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Some meteoroids such as the daytime fireball of August 10, 1972 that went over the Western United States and the European fireball of October 12, 1990 grazed the atmosphere of Earth before returning to space (at reduced speed). Others, such as the October, 1992 impactor (a small fragment of which smashed into the back end of a car in New York State), entered the atmosphere in a near grazing angle but plunged deeply enough into the atmosphere to ultimately plunge to ground. We can anticipate there there must be some range of closest-approach distances and velocities such that the meteoroid would be captured into a bound orbit around Earth after its first passage through the atmosphere. Any such captured object must ultimately plunge to ground due to further atmospheric dissipation in subsequent passages unless the gravitational field of the moon or other intervention is able to raise its perigee above the atmosphere after the initial capture. We have used a spherical atmospheric model to integrate the passage of meteoroids in near grazing encounters. We find that the corrider for capture is narrow, and it becomes narrower as the pre-encounter velocity V increases. If V = 5 km/s (velocity prior to gravitational acceleration by Earth), stony meteoroids with closest-approach distances of h = 40 km above the ground are captured into bound orbits if their radii, R, are between 3 and 9 meters. For V = 15 km/s and h = 40 km, capture only occurs if R is between 1.5 and 2 meters. Irons with V = 5 km/s and h = 40 km are captured if R is between 1 and 3.5 meters, while irons with V = 15 km/s are captured if R is between 0.6 and 0.9 meters.
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