Jose Rodriguez-Canabal Memorial Interplanetary Trajectory design for Rosetta and Solar Orbiter Johannes Schoenmaekers H / Mission Analysis Section (HSO-GFA) Senior Adviser ESA / ESOC Email: johannes.schoenmaekers@esa.int
Outline Patched conics model Tisserand graph Swing-by s Resonant orbits Delta-V gravity assists Application to Rosetta Application to Solar Orbiter ESA Unclassified for Official Use ESA/ESOC March Page
Patched Conics Model: Swing-by Earth co rotating velocity V departure to th orbit normal (Req) to th orbit normal (km/s) V planet V arrival 8 7 9 to sun th velocity (km/s) Velocity modulus (km/s) to sun th position (Req) 7 Earth velocity to sun th velocity (Req) to sun th position (km/s) Time from perigee (days) ESA Unclassified for Official Use ESA/ESOC March Page
Patched Conics Model: Hyperbola m/s at - days => km change in approach point Earth: V infinity = 8 km/s; V infinity = to Req Earth: R infinity = Req; V infinity = 8 km/s 8 Z Y position (Req) Z position (AU) Y X 8 8 8 X position (Req) ESA Unclassified for Official Use ESA/ESOC March Page
Patched conics model: Sumy Motion relative to sun modelled by ellipse segment: Starting and ending at the centre of a planet or DSM location Start time of next segment = End time of previous segment Motion relative to planet modelled by hyperbola: Infinity arrival velocity vector of hyperbola = Final velocity vector of preceding ellipse segment - Planet velocity vector Infinity departure velocity magnitude = Infinity arrival velocity magnitude Control of deflection magnitude and direction by small adjustments of arrival conditions (few m/s) Deflection magnitude limited by minimum peri-centre radius Initial velocity vector of following ellipse segment = Planet velocity vector + Infinity departure velocity vector of hyperbola Motion relative to asteroid or comet: Straight line Rendez-vous Delta-V vector = - Infinity arrival velocity vector Deep space manoeuvre: Delta-V vector = Initial velocity vector of following ellipse segment - Final velocity vector of preceding ellipse segment ESA Unclassified for Official Use ESA/ESOC March Page
Tisserand graph: V-infinity lines Ecliptic projection; V unit = V th / ; V infinity = 9 km/s. Tisserant Graph Perihelion (AU). Aphelion (AU) ESA Unclassified for Official Use ESA/ESOC March Page
Tisserand graph: Resonant orbits Ecliptic projection; V unit = V th / ; V infinity = 9 km/s. Tisserant Graph Perihelion (AU). Aphelion (AU) ESA Unclassified for Official Use ESA/ESOC March Page 7
Tisserand graph: Resonant orbits Ecliptic projection; V unit = V th / ; V infinity = 9 km/s. Tisserant Graph Perihelion (AU). Aphelion (AU) ESA Unclassified for Official Use ESA/ESOC March Page 8
Tisserand graph: Rosetta Landing on Comet Churyumov-Gerasimenko. Tisserant Graph Ecliptic projection. Perihelion (AU)..8.. Venus Earth Mars Jupiter. pow Aphelion (AU) m/s ESA Unclassified for Official Use ESA/ESOC March Page 9
Tisserand graph: Solution types Heliocentric distance m/s Ecliptic projection Heliocentric distance m/s Ecliptic projection Distance to sun (AU) Distance to sun (AU) 8 Date m/s 8 Date m/s Heliocentric distance m/s Ecliptic projection Heliocentric distance m/s Ecliptic projection Distance to sun (AU) Distance to sun (AU) 8 Date m/s 8 Date m/s ESA Unclassified for Official Use ESA/ESOC March Page
Tisserand graph: Rosetta Heliocentric distance flb Ecliptic projection m/s Distance to sun (AU) 7 m/s m/s m/s 78 m/s 79 m/s 8 Date 78 m/s 7 m/s m/s 79 m/s flb ESA Unclassified for Official Use ESA/ESOC March Page
Tisserand graph: DV Gravity assist. Tisserant Graph. Sun ecliptic system.9. Perihelion (AU).8.7......8....8... Aphelion (AU)..... ESA Unclassified for Official Use ESA/ESOC March Page
Tisserand graph: Rosetta... Tisserant Graph Ecliptic projection m/s Perihelion (AU).8.. Venus Earth Mars Jupiter. pow Aphelion (AU) 78 m/s 7 m/s m/s 79 m/s flb ESA Unclassified for Official Use ESA/ESOC March Page
Tisserand graph: Sumy -D plot of pericentre radius versus apocentre radius Simplifications Planar motion Circular planet orbits Timing ignored Content Equal V-infinity lines Lines of full and pseudo resonances Lines of maximum deflection of V-infinity Lines of constant pericentre and apocentre velocity => DV gravity assist Purpose Identify possible sequences of swing-by s and resonances Identify associated solution types (inward and outward) Time gaps solved by Shifting swing-by s by one or more planer revolutions Adding intermediate revolutions Closing residual time gap by local optimisation of given solution type ESA Unclassified for Official Use ESA/ESOC March Page
Inner solar system transfer: Solo Close and high latitude solar observatory mission Perihelion (AU)..9.8.7..... Venus Earth Mars Jupiter pow Tisserant Graph...7.8.9..... Aphelion (AU) out of plane (km/s) S/C absolute velocity deg Velocity w.r.t. Venus Venus absolute velocity S/C relative velocity 9 km/s in plane (km/s) ESA Unclassified for Official Use ESA/ESOC March Page
Inner solar system transfer: Solo.. Heliocentric distance ven. Ecliptic projection Distance to sun (AU).8...8... 8 8 Date Tilt to Y axis (deg) Ecliptic orbit normal tilt mer ven Tilt to X axis (deg)......8 ven...8.......8. ESA Unclassified for Official Use ESA/ESOC March Page
Outer solar system transfer: Juice.. Mission to Jovian moons Europa and Ganymede Tisserant Graph. Perihelion (AU).8.. Venus Earth. Mars Jupiter Aphelion (AU) ESA Unclassified for Official Use ESA/ESOC March Page 7
Outer solar system transfer: Juice Heliocentric distance ven jup Distance to sun (AU) m/s Ecliptic projection 7 8 9 Date m/s ven jup ESA Unclassified for Official Use ESA/ESOC March Page 8