Solar Polar Imager Mission Bernd Dachwald Solar Sail Trajectory Optimization Andreas Ohndorf Bong Wie for the Solar Polar Imager (SPI) Mission Outline Introduction German Aerospace Center (DLR) Modeling Issues German Space Operations Center (GSOC) Bernd Dachwald Mission Operations Section Trajectory Oberpfaffenhofen, 82234 Wessling, Germany Optimization Methods bernd.dachwald@dlr.de Cold Mission German Aerospace Center (DLR) Scenario Institute of Space Simulation Andreas Ohndorf Linder H¨ ohe, 51147 Cologne, Germany Hot Mission andreas.ohndorf@dlr.de Scenario Arizona State University Summary and Department of Mechanical & Aerospace Engineering Bong Wie Conclusions Tempe, AZ 85287, USA bong.wie@asu.edu AIAA/AAS Astrodynamics Specialist Conference 21–24 August 2006, Keystone, CO
Solar Polar Outline Imager Mission Introduction Bernd Dachwald Andreas Ohndorf Mission Rationale Bong Wie Solar Sailcraft Design Reference Solution Outline Hot Solution Preview Introduction Modeling Issues Modeling Issues Trajectory Solar Sail Force Model Optimization Simulation Model Methods Trajectory Optimization Methods Cold Mission Scenario Local Steering Laws Hot Mission Evolutionary Neurocontrol Scenario Cold Mission Scenario Summary and Conclusions Hot Mission Scenario Baseline Scenario Variation of the Sail Temperature Limit Variation of the Characteristic Acceleration Variation of the Hyperbolic Excess Energy Solar Sail Degradation Summary and Conclusions
Solar Polar The Solar Polar Imager Mission Imager Mission Bernd Dachwald Andreas Ohndorf Bong Wie ◮ SPI mission is one of several Sun-Earth Connection solar Outline sail roadmap missions currently envisioned by NASA Introduction ◮ Objectives: Mission Rationale Solar Sailcraft Design ◮ To investigate the global structure and dynamics of the Reference Solution Hot Solution Preview solar corona Modeling Issues ◮ To reveal the secrets of the solar cycle and the origins of Trajectory solar activity Optimization Methods ◮ Target orbit is a heliocentric circular orbit at 0 . 48 AU Cold Mission with an inclination of 75 deg Scenario ◮ 3:1 resonance with Earth Hot Mission Scenario ◮ different target inclinations have been considered in Summary and various previous studies Conclusions ◮ Similar solar sail mission, called Solar Polar Orbiter (SPO), is studied by ESA
Solar Polar Solar Sailcraft Design for the SPI Mission Imager Mission Bernd Dachwald ◮ 160 m × 160 m, 150 kg square solar sail assembly Andreas Ohndorf Bong Wie ◮ 250 kg spacecraft bus Outline ◮ 50 kg scientific payload Introduction ◮ 450 kg total mass Mission Rationale Solar Sailcraft Design Reference Solution ◮ Characteristic thrust (max. thrust at 1 AU): F c = 160 mN Hot Solution Preview Modeling Issues ◮ Characteristic acceleration (max. acceleration at 1 AU): Trajectory a c = 0 . 35 mm / s 2 Optimization Methods Cold Mission Scenario Hot Mission Scenario Summary and Conclusions DLR solar sail deployment test 1999@ESA ATK solar sail deployment test 2005@NASA
Solar Polar Reference Solution Imager Mission Bernd Dachwald Andreas Ohndorf Bong Wie ◮ Sail film temperature: T < 100 ◦ C ◮ Hyperbolic excess energy: C 3 = 0 . 25 km 2 / s 2 Outline Introduction Mission Rationale c Solar Sailcraft Design Reference Solution Hot Solution Preview Modeling Issues Trajectory ≤ Optimization 3 Earth Methods 5 Cold Mission Scenario Hot Mission Scenario 4 Summary and Conclusions 1 2 Sauer 9-14-04 spi340-75-1074 Mission duration: 6.7 years ∆ ∆ ⊥
Solar Polar Preview of Our Hot Solution Imager Mission Bernd Dachwald ◮ Sail film temperature limit: T lim = 240 ◦ C Andreas Ohndorf Bong Wie ◮ Hyperbolic excess energy: C 3 = 0 km 2 / s 2 Outline Introduction Mission Rationale Sail Temp. [K] Arrival at target orbit Solar Sailcraft Design Sail temperature (a = 0.48 AU, i = 75 deg) 520 Reference Solution does not exceed 240°C 500 Hot Solution Preview 450 400 Modeling Issues 350 300 Trajectory Optimization Methods Cold Mission Scenario Hot Mission Scenario Summary and Conclusions Launch at Earth Mission duration: 4.7 years
Solar Polar The Non-Perfectly Reflecting Solar Sail Imager Mission Bernd Dachwald Andreas Ohndorf Bong Wie The non-perfectly reflecting solar sail model Outline parameterizes the optical behavior of the sail Introduction film by the optical coefficient set ρ : reflection Modeling Issues coefficient Solar Sail Force Model s : specular reflection P = { ρ, s , ε f , ε b , B f , B b } Simulation Model factor Trajectory ε f and ε b : emission Optimization The optical coefficients for a solar sail with a coefficients of the Methods front and back side, highly reflective aluminum-coated front side and Cold Mission respectively Scenario with a highly emissive chromium-coated back B f and B b : Hot Mission non-Lambertian side are: Scenario coefficients of the front and back side, Summary and respectively Conclusions P Al | Cr = { ρ = 0 . 88 , s = 0 . 94 , ε f = 0 . 05 , ε b = 0 . 55 , B f = 0 . 79 , B b = 0 . 55 }
Solar Polar Simulation Model Imager Mission Bernd Dachwald Andreas Ohndorf Considerations for high-precision Allowed simplifications for Bong Wie trajectory control: mission feasibility analysis: Outline ◮ Solar sail bends and wrinkles, ◮ Solar sail is a flat plate Introduction depending on actual solar sail Modeling Issues design Solar Sail Force Model ◮ Gravitational forces of all ◮ Solar sail is moving under sole Simulation Model celestial bodies influence of solar gravitation Trajectory Optimization and radiation ◮ Reflected light from close Methods celestial bodies Cold Mission Scenario ◮ Solar wind Hot Mission ◮ Finiteness of solar disk Scenario ◮ Sun is a point mass and a point light source Summary and Conclusions ◮ Finite low-precision attitude ◮ Solar sail attitude can be control maneuvers changed instantaneously ◮ Aberration of solar radiation (Poynting-Robertson effect)
Solar Polar Local Steering Laws (LSLs) Imager Mission Bernd Dachwald Andreas Ohndorf Bong Wie ◮ LSLs give locally optimal thrust direction to Outline a r , a t , a h : change some specific osculating orbital acceleration Introduction components along element of spacecraft with maximum rate the radial, Modeling Issues transversal, and orbit ◮ In an orbital reference frame Trajectory normal direction Optimization Methods O = { e r , e t , e h } , the equations for the e : eccentricity Local Steering Laws semi-major axis a and the inclination i can f : true anomaly Evolutionary Neurocontrol be written as h : orbital angular Cold Mission momentum per Scenario spacecraft unit mass dt = 2 a 2 da e sin f a r + p Hot Mission � � r a t p : semilatus rectum Scenario h Summary and r : radius dt = r cos( ω + f ) di Conclusions a h ω : argument of h perihelion
Solar Polar Local Steering Laws (LSLs) Imager Mission Bernd Dachwald Andreas Ohndorf Bong Wie ◮ LSLs give locally optimal thrust direction to Outline a r , a t , a h : change some specific osculating orbital acceleration Introduction components along element of spacecraft with maximum rate the radial, Modeling Issues transversal, and orbit ◮ In an orbital reference frame Trajectory normal direction Optimization Methods O = { e r , e t , e h } , the equations for the e : eccentricity Local Steering Laws semi-major axis a and the inclination i can f : true anomaly Evolutionary Neurocontrol be written as h : orbital angular Cold Mission momentum per Scenario spacecraft unit mass dt = 2 a 2 da e sin f a r + p Hot Mission � � r a t p : semilatus rectum Scenario h Summary and r : radius dt = r cos( ω + f ) di Conclusions a h ω : argument of h perihelion
Solar Polar Local Steering Laws (LSLs) Imager Mission Bernd Dachwald Andreas Ohndorf Bong Wie a : acceleration vector dt = 2 a 2 da e sin f a r + p � � Outline r a t a r , a t , a h : h Introduction acceleration components along dt = r cos( ω + f ) di Modeling Issues the radial, a h transversal, and orbit Trajectory h normal direction Optimization Methods e : eccentricity can be written as Local Steering Laws Evolutionary f : true anomaly Neurocontrol 2 a 2 h e sin f Cold Mission a r h : orbital angular da Scenario momentum per 2 a 2 = k a · a p dt = · a t spacecraft unit mass Hot Mission h r Scenario a h 0 k : direction vector Summary and p : semilatus rectum Conclusions 0 a r di r : radius · = k i · a 0 dt = a t r cos( ω + f ) ω : argument of a h perihelion h
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