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S. J. Goldstein (Univ. of Virginia), J. W. Rudmin (James Madison Univ.)
Daniel Kirkwood (1888, The Asteroids, Lippincott) proposed that minor planets whose sidereal periods were commensurate with Jupiter's period with ratios 1/2, 1/3, etc., had increasing eccentricity; and at perihelion, collided with the sun in the early history of the solar system. Jack Wisdom (1985, Icarus 63, 262) studied the motion of hypothetical planar asteroids near the 1/3 commensurability, and concluded that chaotic increases in the eccentricity would make these asteroids approach Mars and collide or be strongly deflected from their original orbits. We have made numerical integrations of accurately observed minor planets from the 1997 Ephemerides of Minor Planets near the 1/2 and 1/3 Kirkwood gaps. We find that four (1362, 1922, 3688, and 5370) are exactly synchronized, at 1/2 Jupiter's period. Three (887, 1915, and 6318) are exactly synchronized, at 1/3 Jupiter's period. As seen in a Jupiter-centered coordinate system, all of these asteroids have libration amplitudes greater than 30 degrees, but none circulate in integrations over 1200 Jupiter years. The libration periods vary between 25 and 38 Jyrs. Their Keplerian semi-major axes, listed in the EMP, differ from the Kirkwood gap values by 0.4 to 2.1 percent. Three of the differences are positive, and four negative. Answering the title question, at least seven of them are in orbits about the sun, synchronized to Jupiter, and listed in the EMP. Our orbit calculations show that they all have semi-major axes that oscillate about the Kirkwood values. MP5370 will pass through the Kirkwood gap in about 5 ± 0.5 Jyrs, or 59 ± 6 years, from the Dec 18, 1997 epoch used in our calculations.