Low-thrust trajectory design

ASEN5050 Astrodynamics 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

𝑀 𝑠/𝑐 Δ𝑉 𝑠/𝑐 = 𝑀 𝑒𝑥ℎ𝑎𝑢𝑠𝑡 𝑉 𝑒𝑥ℎ𝑎𝑢𝑠𝑡

Specific impulse

Specific impulse: Rocket equation: 𝐼 𝑠𝑝 = 𝑉 𝑒𝑥ℎ𝑎𝑢𝑠𝑡 𝑔 0 𝑀 𝑓 𝑀 0 = exp( −∆𝑉 𝐼 𝑠𝑝 𝑔 0 )

Rocket equation Dawn

LEO/GTO to GEO

SMART-1

Why is a higher I SP not always better?

𝑇 𝑚𝑎𝑥 = 2𝑃 𝑚𝑎𝑥 𝐼 𝑠𝑝 𝑔 0 (Elvik, 2004)

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 intuitive  Specialized, computationally intensive tools required!

Example Method

Fly by, probe release, etc...

(discontinuous state) Backward integration

Match Points

• JPL’s MALTO – Mission Analysis Low Thrust Optimization Forward integration – Originally: CL-SEP (CATO-Like Solar Electric Propulsion) Small impulsive burns Source: Sims et al., 2006

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 date  Visiting 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)

(Garza, 2013) • • • GEO communications satellite, launched 2010 Stuck in transfer orbit (due to propellant line clog) Mission saved by on-board Hall thrusters

Commercial GEO satellites

(Bostian et al., 2000)

Commercial GEO satellites

Commercial GEO satellites

(Byers&Dankanich, 2008)

Outlook

Electric propulsion developments

• Boeing  Four GEO satellites, 2 tons each  Capable of launching two-at-a-time on vehicles as small as Falcon9  Private endeavor • ESA/SES/OHB  Public-Private partnership  One “small-to-medium” GEO satellite  Possibly the second generation spacecraft of the Galileo constellation • NASA  30kW 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?