1. The unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations
- Author
-
Xiong Yong-qing, Zhao Chang-yin, Sun Rong-yu, Zhang Ming-jiang, and Zhu TingLei
- Subjects
Orbital elements ,Physics ,Geopotential ,media_common.quotation_subject ,Orbital resonance ,General Physics and Astronomy ,Frozen orbit ,Mean motion ,Classical mechanics ,Physics::Space Physics ,Orbital motion ,Libration ,Astrophysics::Earth and Planetary Astrophysics ,Eccentricity (behavior) ,media_common - Abstract
From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J (2) and J (22) of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.
- Published
- 2013