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?