# Aerospace
## 4 Single Small Satellite to Mars Orbit as Secondary Payload
### Orbiter Deflection Maneuver  
The B-plane aim point during the interplanetary hyperbolic approach will be that of the SmallSat, indicated by the green circle in Figure 12. For the small satellite targeting a near-equatorial orbit, the trajectory is defined by \(r_{p}=(3389.5+52)\) km, and \(\psi=3\pi/2\). The orbiter's approach trajectory for insertion into a 250 \(\times\) 70,000 km polar orbit is defined by \(r_{p}=(3389.5+250)\) km, and \(\psi=\pi\) is indicated by the magenta star in Figure 12.  
Figure 13 shows the magnitude of the deflection maneuver \(\Delta V\) as a function of time from SmallSat release until entry and the angular position \(\psi\) on the host aim-point \(|B|\) circle shown in Figure 12. The farther out from the planet the maneuver is performed and the smaller the length of the vector connecting the two aim points on the B-plane, the smaller the magnitude of the deflection maneuver \(\Delta V\). Note that the SmallSat aim point was at \(\psi=3\pi/2\); hence, the deflection \(\Delta V\) is the smallest if the target aim point is also at \(\psi=3\pi/2\), and largest when \(\psi=\pi/2\) (diametrically opposite to the initial aim point). However, the farther out the SmallSat is released, the higher the EFPA error at the entry interface will be. The decision on when the SmallSat can be released is thus a compromise between orbiter deflection \(\Delta V\) and EFPA error for the small satellite at entry. Based on navigation studies for aero capture at Venus by [PERSON] et al. (2014), the SmallSat is released 4 days prior to entry to keep the 3\(\sigma\) EFPA error below \(\pm 0.2\) deg. The magnitude of the deflection maneuver to target \(\psi=\pi\) is 29.5 m/s, within the 30 m/s limit set forth in the mission requirements.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Min.** & **5\%-ile** & **Avg.** & **95\%-ile** & **Max.** \\ \hline Apoapsis alt., km & 1295 & 1685 & 2086 & 2481 & 3210 \\ Periapsis alt., km & 38.0 & 43.9 & 47.1 & 50.1 & 52.0 \\ Deceleration, g & 1.34 & 1.78 & 2.11 & 2.41 & 2.64 \\ Heat rate, W/cm\({}^{2}\) & 32 & 35 & 37 & 39 & 47 \\ Heat load, kJ/cm\({}^{2}\) & 5.3 & 7.0 & 8.2 & 9.4 & 11.2 \\ PRM \(\Delta V\), m/s & 30.4 & 31.5 & 32.8 & 34.4 & 37.0 \\ ACM \(\Delta V\), m/s & \(-\)132.9 & \(-\)49.7 & 2.9 & 59.9 & 122.8 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistics from Mars aerocapture Monte Carlo simulations.  
Figure 12: Small satellite and host orbiter aim points on the Mars B-plane. After releasing the SmallSat, the host orbiter performs a deflection maneuver to target its aim point.  
Figure 14 shows the near-equatorial approach directory of the small satellite until entry and the approach trajectory of the host orbiter over the north pole.  
The host orbiter performs a 790 m/s propulsive burn into its 250 \(\times\) 70,000 km polar orbit. Figure 15 shows the two spacecraft in their capture orbits.  
Figure 14: Hyperbolic near-equatorial approach trajectory of the Mars SmallSat (green), and the polar approach trajectory of the host orbiter spacecraft (magenta) until periapsis.  
Figure 13: Orbiter deflection maneuver \(\Delta V\) as a function of time from SmallSat release until entry, and the angular position \(\psi\) on the host aim-point \(|B|\) circle shown in Figure 12.