Low-thrust trajectory design
ASEN5050Astrodynamics
Jon Herman
Overview• Low-thrust basics
• Trajectory design tools
• Real world examples
• Outlook
Low-thrust• Electric propulsion
– Solar electric propulsion (SEP)– Nuclear electric propulsion (NEP)– SEP is mature technology, NEP not exactly
• Solar sails– Comparatively immature technology– Performance currently low
• All very similar from trajectory design stand point
Electric Propulsion
• Electric Propulsion About 0.2 Newton About 4 sheets of paper
• Engine runs for months-years
• 10 times as efficient
• Chemical propulsion Up to ~17 000 000 N About 4 000 000 000 sheets of
paper
• Engine runs for minutes
Hall thrusters
(University of Tokyo, 2007)
Exhaust velocity: 10 – 80 km/s
Conservation of momentum
Specific impulse
Specific impulse:
Rocket equation:
Rocket equation
LEO/GTO to GEO
SMART-1
Dawn
Why is a higher ISP not always better?
(Elvik, 2004)
𝑇𝑚𝑎𝑥=2𝑃𝑚𝑎𝑥
𝐼 𝑠𝑝𝑔0
Implications for optimal trajectories The optimal transfer properly balances
• Specific impulse• Spacecraft power• Mission ΔV
Unique optimum for every mission
ΔV no longer a defining parameter!(arguably: ΔV no longer a limiting parameter)
Trajectory design
Trajectory example• What is difficult about low-thrust?
– Trajectory is “continuously” changing– No analytical solutions– Optimal thrust solution only partially intuitiveSpecialized, computationally intensive tools
required!
Example Method
• JPL’s MALTO– Mission Analysis
Low Thrust Optimization– Originally: CL-SEP
(CATO-Like Solar Electric Propulsion)Source: Sims et al., 2006
Forward integration
Backward integration
Match Points
Small impulsive burns
Fly by, probe release, etc...(discontinuous state)
MALTO-type tools• Optimize...
Trajectory• Subject to whatever desired trajectory contraints
Specific impulse (Isp)
Spacecraft power supply• Using solar power• Using constant power (nuclear)• Possible: solar sail size, etc.
Strengths• Fast• Robust• Flexible• Optimizes trajectory & spacecraft!
Weaknesses• Ideal for simple (two-body) dynamics
• Limited to low revolutions (~8 revs)– No problem for interplanetary trajectories– ~Worthless for Earth departures/planetary arrivals
Real world applications
Dawn (NASA)
• Dawn ( 2007 – Present day)Most powerful Electric Propulsion mission to dateVisiting the giant asteroids Vesta and Ceres
Dawn
SMART-1 (ESA)
• Launched in 2003 to GTO• Transfer to polar lunar orbit• Only Earth ‘escape’ with low-thrust• Propellant Mass / Initial Mass:
23% (18% demonstrated later)
SMART-1
(ESA, 1999)
Hayabusa (JAXA)
• First asteroid sample return (launched 2003)
• 4 Ion engines at launch• 1 & two half ion engines upon return
Hayabusa end-of-life operation
Engine 1 Engine 2
(University of Tokyo, 2007)
AEHF-1 (USAF)
• GEO communications satellite, launched 2010
• Stuck in transfer orbit (due to propellant line clog)
• Mission saved by on-board Hall thrusters
(Garza, 2013)
Commercial GEO satellites
(Bostian et al., 2000)
Commercial GEO satellites
Commercial GEO satellites
(Byers&Dankanich, 2008)
Outlook
Electric propulsion developments
• BoeingFour GEO satellites, 2 tons eachCapable of launching two-at-a-time on vehicles as small as Falcon9Private endeavor
• ESA/SES/OHBPublic-Private partnershipOne “small-to-medium” GEO satellitePossibly the second generation spacecraft of the Galileo
constellation
• NASA30kW SEP stage demonstrator (asteroid retrieval?)
Conclusion• Electric propulsion rapidly maturing into a
common primary propulsion system
• This enables entirely new missions concepts, as well as reducing cost of more typical missions
• Very capable trajectory design tools exist, but not all desired capability is available or widespread
Questions?