Resonancias orbitales

Transcription

1 gallardo Facultad de Ciencias Universidad de la República Uruguay Curso Dinámica Orbital 2018

2 Orbital motion

3 Oscillating planetary orbits

4 Orbital Resonances Commensurability between frequencies associated with orbital motion: mean motion, nodes and pericenters two-body resonances (λ, λ p ) three-body resonances (λ, λ p1, λ p2 ) secular resonances (Ω, ϖ) Kozai-Lidov mechanism (ω)

5 Some examples Io-Europa-Ganymede Saturn satellites Saturn rings Uranus satellites asteroids with Jupiter, Mars, Earth, Venus... Trans Neptunian Objects with Neptune Pluto - Neptune comets - Jupiter Pluto satellites: Styx, Nix, and Hydra

6 Saturn rings Lissauer and de Pater, Fundamental Planetary Science

7 Two-body resonance k 0 n 0 + k 1 n 1 0

8 Three-body resonance k 0 n 0 + k 1 n 1 + k 2 n 2 0 only the asteroid feels the resonance SUN asteroid

9 Non resonant asteroid: relative positions Mean perturbation is radial: Sun-Jupiter Sun Jupiter

10 Resonant asteroid Mean perturbation has a transverse component. Sun Jupiter

11 from Gauss equations T R F perturb = (R, T, N) SUN Non resonant T = 0 a = constant asteroid da dt (R, T) < da dt > T Resonant T 0 a = oscillating

12 Dynamical effects: a numerical exercise final time: 1 Myrs orbital states initial 0.5 eccentricity a (au)

13 1772: Lagrange equilibrium points

14 1906: (588) Achilles by 500 yrs Sun Jupiter

15 1784: Laplacian resonance 3λ Europa λ Io 2λ Ganymede 180 They are also in commensurability by pairs: 2n Europa n Io 0 3n Europa n Io 2n Ganymede 0 2n Ganymede n Europa 0 It must be the consequence of some physical mechanism.

16 1846: discovery of Neptune quasi resonance Uranus - Neptune: n Uranus 2n Neptune quasi resonance Saturn - Uranus: n Saturn 3n Uranus quasi resonance: Jupiter - Saturn 2n Jupiter 5n Saturn Why the planets are close to resonance? Hint: planetary migration

17 1866: Kirkwood gaps

18 Kirkwood gaps at present log (Strength) 4:7 Mars 1:2 Mars 3:1 Jup 5:2 Jup 2:1 Jup a (au) Main belt of asteroids is sculpted by resonances.

19 Resonance locations k 0 n ast = k 1 n Jup a ast ( k 0 k 1 ) 2/3 a Jup There is an infinite number of resonances... which are the relevant ones?

20 1875: resonant asteroids (153) Hilda 3:2 2n Hilda = 3n Jup a Hilda = ( 2 3 )2/3 a Jup = 3.97ua Sun Jupiter

21 Hildas and Trojans

22 Temporary satellite capture the most probable origin of the irregular satellites

23 Quasi satellite, resonance 1:1 it is not orbiting around the planet, it is synchronized 1:1 with the planet

24 Quasi satellite from Wiegert website:

25 2004 GU9: Earth quasi satellite, resonance 1:1 Sun Earth

26 1999 ND43: Mars horseshoe, resonance 1:1 Sun Mars

27 Janus - Epimetheus 1:1

28 (134340) Pluto in exterior resonance 2:3 Sun Neptune

29 Widths Chaos: at resonance borders superposition of resonances Murray and Dermott in Solar System Dynamics

30 asteroids (proper elements) AstDyS database

31 Resonant structure (zoom) proper e proper a (au) AstDyS database

32 Dynamical Maps take set of initial values (a, e) integrate for some yrs surface (color) plot of a(a, e) initial e Model: real SS. Initial i = initial a

33 Asteroid region initial e Model: real SS initial a

34 Zoom initial e Model: real SS initial a

35 Zoom initial e Model: real SS. Initial i = initial a

36 Orbital inclinations of asteroids

37 Atlas of resonances in the Solar System, low e

38 Atlas of resonances in the Solar System, high e

39 Atlas for DIRECT orbits

40 Atlas for RETROGRADE orbits

41 Atlas from 0 to 2 au Gallardo 2006

42 Atlas in the asteroids region Gallardo 2006

43 Atlas in the trans-neptunian Region Gallardo 2006

44 Stickiness: ability to capture particles Gallardo et al. 2011

45 Bizarre worlds...

46 Coorbital retrograde heliocentric motion relative motion planet asteroid SUN Morais and Namouni 2013

47 2015 BZ509: discovered in January 2015 a = 5.12 au, e = 0.38, i = 163 Sun Jupiter

48 Bizarre extreme: fictitious particle in resonant polar orbit λ J q,a (au) i,ω (degrees) time (Myr)

49 Bizarre extreme: fictitious particle in resonant polar orbit collision with the Sun in the rotating frame Sun Jupiter -0.5 Z X

50 Resonances of Long Period Comets Fernandez et al. 2016

51 Resonances of Long Period Comets :6 1: :3 1: :4 1:10 1: :8 orbital states :1 2:3 1:2 2:5 2:7 2:9 1:5 2:11 2:13 2:15 2:17 1:12 1:13 1:14 1:15 1:16 1:17 1:18 1: :19 1:21 1:22 1: <a> (au) Fernandez et al. 2016

52 Three-body resonance k 0 n 0 + k 1 n 1 + k 2 n 2 0 only the asteroid feels the resonance SUN asteroid

53 Atlas of TBRs: global view (for e = 0.15) Strength ρ e a (au) Gallardo 2014

54 Effects on the distribution of asteroids log (Strength) 1-4J+2S 2-1M 1-4J+3S 2-7J+4S 1-3J+1S 2-7J+5S 2-6J+3S 1-3J+2S 3-8J+4S 2-5J+2S 3-7J+2S 3-8J+5S a (au) Gallardo 2014

55 Density of resonances versus density of asteroids 250 3BRs 2BRs asteroids density of 3-body and 2-body resonances a (au)

56 Galilean satellites

57 Europa: dynamical map a initial e E initial a (au) Gallardo 2016

58 Chronology 1772: Lagrange equilibrium points 1799: Lagrange planetary equations, stability of the SS 1784: Laplacian resonance 3λ E λ I 2λ G 180 Laplace quasi resonances: great inequality 2λ Jup 5λ Sat 1846: Neptune discovered 1866 Kirkwood gaps 1875: first resonant asteroid (153) Hilda 3:2 1882: secular resonances (Tisserand, ν 6 ) 1906: first Trojan asteroid (588) Achilles 1930: Pluto and exterior resonance 2:3 Neptune-Pluto 1962: Lidov-Kozai mechanism 1993: resonant TNOs (2:3 plutino) planetary systems in 2BRs and 3BRs minor bodies in 3BRs high inclination resonant orbits retrograde resonances

59 Bibliografía Efectos dinámicos de las resonancias orbitales en el Sistema Solar. Gallardo 2016, BAAA 58, 291. Resonances in the asteroid and TNO belts: a brief review. Gallardo 2018, Planetary and Space Science 157, 96.