## 3 Results  
### Optimization Results and Analysis  
#### 3.1.1 The Impact of Orbital Altitude on LEO Satellites  
The higher the altitude of the satellite, the larger its coverage area. Factors such as the ionosphere in space, Van Allen radiation belt, and regression orbit should also be taken into consideration [2; 24]. [PERSON] et al. utilized the mean orbital elements to establish a trajectory model for common sub-satellite points under \(J_{4}\) conditions and proposed inclination schemes for different orbital heights to alleviate pressure on ground stations [25]. The satellite adopts a near-circular orbit and only accounts for the \(J_{2}\) perturbation while ignoring the influence of short period terms using the average orbital radical. The variation of the orbital elements and the nodal regression are depicted by the following formulas.  
Figure 4: The staged deployment strategy of constellations.  
\[\left\{\begin{array}{l}\dot{a}=0\quad\dot{e}=0\quad\dot{i}=0\\ \dot{\Omega}=-\frac{3I_{2}R_{1}^{2}}{2a^{2}}\sqrt{\frac{\mu}{a^{2}}}\cos i\\ \dot{\omega}=\frac{3I_{2}R_{2}^{2}}{2a^{2}}\sqrt{\frac{\mu}{a^{2}}}(\frac{5}{2 }\sin^{2}i-2)\\ \dot{M}=\frac{3I_{2}R_{2}^{2}}{2a^{2}}\sqrt{\frac{\mu}{a^{2}}}(1-\frac{3}{2} \sin^{2}i)\end{array}\right.\quad\quad\left\{\begin{array}{l}RT_{\Omega}= DT_{\Omega G}\\ T_{\Omega}=\frac{2\pi}{n_{0}+4i-M}\\ T_{\Omega G}=\frac{2\pi}{\omega_{E}-\Omega}\\ n_{0}=\sqrt{\frac{\mu}{a^{2}}}\end{array}\right. \tag{11}\]  
where \(\omega_{E}=7.292\times 10^{-5}rad/s\) represents the angular velocity of the Earth's rotation, \(R\) and \(D\) are two positive integers that are prime to one another, and R/D is defined as the repetition factor, \(n_{0}\) is the mean angular velocity, \(T_{\Omega}\) is the nodal period of the satellite orbit, and \(T_{\Omega G}\) the nodal day, which represents the time required for the Earth to rotate one revolution relative to the ascending node of its orbit; \(R_{E}\) stands for Earth's radius, and \(\mu=398600.5 km^{3}/s^{2}\) is the terrestrial gravitation constant. \(\dot{\omega}\), \(\dot{M}\), and \(\dot{\Omega}\) denote, respectively, the precession rate of argument of perigee, precession rate of mean anomaly, and right ascension of ascending node under non-spherical perturbation influence from Earth.  
\(\dot{a}\), \(\dot{e}\), and \(\dot{i}\) are the first derivative of the semi-major axis, eccentricity, and inclination.  
As seen in Figure 5b, the repetition factor R/D gradually decreases and changes more obviously with the increase in satellite orbit altitude but increases slowly with the increase in inclination angle, so the return orbit setting is mainly through the selection of a suitable orbit altitude. In addition, if the satellite orbit altitude is too high, the influence of the Van Allen radiation belt will reduce the satellite life and increase the deployment cost. On the other hand, if the orbit altitude is too low, it will be affected by the atmosphere and other regenerative forces, which will increase the frequency of required satellite control maneuvers and reduce the satellite life span. Thus, the satellite altitude optimization range of 1100 km\(\sim\)1200 km is selected after weighing the influencing factors of the three parties.