Fig. 11: Residuals in the osculating orbital elements of Nereid for long time interval. The semi-major axis is given in km, eccentricity in radians and the rest of elements are in degree (Saad & Kinoshita 2001).
Vashkov’yak and Teslenko (2010) in addition to the effects of the mother planet Neptune, they considered the influence of the attraction of the internal satellite Triton on the evolution of the orbit of the external satellite Nereid. The disturbing function of Triton is given by: , (3.8) where is the product of the gravitational constant and mass of Triton, and refer to the radius vectors of Triton and Nereid respectively and .
In spite of the fact that Nereid is classified as a distant satellite, the evolution of its orbit is presented as regular enough with practically secular variations of pericentric argument and node longitude, and with a conditionally periodic change of eccentricity and ecliptic inclinations. …show more content…
Gravitational effects on the planets’ orbits
Planetary theory is originally, developed to be able to predict phenomena, and provide high accuracy ephemerides of the planets. The progression improvement has led to the discoveries of the variable rotation of the Earth, several planets, and a satellite. By means of the mapping techniques, it is now possible to integrate a model of the motion of the entire solar system back for the history of the solar system. (Seidelmann 1993).
Bretagnon (1980, 1981, 1982), Simon and Bretagnon (1984), and Simon (1983) have developed general theories for the inner and outer planets based on iterative methods. Gravitational perturbations due to mutual effects of the planets, attraction of the Sun, in addition to the perturbation of the Moon have taken into account. However, the accuracy of these theories is limited by the number of terms included in the theories and the limit on the order of the expansion based on a long-term integration (Carpino et al.
Vashkov’yak and Teslenko (2010) in addition to the effects of the mother planet Neptune, they considered the influence of the attraction of the internal satellite Triton on the evolution of the orbit of the external satellite Nereid. The disturbing function of Triton is given by: , (3.8) where is the product of the gravitational constant and mass of Triton, and refer to the radius vectors of Triton and Nereid respectively and .
In spite of the fact that Nereid is classified as a distant satellite, the evolution of its orbit is presented as regular enough with practically secular variations of pericentric argument and node longitude, and with a conditionally periodic change of eccentricity and ecliptic inclinations. …show more content…
Gravitational effects on the planets’ orbits
Planetary theory is originally, developed to be able to predict phenomena, and provide high accuracy ephemerides of the planets. The progression improvement has led to the discoveries of the variable rotation of the Earth, several planets, and a satellite. By means of the mapping techniques, it is now possible to integrate a model of the motion of the entire solar system back for the history of the solar system. (Seidelmann 1993).
Bretagnon (1980, 1981, 1982), Simon and Bretagnon (1984), and Simon (1983) have developed general theories for the inner and outer planets based on iterative methods. Gravitational perturbations due to mutual effects of the planets, attraction of the Sun, in addition to the perturbation of the Moon have taken into account. However, the accuracy of these theories is limited by the number of terms included in the theories and the limit on the order of the expansion based on a long-term integration (Carpino et al.