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土星 | Saturn - Sykm

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//======= v2.0 2025.10.24 =======//
Translation：
Celestial Bodies Displayed in the System:
Saturn,Sun,17 moons including Mimas​​(Satellite 1) to Pandora​​(Satellite 17)
Local Calculation Methods:
1.VSOP87 semi-analytical theory (Bretagnon & Francou, 1988)
2.Kepler's Equation Solver: 4th-order Taylor expansion for low eccentricity; 5th-order Householder iterations for moderate eccentricity; Mikkola's cubic method (1987) for high eccentricity.
3.Perturbation Theories: Oblateness perturbations (J₂–J₈ terms); Kaula's theory (1966) first-order + second-order short-period terms.
4.Resonance Dynamics: Mean-motion resonances, Laplace resonance, co-orbital resonance, solar perturbations, N-body perturbations.
5.General Relativity corrections
6.Tidal evolution
7.Radiation pressure perturbations
Accuracy (excluding Hyperion):
1 year: ~±1,000 km
10 years: ~±5,000 km
100 years: ~±50,000 km
For general reference, not for precise applications.
Operation Instructions:
Click the clock to display the simulation system time.

系统显示天体：
土星、太阳、土卫1到土卫17等17颗卫星

本地计算方法：
1.VSOP87半解析理论 (Bretagnon & Francou, 1988)
2.开普勒方程求解：低偏心率4阶泰勒展开，中等偏心率5阶Householder迭代，高偏心率Mikkola三次方法 (1987)；
4.摄动理论：扁率摄动（J₂-J₈项），Kaula理论 (1966)一阶+二阶短周期项；
5.共振动力学：平运动共振、Laplace共振、共轨共振、太阳摄动、N体摄动；
6.广义相对论修正
7.潮汐演化
8.辐射压摄动

精度：（除土卫7 Hyperion外）
1年约±1,000 km
10年约±5,000 km
100年约±50,000 km
翻译成人话：短期内还凑合，超过10年权当图一乐

操作说明：
单击时钟会显示模拟系统的时间

参考资料：
1.Bretagnon, P., & Francou, G. (1988). Planetary theories in rectangular and spherical variables. VSOP87 solutions. Astronomy and Astrophysics, 202, 309-315.
2.Kaula, W. M. (1966). Theory of Satellite Geodesy. Blaisdell Publishing Company.
(Dover reprint: ISBN 978-0486414652)
3.Murray, C. D., & Dermott, S. F. (1999). Solar System Dynamics. Cambridge University Press.
4.Jacobson, R. A., et al. (2006). The Gravity Field of the Saturnian System from Satellite Observations and Spacecraft Tracking Data. The Astronomical Journal, 132(6), 2520-2526.
5.Lainey, V., et al. (2017). New constraints on Saturn's interior from Cassini astrometric data. Icarus, 281, 286-296.
6.French, R. G., et al. (2017). Noncircular features in Saturn's rings IV. Icarus, 290, 14-45.
7.Wisdom, J., Peale, S. J., & Mignard, F. (1984). The chaotic rotation of Hyperion. Icarus, 58(2), 137-152.
8.Dermott, S. F., & Murray, C. D. (1981). The dynamics of tadpole and horseshoe orbits II. Icarus, 48(1), 1-11.
9.Mikkola, S. (1987). A cubic approximation for Kepler's equation. Celestial Mechanics, 40(3-4), 329-334.
10.Danby, J. M. A. (1988). Fundamentals of Celestial Mechanics (2nd ed.). Willmann-Bell.
ISBN: 978-0943396200
11.Soffel, M., et al. (2003). The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology. The Astronomical Journal, 126(6), 2687-2706.
12.Will, C. M. (2014). The Confrontation between General Relativity and Experiment. Living Reviews in Relativity, 17, 4.
13.JPL Solar System Dynamics - Horizons Ephemeris System.
https://ssd.jpl.nasa.gov/horizons/
14.NASA Cassini Mission Archive.
https://solarsystem.nasa.gov/missions/cassini/

更新：
1.优化了卫星轨道计算方法，修改了错误，减小了性能占用
2.自定义文本大小和上下位置可调
btw：多亏deepseek，claude等AI可以帮忙查数据，解释数学物理问题，debug……这些工作放在以前一个人完成，可能要花费数十倍的时间精力~

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