# Circular Orbit Flip Trajectories Generated by E-Sail
## 4 Final Remarks and Conclusions  
In the context of mission scenarios based on the use of E-sails, the present work has proposed a new approach to achieve a complete reversal of the direction of motion along a circular, heliocentric orbit of assigned radius. The orbit reversal maneuver uses a two-dimensional transfer trajectory that is coplanar to the initial parking orbit and uses the continuous thrust provided by a medium-high performance E-sail to suitably change the parameters of the osculating orbit during flight. The concept discussed in this paper stems from observation of the particular shape of a family of H-reversal orbits, originally proposed by [PERSON] more than 25 years ago and subsequently studied in detail in more recent literature.  
What is interesting is that the analysis of two-dimensional \"flip trajectories\", conducted using an optimization approach, revealed the existence of a new class of highly non-Keplerian orbits with the presence of both an H-reversal condition and a close passage to the Sun. Such interesting transfer trajectories allow the two-dimensional orbital flip to be completed in a time interval of a few multiples of the period of the parking orbit, even using a medium-performance E sail. This is an intriguing result, because in the case of a solar sail-based spacecraft, propelled trajectories that include an H-reversal point usually require a high-performance propulsion system, as [PERSON] pointed out in his pioneering work. Therefore, the possibility of achieving this rather exotic orbital transfer with a medium-performance propulsion system indicates a possible new application of the propulsion system invented by [PERSON] 20 years ago.  
The procedure discussed in this paper can be extended, with relatively low effort, to a solar sail-based mission scenario. In this case, the presence of a flip trajectory with a close pass to the Sun would reduce (when assigning the total flight time) the value of the sail characteristic acceleration required to complete the transfer.  
A second possible extension of this work involves comparing the performance of a two-dimensional flip trajectory with that of a cranking maneuver. Indeed, in a mission scenario based on the use of sails (both in the case of the solar sail and the E-sail), when it is necessary to achieve a high variation in the orbital inclination of a heliocentric orbit (as in the case studied in this work), the typical optimal transfer trajectory can ideally be divided into three parts. A first part in which the spacecraft approaches the Sun to increase the maximum modulus of propulsive acceleration, a middle part in which the orbital inclination is changed while keeping the solar distance (usually sufficiently low) essentially constant, and,finally, a third part in which the spacecraft increases the orbital  
Figure 15: Time variation of the two control parameters in a SWA transfer with \(\beta=0.19\). Black circle \(\rightarrow\) starting point; red star \(\rightarrow\) aphelion point; black square \(\rightarrow\) arrival; red triangle \(\rightarrow\) perihelion point; shaded area \(\rightarrow\tau=0\).  
radius to return to the initial solar distance and thus complete the transfer. In this context, an extension of this work could clarify whether the proposed two-dimensional approach provides better performance (in terms of flight time reduction) than the typical three-part procedure for varying orbital inclination. If so, a parametric study of the problem should be conducted, considering both the effect of propulsive performance (i.e., the sail acceleration) and the value of the required change in orbital inclination.  
Conceptualization, A.A.Q.; methodology, A.A.Q.; software, A.A.Q.; writing--original draft preparation, A.A.Q.; writing--review and editing, M.B. and G.M. All authors have read and agreed to the published version of the manuscript.  
The authors