Upload
harold-robinson
View
213
Download
0
Tags:
Embed Size (px)
Citation preview
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
Relativistic perihelion driftRelativistic perihelion drift
~1500 asteroids
Trojans, MBAs,
and NEOs
astorb.dat + simulated astorb.dat + simulated
population NEOspopulation NEOs
sensitivity sensitivity
e.de.d Mercury Mercury
~e.d~e.d Icarus Icarus
Orbit improvementOrbit improvement Assume LLS, or iterativeAssume LLS, or iterative dd=[∂=[∂/∂c].dc=(O-C)/∂c].dc=(O-C)
Partial derivatives Partial derivatives [∂[∂/∂c] = P/∂c] = Pzz.[∂x/∂c].[∂x/∂c]
11stst. closed form from 2-body osculating elts. . closed form from 2-body osculating elts. (Brouwer & (Brouwer &
Clemence 1961) Clemence 1961) ((da/a, de, dlo+dr, dp, dq, e.dr)
22ndnd. variational equations + numerical integration of motion. variational equations + numerical integration of motion
(also for J(also for J22, , , mass, etc.), mass, etc.)
33rdrd. test wrt direct calculation of PD . test wrt direct calculation of PD [x(c[x(coo+h)-x(c+h)-x(coo-h)]/-h)]/22hh
in progress: in progress: [∂x/∂c] [∂x/∂c] for orbit ok, but not for global parametersfor orbit ok, but not for global parameters
(integrator, step,?.. (integrator, step,?.. TBCTBC))
One Trojan asteroidOne Trojan asteroid
Time
Space
One Main-belt asteroidOne Main-belt asteroid
Time
Space
Two NEOsTwo NEOs
Rank defficient!Rank defficient! NormalNormal
5 years 1/4 year
Space
Time
96 obs 11 obs
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
JJ22 corrcorr..
6.E-56.E-5 1.E-81.E-8 0.7750.775
JJ22 corrcorr.. WW00 WW11 corrcorr(max)(max)
6.E-56.E-5 1.E-81.E-8 0.7750.775 3, 3, 113, 3, 11 3, 3, 53, 3, 5 -0.08-0.08
(i.e. 1.5E-11 -- 2.5E-11 rd/yr >> 1E-13
Sun aspect angle Sun aspect angle decrease from decrease from
50° down to 50° down to 45° in new design45° in new design
go to less higher go to less higher elongations (IEO)elongations (IEO)
=45°
Sun aspect angle Sun aspect angle decrease from decrease from
50° down to 50° down to 45° in new design45° in new design
go to less higher go to less higher elongations (IEO)elongations (IEO)
loose interesting loose interesting targets?targets? =45°
Sergei’s champion!
Global parametersGlobal parameters
= 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?
.………... .………... surface/interior?surface/interior?
Asteroid porosityAsteroid porosityfrom Consolmagno & Britt L&PSc XXXIII (2002)
Error (systematic) large for rubble-pile asteroids : Error (systematic) large for rubble-pile asteroids : bulk porosity ~ 20-50%bulk porosity ~ 20-50%