Global Effects on Dynamics Daniel HESTROFFER (IMCCE, Paris) CU4SSO - PowerPoint PPT Presentation

Global Effects on Dynamics Daniel HESTROFFER (IMCCE, Paris) CU4—SSO

Outline Asteroids and others population Simulations Global Effects on Dynamics Ground-based compl ementary data D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 2

Asteroids population Detection: almost any object that is ‣ brighter than mag V ≤ 20 ‣ smaller than ≈ Φ < 0”7 ‣ motion less than ≈ 150mas/s Different objects observed ‣ NEOs ( ≈ 1500), MBAs ( ≈ 250,000), Trojans, Centaurs (few 100), TNOs (e.g. Pluto) ‣ comets (LPC, JFC), satellites (Ma, J, S, U, N ≈ 50) D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 3

Simulations Rendez-vous (F . Mignard) sequence of observations and ephemerides GIBIS CCD proc. (C. Babusiaux, F . Arenou, A. Dell’Oro) focal plane and astrometry Input objects for Initial Conditions (IC) NEOs 2 populations ‣ known NEAs (90% complete Φ >1km) ‣ synthetic population (Bottke et al. 2002) other : astorb.dat (close to completion at V=20) known comets D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 4

Detection size binaries Simulations Simulations D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 5

Astrometry CCD in space — global astrometry astrometry at sub-mas level (conservative for NEOs) homogeneous ref frame ; absolute position One instrument size, shape model, spin = parameters for corrections or dynamical model Simulations Simulations Scanning law not equal for all objects MBAs vs. NEOs & TNOs D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 6

Astrometry 63 obs Simulations Simulations A typical MBA, orbital period ≈ 5 years Different for NEA, Centaur, or faint object Precision σ AL ( λ ) 0.3 - 5mas (on a transit basis) D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 7

Dynamical model Direct computation planets, GR simpl ified , non gravitational simpl ified A i asteroids mutual perturbations — pre-selection of close encounters Inversion only Gaia data, only linear case variational equations for partial derivatives Dynamics Dynamics iterations for linearisation and goodness of fit Variance Analysis D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 8

Inversion Adjustement local (state vector), global parameters Mass close encounters ; binaries Non-gravitational effects comets ; NEOs Global dynamical parameters Dynamics Dynamics test of GR (dG/dt, PPN β ) global rotation (W o + dW/dt) D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 9

State vector Linear Least-Squares: O-C = A.dx = [ ∂ λ / ∂ x].dx Dynamics Dynamics no long period effects (planetary satellites) cases of rank deficiency - no full osculating elements D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 10

Masses Mouret et al. (2007) J. Hilton Close encounters impulse for pre-selection global parameters for inversion Dynamics Dynamics 150 masses better than50% D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 11

Local test of GR large # of test particles through solar system as sensitive as Mercury separate PPN β ( a. ( 1 - e 2 ) ) - 1 solar J 2 ( a. ( 1 - e 2 ) ) - 2 Phaethon Icarus Dynamics Dynamics σ ( β ) 10 -4 Mercury σ (J 2 ) 5x10 -8 D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 12

Ground-based Support P. Tanga N asteroids D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 13

Ground-based Support Observation during mission for critical objects Observations outside mission mass, GR, non gravitational parameters Ground based Ground based similar precision ; secular terms direct (astrometry) or indirect (physical parameters for dynamical model) D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 14

Gaia (DP a (DPAC) MBAs mass NEOs + all GR comets + NEOs A i binaries mass all W, dG/dt post-Gai t-Gaia MBAs mass Ground based Ground based NEOs GR comets NEOs A i satellites orbits, planets Trojans GR TNOs κ D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 15

Discussion Instrument degradation / extended mission Indirect astrometry from (re)reduction with Gaia stellar catalogue Satellites and other long-term effects Planets pseudo-positions Larger system Gaia+GB data Other orbit propagators Dynamical families End (% End (% ... D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 16

End (% End (% so, was angular momentum conserved ?.. D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 17

D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 19

Results Ω x-y-z d Ω /dt Ġ /G κ [ μ as] [ μ as/yr] [yr -1 ] [m/s 2 ] Gaia 5-5-15 1-1-5 2 E -12 [ 8E-11 ] (350,000 obj.) LLR — 100 3 E -13 — (Williams et al. 2004) Ephemerides √ 40 5 E- 13 √ (Folkner et al. 2009) TNOs 2E-10 — — — (Wallin et al. 2007) J 2 J 2 β β correl. alone alone global global Gaia 5E-08 1E-04 5E-08 1E-04 0.1 to 0.9 INPOP — 2 E- 4 — — — (Fienga et al. 2008) LLR - EMP — 1 E- 4 — — — (Williams ‘04, Pitjeva ‘05) Bepi Colombo — — 2 E- 9 2 E- 6 0.997 (Milani et al. 2009) NEOs — — √ √ √ (Margot et al. 2009) D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011 20

Questions / Réponses q q r q r r D. Hestroffer (IMCCE) — CNAP 2011 21