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Our concern here is the nature of secondary resonances--commensurabilitiesbetween apsidal and libration periods lying within first-order mean motionresonances [mmr] in the solar system. At the 4/3 and 3/2 mmr in the asteroidbelt, we find in general that it is possible to identify the positions of theirconsiderably large number and to determine the degree of chaos that theydevelop. The severity of the latter corresponds to the absence of observedasteroids at low eccentricity, e, in both of these mmr and even more so at 2/1.Chaos at higher e is present but weaker so that real bodies can remain over theage of the solar system. This reduced chaos, we suggest, arises because thedenser though weaker secondaries have widths that allow them to overlap and soprovide a continuous quite constant level of chaos over a broad eccentricityrange. We also consider the similar first-order 1/2 mmr with Neptune in theKuiper belt at 47.8 AU and find considerable chaos, probably once again inducedby secondary resonances, among the many orbits with e < 0.10. The instabilityso generated seems very likely to correspond in realistic models to the slowescape from 1/2 of a fair number of its once captured bodies over the solarsystem's age.

Locations and Strengths of Secondary Resonances Lying within Four First Order Mean Motion Resonances