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SPACE MANIFOLD DYNAMICS: THE PRAGMATIC POINT OF VIEW

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Presentation on theme: "SPACE MANIFOLD DYNAMICS: THE PRAGMATIC POINT OF VIEW"— Presentation transcript:

1 SPACE MANIFOLD DYNAMICS: THE PRAGMATIC POINT OF VIEW
Ettore Perozzi Telespazio, Roma (Italy) Workshop on Stability and Instability in Mechanical Systems Barcellona, 1-5 December 2008

2 Being Pragmatic: Kaguya HDTV
13/11/2018 All rights reserved © 2007, Telespazio

3 contents SMD - Space Manifold Dynamics back to the roots
from ISEE-3 to SOHO Where do we go from here? Tisserand and SMD temporary satellite capture of comets ballistic capture The Accessibility of the Moon Hohmann vs SMD STK modelling Case studies Lunar Eploration issues Lagrangian surface drifters 13/11/2018 All rights reserved © 2007, Telespazio

4 SMD recommendations The terminology “Space Manifold Dynamics” (SMD) is adopted for referring to the dynamical systems approach to spaceflight dynamics, thus encompassing more specific definitions (stable/unstable manifolds, lagrange trajectories, weak stability boundary, etc.); There is the need of establishing a strong and continuous link among the research, the industrial communities and the space agencies, even at a basic level (e.g. regular organization of workshops and schools). 13/11/2018 All rights reserved © 2007, Telespazio

5 Space Manifold Dynamics
CELESTIAL MECHANICS H. Poincaré : Les Methodes Nouvelles de la Mechanique Celeste (pag 82, section 36, Chapter III) 1889 That which makes periodic solutions so valuable is that they are, so to speak, the only breach through which we can attempt to penetrate what was previously thought impregnable. ASTRODYNAMICS R.W. Farquhar & A. A. Kamel. Quasi-periodic Orbits about the Translunar Libration Point. Cel Mech 7, 1972 13/11/2018 All rights reserved © 2007, Telespazio

6 Space Manifold Dynamics
CELESTIAL MECHANICS H. Poincaré : Les Methodes Nouvelles de la Mechanique Celeste (pag 82, section 36, Chapter III) 1889 ASTRODYNAMICS R.W. Farquhar & A.A. Kamel. Quasi-periodic Orbits about the translunar libration point, Cel. Mech 7, 1972 13/11/2018 All rights reserved © 2007, Telespazio

7 Space Manifold Dynamics
CELESTIAL MECHANICS H. Poincaré: Les Methodes Nouvelles de la Mechanique Celeste (pag 82, section 36, Chapter III) 1889 C.C. Conley: : Low Energy Transit Orbit in the Restricted Three-Body Problem. SIAM J Appl. Math, 16, 4, 1968. ASTRODYNAMICS R.W. Farquhar & A.A. Kamel. Quasi-periodic Orbits about the translunar libration point. Cel. Mech. 7, 13/11/2018 All rights reserved © 2007, Telespazio

8 Space Manifold Dynamics
CELESTIAL MECHANICS H. Poincaré: Les Methodes Nouvelles de la Mechanique Celeste (pag 82, section 36, Chapter III) 1889 C.C. Conley: Low Energy Transit Orbit in the Restricted Three-Body Problem. SIAM J Appl. Math, 16, 4, 1968. HINODE SOHO ASTRODYNAMICS D.L. Richardson: A Note on a Lagrangian Formulation for Motion around the Collinear Points. Cel. Mech. 22, R.W. Farquhar & A.A. Kamel. Quasi-periodic Orbits about the translunar libration point. Cel. Mech. 7, ISEE-3 13/11/2018 All rights reserved © 2007, Telespazio

9 Space Manifold Dynamics
Simo’. Gomez, Masdemont, Jorba Llibre,, Marchal et al. stable/unstable manifolds halo orbits, lissajous orbits Belbruno, Miller, Carrico, Teofilatto et al. weak stability boundary (WSB) ballistic capture Lo, Ross, Marsden, Parker, Campagnola et al. lagrangian trajectories interplanetay superhighways LL 1 13/11/2018 All rights reserved © 2007, Telespazio

10 Exploiting stability / instability
Where do we go from here? EL1 EL2 mission profiles well established for scientific missions Exploration missions? BepiColombo ballistic capture / outer planets satellite tour design Moon? Mars? (the Vision for Solar System Exploration) Innovation is not always welcome (safety and cost of operations) Communication problems (needs different thinking) Merging scientific and technological constraints/requirements is a key issue ESA ITT “Interplanetary Trajectory Design” 13/11/2018 All rights reserved © 2007, Telespazio

11 Exploration missions CELESTIAL MECHANICS ASTRODYNAMICS 13/11/2018
All rights reserved © 2007, Telespazio

12 Tisserand and SMD In the R3BP Sun-Jupiter-Comet when far from close encounters the Jacobian integral reduces to the so-called Tisserand invariant, which (in normalized units) can be expressed as: This quantity is related to the unperturbed relative velocity of a comet (in units of the orbital velocity of the planet) at close encounter with Jupiter 13/11/2018 All rights reserved © 2007, Telespazio

13 Tisserand and SMD CELESTIAL MECHANICS: temporary satellite capture of comets T > 2.9 Chebotarev (1964), Kazmirchak-Polonskaya (1972), Everhart (1973), Rickman (1979), Carusi & Valsecchi (1983) ASTRODYNAMICS: lunar ballistic capture T = 2.95 Belbruno & Miller (1990), Parker (2006) 13/11/2018 All rights reserved © 2007, Telespazio

14 Tisserand and SMD CELESTIAL MECHANICS: temporary satellite capture of comets T > 2.9 Chebotarev (1964), Kazmirchak-Polonskaya (1972), Everhart (1973), Rickman (1979), Carusi & Valsecchi (1983) EL1 ASTRODYNAMICS: lunar ballistic capture T = 2.95 Belbruno & Miller (1990), Parker (2006) 13/11/2018 All rights reserved © 2007, Telespazio

15 Accessibility DV1 = m ½ [( 2/r1 - 1/a ) ½ - (1/r1) ½]
In his book DIE ERREICHBARKEIT DER HIMMELSKORPER (The Attainability of Celestial Bodies), published in 1925, Walter Hohmann gives the basis of interplanetary travelling. Here he introduces the concept of DV change in velocity of a spacecraft as a measure of accessibility r2 DV1 = m ½ [( 2/r1 - 1/a ) ½ - (1/r1) ½] DV2 = m ½ [(1/r2) ½ - ( 2/r2 - 1/a ) ½] r1 ”Hohmann’s great contribution to astronautical progress was the discovery of a new use for an old object: the ellipse.” W.I.McLaughlin: ‘Walter Hohmann’s Roads in Space’, JSMA 2, 2000. 13/11/2018 All rights reserved © 2007, Telespazio

16 Hohmann vs Bi-elliptic
the Hohmann transfer represents an optimal strategy only if the ratio between the radius of the target and that of the departure orbits is less than Exceeding this value the choice of a suitable bi-elliptic transfer is more convenient, while if r2=r1>15:58 any bi-elliptic transfer is favourable in terms of DV expenditure A bi-elliptic transfer is a three-impulse strategy which foresees an intermediate orbit with an apocenter distance larger than the target orbit, and this implies long transfer times 13/11/2018 All rights reserved © 2007, Telespazio

17 Bi-elliptic vs WSB 13/11/2018 All rights reserved © 2007, Telespazio
E. Perozzi and A. Di Salvo: Novel Spaceways for Reaching the Moon: an Assessment for Exploration. Cel Mech Dyn Astr 102, 207–218 (2008). 13/11/2018 All rights reserved © 2007, Telespazio

18 Earth centered H-plot 13/11/2018
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19 Moon centered H-plot ballistic capture 13/11/2018
All rights reserved © 2007, Telespazio

20 STK modelling SMD internal
Satellite ToolKit (STK) is a commercial software for near-Earth mission design, recently upgraded to treat interplanetary mission analysis. 13/11/2018 All rights reserved © 2007, Telespazio 20

21 STK modelling SMD external 13/11/2018
All rights reserved © 2007, Telespazio 21

22 ballistic capture event
STK modelling ballistic capture event 13/11/2018 All rights reserved © 2007, Telespazio 22

23 MAGIA study Hohmann SMD internal SMD external Transfer Time: 4 days
Total delta-V = 3.9 km/s Total delta-V = 4.2 km/s Total delta-V = 3.8 km/s 2 manoeuvres: TLI, LOI 3 manoeuvres: BOI, TLI, LOI TLI=3.1; LOI=0.8 BOI=2.9; TLI=0.7; LOI=0.0; NOI=0.6 TLI=3.2; LOI=0.0; NOI=0.6 Elliptic trajectory (high LOI) BLT trajectory (low LOI) WSB trajectory (low LOI) LOI critical Ballistic Capture (LOI non-critical) consolidated guidance innovative guidance Needs quick reaction time Allows slow reaction time - Possible E-M cruise science Possible E-M-S cruise science Apollo-like Science & Exploration precursor Science & Exploration precursor TLI =Trans Lunar Injection; BOI = Bridging Orbit Insertion; LOI = Lunar Orbit Insertion; NOI = Nominal Orbit Insertion 13/11/2018 All rights reserved © 2007, Telespazio 23 23

24 Moon Base Conference VENICE WASHINGTON MOSCOW 13/11/2018
All rights reserved © 2007, Telespazio

25 Being Pragmatic: Moon Base proceedings
Information is not knowledge, knowledge is not wisdom Frank Zappa 13/11/2018 All rights reserved © 2007, Telespazio

26 The Accessibility of the Moon
LL1 LL distance from the Earth km EL2/EL2 DV km/sec Description DV mission type DV km/sec cumulative Transfer to the Moon flyby 3.2 Lunar Orbit Insertion orbiter 4.0 Landing lander/rover 6.1 Ascent unar operations 8.1 Transfer to Earth sample return 8.9 Earth Orbit Insertion round-trip 13/11/2018 All rights reserved © 2007, Telespazio

27 SMD lunar applications
Moon harbor: a LL1 halo orbiting infrastructure for manned / unmanned missions support (e.g refurbishing space relescopes, space elevator) Low altitude lunar orbiters / landers High altitude lunar constellations for satellite navigation High eccentricity orbits / halo orbiters for telecommunications Operations safety (avoiding critical events) Flexibility of mission profile (e.g. different launch scenario) Long transfers: cruise science (e.g. gravitational redshift, solar/magnetosphere interactions) Manned vs unmanned missions (radiation issue, non–critical cargo delivery) 13/11/2018 All rights reserved © 2007, Telespazio

28 SMD recommendations Workshop recommendation:
focus on the effect of dissipative systems on SMD in terms of outcomes, methods and applications (e.g. low-thrust engines, non-gravitational forces, tethered systems etc.); 13/11/2018 All rights reserved © 2007, Telespazio

29 surface drifters dynamics
Dispersione nel Mare Ligure 14 maggio settembre 2007 Source: 13/11/2018 All rights reserved © 2007, Telespazio

30 surface drifters dynamics
Source: Traiettorie nel Mar Mediterraneo (1986 – 2008) 13/11/2018 All rights reserved © 2007, Telespazio

31 surface drifters dynamics
Source: 13/11/2018 All rights reserved © 2007, Telespazio

32 thank you 13/11/2018 All rights reserved © 2007, Telespazio

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