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Because of their trajectories and small size, these objects will not remain on their current orbits for very long periods. The cumulative effect of frequent flybys of the Earth itself is considerable, but not necessarily devastating.

Deep Impact
July 23, 2001
A recent study portrays the paths of asteroids in the inner solar system as a vast Los Angeles-style traffic system crisscrossed with superhighways along which are hurtling huge, rocky projectiles. The study estimates that an armada of asteroids, 900 strong, all a kilometer in diameter or larger, present a potential hazard to life on Earth. Some pass within a few moon distances of Earth every year. William Bottke at Cornell University is lead researcher on a U.S.-French team that has discovered the spatial and size distribution of a large group of asteroids called NEAs (for near-Earth asteroids), a vast system of orbiting rocks in inner space, ranging in size from mere specks to more than 64 kilometers (40 miles) in diameter. Most of the asteroids in the solar system revolve around the sun on independent orbits, corralled between Mars and Jupiter in a formation known as the main belt.