# Novel 3U Stand-Alone CubeSat Architecture for Autonomous Near Earth Asteroid Fly-By
## 4 Subsystems Analysis
### Propulsion System
#### 4.2.2 Electric Micro-Propulsion  
Electric micro-propulsion systems evaluation requires the generation of low-thrust trajectories, whose design (and optimization) is not an easy process. JPL Small-Body Database Browser Mission Design Tool gives some \(\Delta V\) reference values for low-thrust trajectories towards certain asteroids. Trajectory optimization for NEAs fly-by has been widely explored in recent years, showing the feasibility of such missions. In Reference [47], a solar electric propulsion system, with \(\mathrm{Isp}=1200\) s and thrust level at 1 AU equal to 0.006 N, was considered, showing small \(\Delta V\) for more than 10 NEAs, and comparing them with rendezvous missions. In Reference [48], an electrospray thruster characterized by \(\mathrm{Isp}=2300\) s and T = 100 \(\upmu\)N was considered, and the mission feasibility with low \(\Delta V\) (less than 85 m/s) was demonstrated for more than 40 targets (using as initial condition Sun-Earth Mean Barycenter L1 and L2). However, given the \(\Delta V\), which can be retrieved from literature, the rocket equation cannot be used to compute the required propellant mass, since it is based on a constant ejection velocity assumption. This is clearly not the case of low-thrust trajectory with electric thrusters, which are based on a variable thrust. This limits the applicability of previous studies for preliminary evaluation of COTS electric micro-propulsion systems for asteroid fly-by. Indeed, the best approach would be passing through an optimization process for each thruster, giving as output the required control law to reach the target. However, a shape-based low-thrust trajectory design approach can be exploited to preliminary quantify the amount of propellant mass needed to reach the target, without passing through a proper optimization process. The spherical coordinates shaping trajectory design approach [49], as the name suggests, is based on imposing the shape to the trajectory, constraining the initial condition (Earth) and the final condition (target asteroid). It can be used to generate a first guess solution before the optimization, as it is done in Reference [47]. The method is particularly suited for rendezvous low-thrust trajectory design, since it imposes the match with the velocity and position of the target asteroid as final condition. Since usually rendezvous missions are more expensive than a fly-by from the required \(\Delta V\) (and the propellant mass) perspective, this method is not perfectly suited for a fly-by trajectory design, since it would overestimate the required propellant mass. However, the shaping method solution, which can differ significantly from the optimal one, can be triggered towards the fuel optimal solution by means of some particular constraints and by means of three grid searches on ToF, departure date (node passage), and final velocity norm. Figure 4: (a) Micro-propulsion systems evaluation chart (blue lines from left to right represent CubeSat Beginning-Of-Life (BOL) mass 1–12 kg); (b) Performances of the ECAPS HPGP thrusters. First, it is possible to constrain the encounter at one of the two nodes (descending or ascending) of the asteroid orbit. This is because NEAs orbits are characterized by a various range of inclinations, and setting the encounter at the node would in principle avoid expensive change-of-plane maneuvers. However this is not sufficient to guarantee no plane changes, because the asteroid velocity at the node is not necessarily coplanar with Earth's orbit, and since the shaping approach will be based on imposing that final velocity, the resulting trajectory will be expensive and out-of-plane. To limit this, it is possible to impose the final condition (corresponding to the encounter at the node) based on a 'fictitious' orbit which has all the same orbital elements with the original asteroid orbit, but the inclination imposed to zero. In other words this translates into a final velocity constraint coplanar with Earth's orbit, which is sufficient to avoid plane-changes.