Main characteristicsMain characteristics: systematic global search algorithm of quasi-ballistic trajectories; Gravity assist (GA) and : systematic global search algorithm of quasi-ballistic trajectories; Gravity assist (GA) and Aerogravity assist (AGA) manoeuvres; No propulsive manoeuvres during transfers; Discretisation of the variables that Aerogravity assist (AGA) manoeuvres; No propulsive manoeuvres during transfers; Discretisation of the variables that characterise trajectories and minimisation of predefined measures of merit; MATLAB software tool.characterise trajectories and minimisation of predefined measures of merit; MATLAB software tool.Physical modelPhysical model: Circular and coplanar planetary orbits, S/C motion in the same plane, linked-conic model for flybys: Circular and coplanar planetary orbits, S/C motion in the same plane, linked-conic model for flybysDifferent analyses:Different analyses:(A) Energy-based feasibility study(A) Energy-based feasibility study: NO phasing considerations; Discretised variables: v: NO phasing considerations; Discretised variables: v,L,L (magnitude and direction) (magnitude and direction)

and and (both + and -); (both + and -); Resonant transfers and all possible different transfers on the same orbit are considered.Resonant transfers and all possible different transfers on the same orbit are considered. (B) Phasing feasibility study(B) Phasing feasibility study: : Basic structure of the A-type algorithm is preserved; Improved model of Solar System, Basic structure of the A-type algorithm is preserved; Improved model of Solar System, based on the mean motion of the planets in circular and coplanar orbits; Finite number of bound orbits; based on the mean motion of the planets in circular and coplanar orbits; Finite number of bound orbits; Variable Variable launch date; Constraints on the position of the swingby planets and of the spacecraft at the rendezvous launch date; Constraints on the position of the swingby planets and of the spacecraft at the rendezvous dates; dates; Automated trade-offs, choosing suitable measures of merit (MM); general form: MM = wAutomated trade-offs, choosing suitable measures of merit (MM); general form: MM = w 11**VVLL+w+w22+w+w33**VVAA

Verification of PAMSIT: Verification of PAMSIT: Some of the obtained solutions are used as a first guess in a direct method optimisation Some of the obtained solutions are used as a first guess in a direct method optimisation tool, called DITAN. The optimised solutions resulted to be very close to the first guesses in terms of planetary tool, called DITAN. The optimised solutions resulted to be very close to the first guesses in terms of planetary encounters dates; the total encounters dates; the total V-costs necessary to restore feasibility remain low (in all tested cases, below 300 m/s). An V-costs necessary to restore feasibility remain low (in all tested cases, below 300 m/s). An example is shown in Figure 7 and 8: comparison 1example is shown in Figure 7 and 8: comparison 1ststguess-optimised trajectories (total corrective guess-optimised trajectories (total corrective V=77 m/s).V=77 m/s).The physical model seem to be consistent and the assumed tolerance at planetary rendezvous conservative.The physical model seem to be consistent and the assumed tolerance at planetary rendezvous conservative.The solutions found by PAMSIT can be used for preliminary mission analysis studies, but also as initial guesses for local The solutions found by PAMSIT can be used for preliminary mission analysis studies, but also as initial guesses for local optimisation tools, in order to restore the feasibility in a more complete model, using very limited optimisation tools, in order to restore the feasibility in a more complete model, using very limited Vs.Vs.

PAMSITPAMSIT

Figure 7:First guess solution (PAMSIT)Figure 7:First guess solution (PAMSIT) Figure 8: Optimised trajectory (DITAN)Figure 8: Optimised trajectory (DITAN)

PHASING FEASIBILITY STUDY:PHASING FEASIBILITY STUDY:MISSIONS TO JUPITERMISSIONS TO JUPITER

Time spanTime span: 5 years, from 1/1/2007 to : 5 years, from 1/1/2007 to 1/1/2012, step 1 Julian Day1/1/2012, step 1 Julian DayLaunch excess velocityLaunch excess velocity:from 2.5 to :from 2.5 to 7 km/s, step 0.25 km/s7 km/s, step 0.25 km/sPaths analysedPaths analysed::13 for GA-only, 18 for AGA+GA13 for GA-only, 18 for AGA+GARRRR (=N/D): both N and D from1 to 4 (=N/D): both N and D from1 to 4Bound orbitsBound orbits: max 4: max 4Maximum g-loadMaximum g-load: 12: 12Maximum ToFMaximum ToF: 7 sidereal years: 7 sidereal yearsToleranceTolerance: 5°: 5°EE*:*: 3.73 3.73MM:MM: ( ( ww=[w=[w11, w, w22, w, w33]] ))

MM1 -> MM1 -> ww=[0.75, 1, 1]=[0.75, 1, 1]MM2 -> MM2 -> ww=[0.75, 1, 0]=[0.75, 1, 0]MM3 -> MM3 -> ww=[0, 1, 1]=[0, 1, 1]Figure 9:Figure 9:To Jupiter; GA-only case; trajectory minimising MM1To Jupiter; GA-only case; trajectory minimising MM1 Figure 10:Figure 10:To Jupiter; AGA+GA; trajectory minimising MM1To Jupiter; AGA+GA; trajectory minimising MM1Table 6: To Jupiter; Best trajectories in the GA-only caseTable 6: To Jupiter; Best trajectories in the GA-only case Table 7: To Jupiter; Best trajectories in the AGA+GA caseTable 7: To Jupiter; Best trajectories in the AGA+GA case

PHASING FEASIBILITY STUDY:PHASING FEASIBILITY STUDY:MISSIONS TO NEPTUNEMISSIONS TO NEPTUNE

Time spanTime span: 15 years, from 1/1/2005 : 15 years, from 1/1/2005 to 1/1/2020, step 1 Julian Dayto 1/1/2020, step 1 Julian DayLaunch excess velocityLaunch excess velocity:from 2.5 to :from 2.5 to 9 km/s, step 0.25 km/s9 km/s, step 0.25 km/sPaths analysedPaths analysed::36 for GA-only, 37 for AGA+GA36 for GA-only, 37 for AGA+GARRRR (=N/D): both N and D from1 to 4 (=N/D): both N and D from1 to 4Bound orbitsBound orbits: max 4: max 4Maximum g-loadMaximum g-load: 12: 12Maximum ToFMaximum ToF: 15 sidereal years: 15 sidereal yearsToleranceTolerance: 5°: 5°EE*:*: 5 5MM:MM: ( w=[w( w=[w11, w, w22, w, w33]] ))

MM1 -> MM1 -> ww=[1.5, 1, 1]=[1.5, 1, 1]MM2 -> MM2 -> ww=[1.5, 1, 0]=[1.5, 1, 0]MM3 -> MM3 -> ww=[0, 1, 1]=[0, 1, 1] Figure 12:Figure 12:To Neptune; AGA+GA; trajectory minimising MM1To Neptune; AGA+GA; trajectory minimising MM1Table 9: To Neptune; Best trajectories in the AGA+GA caseTable 9: To Neptune; Best trajectories in the AGA+GA caseFigure 11:Figure 11:To Neptune; GA-only case; trajectory minimising MM1To Neptune; GA-only case; trajectory minimising MM1 Table 8: To Neptune; Best trajectories in the GA-only caseTable 8: To Neptune; Best trajectories in the GA-only case

ENERGY-BASED ANALYSIS: HIGH ENERGY MISSIONENERGY-BASED ANALYSIS: HIGH ENERGY MISSIONMissions to Outer planetsMissions to Outer planets: target is the sphere of influence of the selected celestial body: target is the sphere of influence of the selected celestial body

Sun observation missionSun observation mission: target is a perihelion distance of four solar radii: target is a perihelion distance of four solar radiiLaunch excess velocityLaunch excess velocity: 3 km/s, 5 km/s and 7 km/s; : 3 km/s, 5 km/s and 7 km/s; EE*:*: 3.73 3.73

FlybysFlybys: A maximum of 4 intermediate planetary encounters for GA-only, 3 in case of AGA+GA. : A maximum of 4 intermediate planetary encounters for GA-only, 3 in case of AGA+GA. Obtained results (see Table 5 and 6).Obtained results (see Table 5 and 6).

From energy-based considerations, unfeasible solutions can be now disregarded, thus reducing the computational time of the From energy-based considerations, unfeasible solutions can be now disregarded, thus reducing the computational time of the subsequent analysis, which introduces the phasing model.subsequent analysis, which introduces the phasing model.

Table 4: Table 4: GA-only strategies that allow minimum ToFGA-only strategies that allow minimum ToF Table 5: ATable 5: AGA+GA strategies that allow minimum ToFGA+GA strategies that allow minimum ToF

COMPARISON BETWEEN AGA AND GA STRATEGIES COMPARISON BETWEEN AGA AND GA STRATEGIES

Paths involving only GA (Paths involving only GA (GA-onlyGA-only) are compared to strategies with AGA in combination with or in substitution to GA () are compared to strategies with AGA in combination with or in substitution to GA (AGA+GAAGA+GA).).1)1) A preliminary purely energetic analysis will be performed (phasing is not taken into account; we look for the maximum performances theoretically achievable in both cases).A preliminary purely energetic analysis will be performed (phasing is not taken into account; we look for the maximum performances theoretically achievable in both cases).

2)2) Considering the actual phase of the planets, two missions of great scientific interest, to Jupiter and to Neptune, will be studied, showing optimal launch options in the two casesConsidering the actual phase of the planets, two missions of great scientific interest, to Jupiter and to Neptune, will be studied, showing optimal launch options in the two cases

GA model: GA model: Keplerian hyperbolasKeplerian hyperbolasAGA main idea: AGA main idea: Phase1 -> Hyperbolic incoming trajectory;Phase1 -> Hyperbolic incoming trajectory;

Phase2 -> Constant altitude flight in the atmosphere;Phase2 -> Constant altitude flight in the atmosphere;Phase3 -> Hyperbolic outgoing trajectory;Phase3 -> Hyperbolic outgoing trajectory;

Lower vLower v++, but higher , but higher => greater => greater V than GA; Drag losses in velocity can be V than GA; Drag losses in velocity can be

minimized by hypersonic vehicles (waveriders) with high maximum minimized by hypersonic vehicles (waveriders) with high maximum aerodynamic efficiency E*aerodynamic efficiency E*

AGA models: AGA models: Incoming and outgoing arcs -> unperturbed hyperbolas; Incoming and outgoing arcs -> unperturbed hyperbolas; Constant altitude phase -> Three analytical solutions of the real dynamics, Constant altitude phase -> Three analytical solutions of the real dynamics,

corresponding to n=1, n=1.5 and n=2 incorresponding to n=1, n=1.5 and n=2 in

GRAVITY ASSIST (GA) AND AEROGRAVITY ASSIT (AGA) MODELSGRAVITY ASSIST (GA) AND AEROGRAVITY ASSIT (AGA) MODELS

Figure 1:Generic GA trajectory(relative r. frame)Figure 1:Generic GA trajectory(relative r. frame)

v+

VPlanet

v-

Figure 2: Generic GA vector diagramFigure 2: Generic GA vector diagram

v+

VPlanet

V -

V +

V

v-

+ -

Figure 3: Generic AGA trajectory(relative r.frame)Figure 3: Generic AGA trajectory(relative r.frame) Figure 4: Generic AGA vector diagramFigure 4: Generic AGA vector diagram

v +

VPlanet

V -

V +

V

v -

+ -

Cases analysed:Cases analysed:- Case 1Case 1: Three set of solutions : Three set of solutions corresponding to the three models of corresponding to the three models of the entire AGA-manoeuvre.the entire AGA-manoeuvre.- Case 2Case 2: Solutions for a model with : Solutions for a model with unperturbed incoming and outgoing unperturbed incoming and outgoing arcs, solving the dynamic in the arcs, solving the dynamic in the atmospheric phase by numerical atmospheric phase by numerical integration with n=1.75.integration with n=1.75.- Case 3Case 3: Numerical integrations of : Numerical integrations of the dynamics of the entire the dynamics of the entire trajectories. Zero-lift attitude (Ctrajectories. Zero-lift attitude (CLL=0 =0

and Cand CDD= C= CD0D0) during the incoming ) during the incoming

and outgoing arcs. and outgoing arcs.

Conclusions:Conclusions: (see Table 2 and 3)(see Table 2 and 3)- Approximations due to different n Approximations due to different n appear negligible (the best is n=2)appear negligible (the best is n=2)- Mean errors remain always low => Mean errors remain always low => we chose n=1 for sake of simplicity.we chose n=1 for sake of simplicity.

Hypotheses for the comparison:Hypotheses for the comparison:- AGA bodies: Venus, Earth and MarsAGA bodies: Venus, Earth and Mars- Maximum aerodynamic efficiency Maximum aerodynamic efficiency E* reached at the beginning of the E* reached at the beginning of the atmospheric flight => Periapsis radii atmospheric flight => Periapsis radii of the incoming trajectory are taken of the incoming trajectory are taken from Figure 5 a-b-c.from Figure 5 a-b-c.- Waverider characteristics are taken Waverider characteristics are taken from Table 1from Table 1- Only trajectory with total deflection Only trajectory with total deflection angle angle less than 180° are considered less than 180° are considered- vv

-- is varied from 0 to 30 km/s and is varied from 0 to 30 km/s and

from 0° to 180°from 0° to 180°

Percentage error definition:Percentage error definition:In order to analyse the quantity z In order to analyse the quantity z (where z is (where z is or v or v

++) while comparing ) while comparing

Case xCase x and and Case y, we defineCase y, we define::

NUMERICAL COMPARISON NUMERICAL COMPARISON OF AGA MODELSOF AGA MODELS

Figure 5a: Venus,Figure 5a: Venus,AGA atmospheric flight altitudesAGA atmospheric flight altitudes

Figure 5c: Mars, Figure 5c: Mars, AGA atmospheric flight altitudesAGA atmospheric flight altitudes

Table 1: Features of the nominal waverider vehicleTable 1: Features of the nominal waverider vehicle

Figure 5b: Earth, Figure 5b: Earth, AGA atmospheric flight altitudesAGA atmospheric flight altitudes

Figure 6: Example of the trend of the percentage error on Figure 6: Example of the trend of the percentage error on v v++

; surface and contour plot; surface and contour plot

Table 2: Comparison between Case 1 and Case 2Table 2: Comparison between Case 1 and Case 2 Table 3: Comparison between Case 1 and Case 3 Table 3: Comparison between Case 1 and Case 3

PRELIMINARY ANALYSIS OF INTERPLANETARY TRAJECTORIESPRELIMINARY ANALYSIS OF INTERPLANETARY TRAJECTORIESWITH AEROGRAVITY AND GRAVITY ASSIST MANOEUVRES WITH AEROGRAVITY AND GRAVITY ASSIST MANOEUVRES

Stefano M. Pessina, Stefano M. Pessina, Politecnico di Milano university, Milan, Italy; stepex@tin.itPolitecnico di Milano university, Milan, Italy; stepex@tin.itStefano CampagnolaStefano Campagnola, ESA/ESOC - Mission Analysis Office, Darmstadt, Germany; Stefano.Campagnola@esa.int, ESA/ESOC - Mission Analysis Office, Darmstadt, Germany; Stefano.Campagnola@esa.int

Massimiliano VasileMassimiliano Vasile, ESA/ESTEC - Advanced Concepts Team , Noordwijk, The Netherlands; Massimiliano.Vasile@esa.int, ESA/ESTEC - Advanced Concepts Team , Noordwijk, The Netherlands; Massimiliano.Vasile@esa.intPaper IAC-03-A.P.08,  54th International Astronautical Congress, September 29 – October 3, 2003, Bremen, GermanyPaper IAC-03-A.P.08,  54th International Astronautical Congress, September 29 – October 3, 2003, Bremen, Germany