Abstract
It is not yet known (1997) whether the Solar system is stable or not. Common belief is that the Solar system is stable if and only if it is not a resonant system, i.e., whenever its orbital frequencies ωi satisfy an inequality |Σ niωi| ≤ ε for Σi|ni| ≤ N; a similar inequality is true for randomly chosen frequencies. In this paper, we show that the Solar system does not have such resonances, and therefore (if the above-mentioned belief is correct), it is stable.
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Kreinovich, V., Bernat, A. Is Solar System Stable? A Remark. Reliable Computing 3, 149–154 (1997). https://doi.org/10.1023/A:1009985822160
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DOI: https://doi.org/10.1023/A:1009985822160