Small divisors in the solar system
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
CC0 1.0 Universal
CC0 1.0 Universal
Özet
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.
Açıklama
Anahtar Kelimeler
Small divisors, Perturbations
Kaynak
International Conference of Mathematical Sciences (ICMS 2019)
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Zhivkov, A. (2019). Small divisors in the solar system. International Conference of Mathematical Sciences (ICMS 2019). s. 162.
