# Aerospace
## 4 Single Small Satellite to Mars Orbit as Secondary Payload
### Performance Analysis  
Nominal values of the parameters used in the Monte Carlo simulations and the uncertainties are listed in Table 4. For the navigation delivery uncertainty, only the uncertainty in the EFPA is considered, as this is the most important parameter of interest for aerocapture. The assumed \(\pm 3\sigma\) uncertainty of 0.20 deg. is based on data available in the literature for a small satellite released by the host spacecraft 4 days prior to entry at Venus [42]. The atmospheric mean density uncertainty (\(\pm 3\sigma\)) and random high-frequency perturbations are supplied by Mars-GRAM [43]. The minimum, average, and maximum mean density profiles are computed at the entry location (latitude, longitude) and a single local solar time. For the aerodynamic uncertainty, a nominal \(\pm 3\sigma\) of 10% is assumed for the vehicle \(\beta_{2}/\beta_{1}\). The entry state used for the Monte Carlo simulations is defined in Table 1 with the EFPA distribution from Table 4. The target apoapsis altitude is 2000 km. If the guidance algorithm detects the predicted apoapsis altitude at atmospheric exit is within the prescribed tolerance or below the target value, drag skirt jettison is commanded. A total of 1000 entry trajectories were propagated, all of which achieved successful orbit insertion. No trajectories resulted in the vehicle escaping the planet or crashing into the surface. Figure 10 shows the distribution of the apoapsis and periapsis altitude at atmospheric exit. Figure 11 shows the distribution of the peak g-load, stagnation-point heat rate, and the total heat load. The achieved orbit apoapsis distribution is shown in Table 5. In total, 88.1% of the cases achieved apoapsis within \(\pm 400\) km of the target, and 99.5% achieved apoapsis within \(\pm 800\) km of the target. Table 6 shows the statistics from the Monte Carlo simulations. The 95 percentile peak deceleration and peak heat rate are 2.41 g and 39 W/cm\({}^{2}\). The 95 percentile periapsis raise \(\Delta V\) is 34 m/s. The apoapsis correction maneuver (ACM) \(\Delta V\) is the magnitude of the maneuver performed at the periapsis to correct the apoapsis error after aerocapture. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Variable** & **Nominal** & **Uncertainty** & **Distribution** \\ \hline Navigation & EFPA & \(-9.25\) deg. & \(\pm 0.20\) deg. (\(3\sigma\)) & Normal \\ Atmosphere & Mean density & - & \(\pm 3\sigma\) & Normal \\  & Random & - & rpscale = 1 & Uniform \\ Aerodynamics & \(\beta_{2}/\beta_{1}\) & 7.5 & \(\pm 10\%\) (\(3\sigma\)) & Normal \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mars aerocapture Monte Carlo uncertainties. Figure 9: Evolution of altitude rate and altitude during Mars aerocapture. The green diamond indicates the time when a preset altitude rate threshold (\(-200\) m/s) is exceeded, at which point density estimation is cut off and apoapsis prediction is initiated. The red circle indicates the jettison event. The ACM \(\Delta V\) in Table 6 is reported as negative if the achieved orbit is larger than the target value and positive otherwise. The 95 percentile ACM \(\Delta V\) is slightly higher than what may be acceptable for science missions. This is attributed to the simple guidance scheme used, which is sufficient for preliminary design but is not fully optimized. More advanced schemes, such as the ensemble correlation filter developed by [PERSON] et al., can significantly improve performance and reduce the \(\Delta V\) required for apoapsis correction [41]. Figure 11: Scatter plots of the peak deceleration, peak stagnation-point heat rate and the total heat load for aerocapture at Mars. The dotted lines indicate the 99.87 percentile values. Figure 10: Histogram of the apoapsis altitude (**left**) and the apoapsis altitude and periapsis altitude (**right**) for aerocapture at Mars. The dashed line indicates the target apoapsis altitude of 2000 km.