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    Small divisors in the solar system
    (Maltepe Üniversitesi, 2019) Zhivkov, Angel
    Consider the Sun, Mercury, Venus, Earth+Moon, Mars, Jupiter, Saturn, Uranus and Neptune as point masses, moving according Newton’s inverse–square law of gravitation. Poincar´e proved [1] that the general solution of the N–body problem can be expressed as a formal Fourier series. But Poincar´e also proved that such a series generally diverges. This happens because some small divisors appear when we apply the method of variation of arbitrary constants [2, 3]. A divisor which may vanish during the next 1010 years we define as a small divisor. For each pair of planets, there always exists a principal small divisor which could spoil the stability of their orbits after certain time. Finally we estimate the impact of the small divisors to conclude that they would not destroy the stability of the solar system at least for the next 1010 years.