## 3 Target Degradation Strategy (TDOS)
### Energy Reduction Method  
The energy of the target orbit \(E\) can be described as follows [19]:  
\[E=-\frac{\mu}{2a_{f}} \tag{4}\]  
This paper downgrades the perigee altitude \(h_{p}\) and apogee altitude \(h_{a}\) of the target orbit to adjust the eccentricity and semimajor axis (energy). \[\left\{ \begin{array}{l}h_{p}(n+1)=h_{p}(n)-\Delta h\\ h_{a}(n+1)=h_{a}(n)-\Delta h\\ a_{f}=R_{e}+\frac{1}{2}\big{(}h_{a}+h_{p}\big{)}\\ e_{f}=\frac{h_{a}-h_{p}}{h_{e}+h_{p}+2R_{e}}\end{array} \right. \tag{5}\]  
where \(h_{p}(n+1)\) and \(h_{p}(n)\) are the perigee altitudes of the target orbit from the \(n+1\) and \(n\) degradations, respectively; \(h_{a}(n+1)\) and \(h_{a}(n)\) are the apogee altitudes of the  
Figure 1: Orbit-injection strategy based on target degradation rules. target orbit from the \(n+1\) and \(n\) degradations, respectively, the mean radius of the Earth \(R_{e}=6,371,004\) m, and the altitude degradation gradient \(\Delta h=10\) km. The perigee and apogee altitudes of the target orbit need to be degraded at the same time according to the failure and mission attributes. Although transfer orbiting is more fuel-efficient than direct orbiting, the final orbiting approach still needs to be selected according to the mission and engine failure attributes. When the power system failure mode requires the launch vehicle to minimize the orbit-injection time or the mission requires a fast response, the launch vehicle should adopt the direct orbiting method; otherwise, the launch vehicle adopts the transfer orbiting method. In this study, the elliptical orbit with the apogee altitude equal to the perigee altitude of the target orbit and the perigee altitude equal to the minimum safety height is selected as the transfer orbit. 1. Downgrading strategy when the original target mission is a circular orbit  
First, it is necessary to determine whether the original target orbit is a sun-synchronous orbit (SSO). 1. [label=()]
2. SSO downgrade strategy  
In the case of an SSO, it is necessary to adjust the target orbit inclination according to the relationship between the SSO orbit inclination and orbit altitude while adjusting the orbit altitude [20]. \[i_{f}=\arccos\left(-0.09886\left(\frac{a_{f}}{R_{e}}\right)^{3.5}\right) \tag{6}\]  
The mission degradation schematic diagram of SSO is shown in Figure 2.  
Specifically: 1 when adopting the direct orbiting approach, the perigee altitude and apogee altitude need to be reduced simultaneously, and the target orbit inclination needs to be updated simultaneously; when it is reduced to \(h_{p}=h_{a}=h_{\kappa}+\delta_{0}\), if the launch vehicle still does not have the orbit-injection capability, the payload reduction approach will be adopted; 2 when adopting the transfer orbiting approach, it is assumed that the injection occurs at the apogee. First, the apogee altitude is maintained, the perigee altitude is reduced, and the fuel consumption of the transfer process is calculated. When the perigee altitude is reduced to \(h_{p}=h_{\text{pmin}}\), if the launch vehicle still does not have the capability of transfer orbit, it needs to maintain the minimum perigee altitude, reduce the apogee altitude, and update the target orbit inclination according to the change of apogee altitude. Figure 2: Schematic diagram of sun-synchronous orbit degradation. When the apogee altitude drops to \(h_{a}=h_{\kappa}+\delta_{0}\), if the launch vehicle still cannot enter the orbit, it will switch to the payload reduction mode. Non-SSO circular orbit degradation strategy  
When the direct orbiting approach is adopted, the perigee altitude should be lowered for the analysis of the orbiting capability; when it is lowered to \(h_{p}=h_{p\min}\), if the launch vehicle still does not have the orbiting capability, the minimum perigee altitude is maintained, and the apogee altitude is lowered; when it is lowered to \(h_{a}=h_{\kappa}+\delta_{0}\), if the launch vehicle still does not have the orbiting capability, the payload lowering approach will be adopted.