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Lunar Trajectories Transportation for Exploration: New Thoughts About Orbital Dynamics Ed Belbruno Innovative Orbital Design, Inc & Courant Insitiute(NYU) January 4, 2012 NASA FISO 1 Evolution of Astrodynamics Conic; Stable (Hohmann, 20s) (Hohmann transfers, Gravity assist(Voyager, Galileo)) Nonlinear; Stable (Apollo, 60s) Nonlinear; Unstable (ISEE-3, 70s) (Transfer to and from halo orbits, no utilization of fuel savings via dynamics – Farquhar …) Nonlinear; Unstable; Low Energy/Fuel (Hiten, 91) (First use of utilization of chaotic dynamics/manifolds to achieve new approach to space travel for ballistic capture(EB, 86, 91) and for the study of halo orbit dynamics (Llibre-Simo, 85 – Genesis, 2001) Weak Stability Boundary Theory (EB 86) 2 Hohmann Transfer Conic, Stable – 2-body 3 Figure Eight(Apollo) Nonlinear, Stable – 3-body 4 ISEEC-3 Nonlinear-Unstable – 4 body 5 Ballistic Capture Transfers Weak Stability Boundary Theory(EB 86) • Way to transfer to the Moon, and other bodies, where no DeltaV is needed for capture • New methodology to trajectory design • Thought in 1985 to be impossible 6 Background • Capture Problem Earth -> Moon (LEO -> LLO) • Hohmann Transfer: Fast (3days), Fuel Hog (Need to slow down! 1 km/s to be captured – large maneuver ) Risky Used in Apollo 7 Idea of Achieving Ballistic Capture • Sneak up on Moon - very carefully (next figure A-B-C-D) • Like a surfer catching a wave • Want to ride the „gravity transition(weak stability) boundary‟ between the Earth-Moon-Sun 8 Top – Lagrange points Bottom – Sneaking up on Moon 9 Ballistic capture is chaotic (chaos – leaf blowing in wind) 10 • WSB – generalization of Lagrange points • Forces(GM, GE, CF) balance while spacecraft moving wrt Earth-Moon (L-points – forces balance for spacecraft fixed wrt Earth-Moon) • Get a multi-dimensional region about Moon. Can map out on computer via algorithm. • While in WSB, motion unstable, chaotic, but capture wrt Moon obtained - weak. 11 12 13 • In 1986 found ballistic capture transfer to Moon for first time – 2 yr route. (Taken as oddity at that time) (low energy since no DV for capture) • Lunar Get Away Special(LGAS) – first use of chaos in space travel for capture (E. Belbruno). (In Spain, Llibre, Simo used chaos to control halo orbits in 1985) • Shorter time ballistic capture transfer not found in 1990. I luckily found a short one(5 months) to rescue a Japanese lunar spacecraft Hiten. 14 Idea to find low energy transfer 15 Key Observations Hiten transfer • Four-Body Problem • Interlink weak stability boundaries: E-S M-E 16 17 18 • Hiten reached Moon on a new transfer on October 2, 1991 – first operational demo of a low energy ballistic capture transfer, proving methodology – See http://en.wikipedia.org/wiki/Hiten 19 20 Missions Using WSB Approach: • First: Hiten – 1991 (exterior WSB transfer) (EB 1991) • Second: SMART-1 (ESA) – 2004 (interior WSB transfer) (first found by EB in 1986 for LGAS) • Genesis – 2001 - used some WSB dynamics (and ideas of Llibre-Simo 1985) • GRAIL – September 10, 2011 – same transfer type as Hiten – See current article in Time Magazine http://www.time.com/time/health/article/0,8599,2103466, 00.html 21 Other Applications • WSB transfer planned for ESA BepiColombo Mercury mission • Three month WSB transfer saves 25% in DV to place payloads onto the Moon or into lunar orbit – can double payload. • Ideal choice for a lunar base construction 22 Low energy trajectories and manifolds • Ballistic capture transfers move from the Earth to ballistic capture at the Moon by following manifolds – These minimize energy • These are tubes in the position-velocity space that the trajectories travel on • A WSB is a complex network of manifolds 23 24 25 26 Manifold to lissajous orbit about L1. The trajectory(in red) lies on the manifold(Llibre, Simo 1985) 27 Weak Stability Boundary Structure • New paper gives a rigorous result on the structure of this boundary – as complex set of intersections of manifolds forming a Cantor set of fractional dimension. E. Belbruno, M. Gidea, F. Topputo, “Weak Stability Boundary and Invariant Manifolds”, SIAM J Appl. Dynamical Systems, V9, 1061-1089, 2011 28 29 The manifolds to lissajous orbits can be used together with a low thrust engine and optimized • The optimization algorithm is complicated and uses extensive computer simulation – This study uses a three-dimensional Newtonian four-body problem with a high precision numerical integrator and optimizer (sophisticated gradient method) - due to Francesco Topputo, Politechnico di Milino • Computing the manifolds used methods developed by F. Topputo. • The engine parameters are used: Isp, Thrust magnitude and direction • New types of trajectory pathways are obtained 30 Boeing architecture • Interesting exploration architecture proposed by Michael Raftery and Jeffrey Hoffmann(ref A) – • Idea: Place a mini-space station(ISS-EP) in a lissajous orbit about EM L1 to be used as an exploration outpost far from the Earth – but near the Moon. ( ISS-EP a piece of ISS.) Move to and from the Earth, Moon, L1, L2, using suite of different spacecraft: SEP (tug), Orion, LL (Lunar lander), iHab(crew habitat). A payload PD is also included. (A) Michael Raftery, Jeffrey Hoffman, “International Space Station as a Base Camp for Exploration Beyond Earth” Orbit, 62nd International Astronautical Congress, IAC-11-B3.1, Capetown, SA 2011 31 Spacecraft parameters • SEP dry 10K kg prop 37.6K kg Thrust 64N Isp = 2200 s • iHab 20K kg • Orion wet 18K kg Thrust 33,800 N, Isp = 327.5s • PLD 20k kg 32 CE radius (70K, 75K km) and lissajous size determination 33 Validation of Boeing Model: Goal: Minimize fuel • STEP 1 : A reference circular orbit CE is used about E for all the spacecraft to link up: SEP+iHab from ISS-EP & Orion+PD from E. A. SEP+iHab use SEP engines to phase into exiting trajectory from ISS-EP on „unstable manifold‟ with tiny fuel– coast with 0 fuel to CE then engines again to rendezvous with Orion+PD. - Trajectory 1 B. Using SEP, Orion+PD+SEP+iHab phase into stable manifold trajectory to L1 lissajous from CE where ISS-EP is loacted. Coast with 0 fuel and tiny fuel for rendezvous. - Trajectory 2 C. Radius of CE is determined to minimize fuel for phasing into CE from unstable manifold trajectories arriving from EP & for stable manifold trajectories leaving CE. 34 Trajectory 1 SEP+iHab black – thrusting, red – traj on unstable manifold traj EM-rotating 75K CE in following slides Time = 55 days 35 Propellant mass consumption on thrusting arc 36 Trajectory 2 SEP+iHab+Orion+PD blue – stable manifold traj Time =63 days Note – could go from LEO direct via Hohmann of Orion+PD using impulsive DV, more propellant required in order to rendezvous at ISS-EP – but Time about 8 days 37 • STEP 2 : A. SEP+iHab+Orion use SEP engines to phase into escaping trajectory from ISS-EP on „unstable manifold‟ of L1 with small fuel. B. Using SEP, SEP+iHab+Orion phase into stable manifold trajectory to L2 lissajous. - Trajectory 3 C. Using SEP, SEP+iHab+Orion phase into unstable manifold trajectory to L2 lissajous. It escapes onto trajectory that phases into L1 lissajous via stable manifold. Small propellent used. - Trajectory 4 38 Trajectory 3 SEP+iHab+Orion L1 lissajous to L2 lissajous Time = 56 days 39 Trajectory 4 SEP+iHab+Orion L2 lissajous to L1 lissajous Time = 56 days 40 • STEP 3 : A. SEP+iHab+Orion use SEP engines to phase into escaping trajectory from ISS-EP on „unstable manifold‟ of L1 with small fuel and phase into CE using SEP. This is a low energy transfer to CE. – Trajectory 5 B. iHab+Orion use Orion‟s engines, escape L1 lissajous and phase into CE. This is a high energy transfer. - Trajectory 6 41 Trajectory 5 SEP+iHab+Orion L1 lissajous to CE Time = 61 days Low Energy Transfer 42 Trajectory 6 iHab+Orion L1 lissajous to CE Time = 12 days High Energy ImpulsiveTransfer 43 Lunar Exploration • The transportation system described is easily adapted for lunar exploration. • A lunar lander with other payload materials, can descend to the lunar surface using a new type of trajectory associated to the WSB. • This descent trajectory class reduces lunar velocity at the surface by 25%. It takes negligible propellant to leave ISS-EP and phase onto these descent trajectories – labled EL50. Likewise, the return from the lunar surface yields the same savings. 44 Paper on lunar descent(ascent) trajectories • Belbruno, E., “A New Class of Lunar Orbits and Applications”, in New Trends in Astrodynamics and Applications III , V886, Am. Inst. of Physics, pp 1-12, 2007. 45 Exploration beyond the Earth-Moon System using low energy trajectories • The structure of manifolds exiting the Earth-Moon- system has been uncovered in recent work. This gives a road map on how to reach Earth-Sun L1, L2 regions and their WSB‟s with negligible DeltaV • From The WSB region of ES-L1,L2 it is possible to transfer to Mars and beyond with little Delta-V. 46 Manifolds from EM system(green) to ES L1 lissajous (red orbit) 47 Conclusions • The Boeing architecture is feasible under given assumptions and lies well within the propellant margin. • ISS-EP can be placed around L1 or L2 with little penalty in propellant. • Going to L1 or L2 is equally viable requiring about the same propellant. • Lunar exploration can be done with ISS-EP well within propellant margin. • Placing ISS-EP near L1 lies near manifolds that go to ES-L1 within propellant margin 48 Acknowledgements Research sponsored by NASA and Boeing Many thanks to Kevin Post for discussions that defined key parameters. Thanks to Dan Lester for interesting discussions. 49 General References • EB , “Feasibility of an Earth-Moon Transportation System for Exploration”, Boeing Report Number 2011- 1, 2011 (pp 1-46) Books • EB, Capture Dynamics and Chaotic Motions in Celestial Mechanics( With the Construction of Low Energy Transfers), Princeton University Press, 2004 • EB, Fly Me to the Moon: An Insiders Guide to the New Science of Space Travel, Princeton University Press, February 2007 • See www.edbelbruno.com for additional references.
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