## 2 NEOs Environment
### Close-Proximity Dynamics  
In the complex dynamics of a spacecraft orbiting an asymmetric and irregularly rotating NEO, orbital linear and angular momenta may undergo significant changes in a relatively short period. For instance, assuming a slightly aspheric NEO, the force field engendered by mass asymmetry may cause oscillations in the orbit's inclination and eccentricity [49], much like those effects experienced by in-orbit servicing geosynchronous Earth satellites [50]. An effective approach is to place the spacecraft around existing stable relative equilibrium or libration points of a Sun-NEO 2-Body-Problem model [51; 52; 53] or, in the case of a less asymmetric, more massive and regularly spinning central body, to use existing equilibrium points on the Zero-Velocity Surfaces, mimicking a dead-zone control strategy [54; 55; 33; 56; 57; 58]. Thus, any search for equilibria, or their respective periodic orbits, will be fundamentally guided by the NEO's mass and spin state as these properties are inversely proportional to the distance of the equilibrium points to the attracting body and also affect the stability of these equilibrium points [38]. Alternatively, unstable natural orbits around NEOs may turn into a benefit for controlling fuel expenditure and, consequently, the lifetime of a rendezvous mission. According to [42; 59], a spacecraft whose orbit wanders outside the sphere of influence of the attracting NEO (\(\tau_{orb}>R_{\rm Hill}\)) may fall under the destabilizing influence of external disturbing forces. On the other hand, circular orbits that start with radii smaller than one-half of this reference distance are generally stable against escape from the body [59; 60]. Approaching orbits starting outside this sphere of influence, provided they are far enough from the destabilizing external forces [48], may be under weak, unstable dynamics, a condition that can be used to the mission's benefit as these weak, disturbing accelerations can be actively counteracted with small fuel expenditure while keeping a spacecraft motion relative to the NEO. When it comes to rendezvous missions targeting multibody-systems, even considering that the spacecraft may have to navigate within the system's bodies under the effect of previously mentioned force-entanglement that generates a highly disturbed environment, which [38] inputted as the most strongly perturbed astrodynamic environment found in the Solar System, a still effective approach would be to place a spacecraft in an equilibrium point of the system if there exists any. Particularly for binary systems, which generally present small mass ratios, the synchronous orbits relative to a synodic reference frame are good candidates [42]. However, the position may not be fully satisfying regarding the distance for detailed observation of the bodies' surfaces. For triple systems, a third-body-disturbing version might be used in the case of one or two moonlets presenting small mass ratios, as is the case with (87) Sylvia [60], the first identified triple system, comprised of an asymmetric central body and two tinny moonlets with \(\sim\)10\({}^{-5}\) of the main body's mass and traveling prograde orbits quasi-circular and quasi-coplanar relative to the main body's equator. This has put on stage the search for naturally stable or at least weakly unstable orbits around NEO systems where to place a spacecraft within the system so as to observe the bodies and proceed to close approaches [43; 46; 61; 62; 63; 64]. Using the _mascon_ approach [64] to determine Sylvia's mass properties, ref. [60] found that all the equilibrium points are unstable but there are sufficiently long-lasting prograde orbits after 500 km from main body, approximately half-way to the inner moonlet orbit (\(\sim\)700 km radius), with variation up to 6 km in semi-axis and up to 0.05 in eccentricity for a period of 100 days, which may be enough for an initial approach-and-acquaintancephase. For a general three-body problem, ref.