## 2 Mathematical Programming Model
### MILP Model Formulation
\[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\] \[\sum_{k\in S}^{m\in O_{k}}x_{i,m,k}\leq 1\] (2) \[\sum_{j\in G}^{i\in O_{k}}y_{i,j,m,k}=\sum_{m\in O_{k}}x_{i,m,k}\] (3) \[\sum_{i\in T}y_{i,j,n,k}\leqslant g_{j,n,k}*M\] (4) \[x\_time_{i,k}=\sum_{m\in O_{k}}x_{i,m,k}*time_{i}\] (5) \[g\_time_{j,n,k}=\sum_{i\in T}y_{i,j,n,k}*timed_{i}\] (6) \[x\_end_{i,k}\leqslant\sum_{m\in O_{k}}x_{i,m,k}*wet_{i,m,k}\] (7) \[x\_start_{i,k}\geqslant\sum_{m\in O_{k}}x_{i,m,k}*wet_{i,m,k}\] (8) Figure 1:0 (9) Figure 1:1 (10) Figure 1:2 (11) Figure 1:3 (12) Figure 1:4 (13) Figure 1:5 (14) Figure 1:6 (15) Figure 1:7 (16) Figure 1:8 (17) Figure 1:9 (18) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]0 (19) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]1  
\begin{table}
\begin{tabular}{c c} \hline
**Decision Variables** & **Definition** \\ \hline \(g_{j,n,k}\) & Whether the ground station \(j\) communicates with the satellite \(k\) in the \(n\)th orbit \\ \(x_{i,m,k}\) & Whether target \(i\) is observed in the mth orbit of satellite \(k\) \\ \(y_{i,j,n,k}\) & Whether target \(i\) transmitted at ground station \(j\) through the nth orbit of satellite \(k\) \\ \(x\_time_{i,k}\) & Observation time of target \(i\) on satellite \(k\) \\ \(x\_start_{i,k}\) & Observation start time of target I on Satel-lite K \\ \(x\_end{tabular} \(\begin{array}{c}x\_end{array}\)\\[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]2 (21) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]3 (22) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]4 (23) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]5 (24) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]6 (25) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]7 (26) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]8 (27) \[\max\sum_{i,m,k}x_{i,m,k}c_{i} \tag{1}\]9 (28) \[\sum_{k\in S}^{m\in O_{k}}x_{i,m,k}\leq 1\]0 (29) \[\sum_{k\in S}^{m\in O_{k}}x_{i,m,k}\leq 1\]1 (30) \[\sum_{k\in S}^{m\in O_{k}}x_{i,m,k}\leq 1\]2 (31) \[\sum_{k\in S}^{m\in O_{k}}x_{i,m,k}\leq 1\]3 (32) \[z1_{\_}{i1,j2,k}=1\Rightarrow p_{\_}{i1  
Equation (1) is the Objective function, aiming to maximize task benefits. Equation (2) describes the task execution count constraints. Equations (3) and (4) describe the tasking relationship constraints. Equation (5) represents the observation mission time constraints. Equation (6) indicates the data transmission time constraint. Equations (7)-(9) indicate the observation mission time window constraints. Equations (10)-(12) indicate the time Window Constraints for data transmission Tasks. Equations (13) and (14) represent the constraints on the order of observational tasks. Equations (15)-(18) represent the Observation and data transmission task sequencing constraints. Equations (19) and (20) represent the sequential relationship constraints for on-planet data transmission tasks. Equation (21) indicates the logical relationship between target digitizing assignments and imaging digitizing sequential relationships. Equation (22) indicates the logical relationship between the distribution of target passes and the start and end times of missions. Equations (23) and (24) indicate the relationship between imaging tasks' order and start and finish times. Equations (25)-(28) indicate the relationship between imaging and data transmission tasks sequencing and tasks' start and finish times. Equations (29) and (30) indicate the relationship between the sequence of digital transmission missions on satellites and the start and end times of missions. Equations (31) and (32) indicate that similar missions on satellites may not be carried out simultaneously. Equations (33)-(40) indicate the relationship between the capacity utilization of on-planet tasks and task sequencing. Equations (41) and (42) indicate the sequencing of tasks at Earth stations. Equations (43)-(45) indicate the relationship between the sequence of data transmission tasks on ground stations and the start and end times of the tasks. Equation (46) indicates the attitude transition time constraints between ground station data transmission missions.