Determination of Determination of PPN PPN and Solar J and Solar J 2 2 from asteroids orbits from asteroids orbits (update) (update) D. Hestroffer, J. Berthier, D. Hestroffer, J. Berthier, S. Mouret S. Mouret (IMCCE, Paris (IMCCE, Paris Observatory) Observatory) & & F. Mignard F. Mignard (OCA, Nice) (OCA, Nice)
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Determination of PPN and Solar J 2 from asteroids orbits (update) D. Hestroffer, J. Berthier, S. Mouret (IMCCE, Paris Observatory) & F. Mignard (OCA,
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Determination of Determination of PPN PPN and Solar J and Solar J22
from asteroids orbits (update)from asteroids orbits (update)
D. Hestroffer, J. Berthier, S. Mouret D. Hestroffer, J. Berthier, S. Mouret (IMCCE, Paris Observatory)(IMCCE, Paris Observatory)
&&
F. MignardF. Mignard (OCA, Nice)(OCA, Nice)
Orbit perturbationsOrbit perturbations
PPN PPN : only : only oror dd/dt/dt a a-5/2-5/2 . (1-e . (1-e22))-1-1 . .
Solar JSolar J2 2 : perihelion : perihelion , node , node , and mean , and mean anomaly Manomaly M (consider Sun equator = ecliptic)(consider Sun equator = ecliptic)
dd/dt, d/dt, d /dt /dt a a-7/2-7/2 . (1-e . (1-e22))-2-2 . . JJ22
dMdM a a-7/2-7/2 . (1-e . (1-e22))-3/2-3/2 . . JJ22
1500 asteroids (NEAs + MBAs + Trojans)1500 asteroids (NEAs + MBAs + Trojans) distribution in (e,a) planedistribution in (e,a) plane
Rank defficiency for some NEAsRank defficiency for some NEAs Better for MBAs, Hildas and even TrojansBetter for MBAs, Hildas and even Trojans
Trojans & Hildas
MBAs
NEOs
rank defficiency
Global parametersGlobal parameters
PPN PPN (with (with known) and known) and JJ22
Also global rotation vector Also global rotation vector WW00 and rateand rate WW11==
ddWW00/dt/dt (ecliptic and equinox): (ecliptic and equinox):
dxdx|rot|rot==WW x xx ; dx ; dx|rot|rot==WW11 x xx . (t-t . (t-too))
total of total of N=8N=8 global parameters with ~ 1500 global parameters with ~ 1500 target asteroids target asteroids (1500*6 unknowns)(1500*6 unknowns)
Sparse matrix, solve a Sparse matrix, solve a NxNNxN matrix problem matrix problem
ResultsResults
No frame rotation (No frame rotation (, J, J22))
With frame rotation With frame rotation WW in in as and as and as/yearas/year
= 45° not to constraining? may loose most = 45° not to constraining? may loose most
powerful (a,e) targets. Need to know mag, nobs.powerful (a,e) targets. Need to know mag, nobs.
Only 1500 targets in this run (instead of ~500,000) Only 1500 targets in this run (instead of ~500,000) butbut not much more NEOs with large eccentricity not much more NEOs with large eccentricity
howeverhowever better for rotation rate better for rotation rate (<10(<10-11-11rad/yr)rad/yr)
Can we observe secular changes of JCan we observe secular changes of J22?... ?...
i.e. di.e. d22/dt/dt22 (2011 Solar activity) (2011 Solar activity)
Get Nordtvedt effect Get Nordtvedt effect , strong test of PE , strong test of PE with with
Trojans Trojans (e.g. Orellana 1993)(e.g. Orellana 1993)? Time scales?..? Time scales?..
A short comment A short comment On asteroids mass, taxonomy, On asteroids mass, taxonomy,
and densityand density
On asteroids mass and densityOn asteroids mass and density
Important for modern planetary ephemeris Important for modern planetary ephemeris (Standish & Fienga, Pitjeva, ...)(Standish & Fienga, Pitjeva, ...)
The ‘astrophysical method’ The ‘astrophysical method’ volume * bulk-density = massvolume * bulk-density = mass absolute mag. H => diamabsolute mag. H => diam…........…........ (H,G) system? (H,G) system? size/diam => volumesize/diam => volume.………..…...………..….. generally ≈ ok generally ≈ ok Taxonomy => densityTaxonomy => density………………………… bulk-porosity? bulk-porosity?