Perturbation Motion
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
Under the action of perturbation forces, the trajectory of an aerospace vehicle deviates from the ideal Keplerian orbit. The small additional motion of a satellite caused by perturbation forces is called perturbation motion. In contrast, the two-body motion is called unperturbed motion. Perturbation forces include non-spherical Earth gravity, lunar and solar gravitational attraction, atmospheric drag, and solar radiation pressure, all of which are small quantities relative to the Earth's central gravitational force.
Core Elements
Fundamental Forms of Perturbation
| Perturbation Type | Description | Characteristics |
|---|---|---|
| Secular perturbation | Causes orbital elements to increase or decrease monotonically | Cumulative effect, irreversible |
| Long-period perturbation | Periodic perturbation with a period longer than the orbital period | Long cycle, sometimes treatable as secular |
| Short-period perturbation | Periodic perturbation with a period shorter than the orbital period | Returns to zero after one orbital period, non-cumulative |
Classification of Perturbation Analysis Methods
| Category | Methods | Characteristics |
|---|---|---|
| Special perturbation | Cowell's method, Encke's method, variation of parameters | Numerical integration, suitable for short-term precision prediction |
| General perturbation | Series expansion, mean element method, semi-analytical methods | Analytical or semi-analytical solutions, reveals physical mechanisms |
Typical Perturbation Force Magnitudes (Low Earth Orbit)
| Perturbation Force | Magnitude | Nature |
|---|---|---|
| (Earth oblateness) | Conservative | |
| Atmospheric drag | Dissipative | |
| Lunar-solar perturbation | ~ | Conservative |
| Solar radiation pressure | Dissipative |
Relationship with Unperturbed Motion
In unperturbed motion (the two-body problem), the size, shape, and orientation of the orbit all remain constant, following Kepler's laws. In reality, the Earth's shape and mass distribution are complex, causing gravitational deviation from the homogeneous sphere assumption. Additionally, the orbit is subject to lunar and solar gravitational attraction, atmospheric drag, and solar radiation pressure. These perturbation forces cause orbital elements to change over time, making the motion far more complex than the two-body problem.
Application Value
Perturbation motion is the core research subject of orbital mechanics. By establishing perturbation motion equations, the effects of various perturbation forces on orbits can be analyzed, providing the theoretical foundation for orbit prediction, orbit control, and mission design. Perturbation analysis methods (special perturbation and general perturbation) are fundamental tools for spacecraft orbit determination and prediction.
References
- 郑伟, 安雪滢, 周祥, 何睿智. 空天飞行力学[M]. 国防科技大学, 2026.
- 刘林. 航天器轨道理论[M]. 国防工业出版社.