SLIDE 1
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Outline
Asteroids and others population Simulations Global Effects on Dynamics Ground-based complementary data
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Global Effects on Dynamics Daniel HESTROFFER (IMCCE, Paris) CU4SSO - - PowerPoint PPT Presentation
Global Effects on Dynamics Daniel HESTROFFER (IMCCE, Paris) CU4SSO - - PowerPoint PPT Presentation
Global Effects on Dynamics Daniel HESTROFFER (IMCCE, Paris) CU4SSO Outline Asteroids and others population Simulations Global Effects on Dynamics Ground-based compl ementary data D. Hestroffer (IMCCE) GREAT-SSO, Pisa 2011 2 Asteroids
SLIDE 2
SLIDE 3
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
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)
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SLIDE 4
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
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)
- ther : astorb.dat (close to completion at V=20)
known comets
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SLIDE 5
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Simulations
Detection
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Simulations size binaries
SLIDE 6
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
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
Scanning law
not equal for all objects MBAs vs. NEOs & TNOs
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Simulations Simulations
SLIDE 7
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Astrometry
A typical MBA, orbital period ≈ 5 years Different for NEA, Centaur, or faint object Precision σAL(λ) 0.3 - 5mas (on a transit basis)
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Simulations Simulations
63 obs
SLIDE 8
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Dynamical model
Direct computation
planets, GR simplified, non gravitational simplified Ai asteroids mutual perturbations — pre-selection
- f close encounters
Inversion
- nly Gaia data, only linear case
variational equations for partial derivatives iterations for linearisation and goodness of fit
Variance Analysis
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Dynamics Dynamics
SLIDE 9
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Inversion
Adjustement
local (state vector), global parameters
Mass
close encounters ; binaries
Non-gravitational effects
comets ; NEOs
Global dynamical parameters
test of GR (dG/dt, PPN β) global rotation (Wo + dW/dt)
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Dynamics Dynamics
SLIDE 10
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
State vector
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Dynamics Dynamics
Linear Least-Squares: O-C = A.dx = [∂λ/∂x].dx no long period effects (planetary satellites) cases of rank deficiency - no full osculating elements
SLIDE 11
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Masses
Close encounters
impulse for pre-selection global parameters for inversion 150 masses better than50%
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Dynamics Dynamics
- J. Hilton
Mouret et al. (2007)
SLIDE 12
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Local test of GR
large # of test particles through solar system separate PPN β (a.(1-e2))-1
solar J2 (a.(1-e2))-2 σ(β) 10-4 σ(J2) 5x10-8
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Dynamics Dynamics
Mercury Icarus Phaethon as sensitive as Mercury
SLIDE 13
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Ground-based Support
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- P. Tanga
N asteroids
SLIDE 14
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Ground-based Support
Observation during mission for critical
- bjects
Observations outside mission
mass, GR, non gravitational parameters similar precision ; secular terms direct (astrometry) or indirect (physical parameters for dynamical model)
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Ground based Ground based
SLIDE 15
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Ground based Ground based
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Gaia (DP a (DPAC) MBAs mass NEOs + all GR comets + NEOs Ai binaries mass all W, dG/dt post-Gai t-Gaia MBAs mass NEOs GR comets NEOs Ai satellites
- rbits, planets
Trojans GR TNOs κ
SLIDE 16
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
End (%
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 ...
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End (%
SLIDE 17
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
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so, was angular momentum conserved ?..
End (% End (%
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SLIDE 19
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
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SLIDE 20
- D. Hestroffer (IMCCE) — GREAT-SSO, Pisa 2011
Results
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Ωx-y-z
[μas]
dΩ/dt
[μas/yr]
Ġ/G
[yr-1]
κ
[m/s2]
Gaia
(350,000 obj.)
5-5-15 1-1-5 2 E-12 [ 8E-11 ]
LLR
(Williams et al. 2004)
— 100 3 E-13 —
Ephemerides
(Folkner et al. 2009)
√ 40 5 E-13 √
TNOs
(Wallin et al. 2007)
— — — 2E-10 J2
alone
β
alone
J2
global
β
global
correl.
Gaia 5E-08 1E-04 5E-08 1E-04 0.1 to 0.9
INPOP
(Fienga et al. 2008)
— 2 E-4 — — —
LLR - EMP
(Williams ‘04, Pitjeva ‘05)
— 1 E-4 — — —
Bepi Colombo
(Milani et al. 2009)
— — 2 E-9 2 E-6 0.997
NEOs
(Margot et al. 2009)
— — √ √ √
SLIDE 21
- D. Hestroffer (IMCCE) — CNAP 2011
Questions / Réponses
q q
r
q
r r
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