they calculate orbit. Some meteoroids (only the very smallest masses they see) don't seem to have orbits around the Sun, but instead seem to come from outside of our Solar System. They map those trajectories onto the Milky Way, and seem to get some a couple of "patches" where those meteoroids seem to come from. She then speculated very shortly on what might/could constitute the source stars (pulsars), which might eject macroscopic particles.

(Sorry, it was late yesterday, I was tired, and just wanted to post this before falling asleep… should have included this in the first place :-)

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Maybe you could provide a link to the video, and what is 36:45? Thanks. –  Mike Dunlavey Apr 10 at 20:15
    
Added a link, and 36:45 is the time at which the relevant part of the talk/video starts. (Sorry, it was late yesterday :-) –  Tony Mach Apr 11 at 7:53
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