How GAIA Asteroids Can Improve Planetary Ephemerides ?

GREAT-SSO: Solar System science before and after Gaia tugraz

How GAIA asteroids can improve planetary ephemerides ?

A. Fienga1,2

1Institut UTINAM, Universit´ede Franche-Comt´e,France 2IMCCE, Observatoire de Paris, France

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 1 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Outline

Overview of the planetary ephemerides INPOP and the asteroids Use of GAIA asteroid observations to improve Jupiter orbit

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 2 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz JPL DE/IAA EMP/INPOP Direct numerical integration of equations of motion 9 planets + Moon + asteroids, GR, J2 Sun, TDB/TCB Fitted to observations Fit of asteroid masses and densities

INPOP: www.imcce.fr/inpop Numerical integration with extended precision 80b Earth and Moon Rotations INPOP(TCB) for GAIA and INPOP(TDB) from IAU 2006

INPOP10a (Fienga et al. 2011), INPOP06 (Fienga et al. 2008), INPOP08 (Fienga

et al. 2009), Tests of fundamental physics / Use for paleoclimats

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 3 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Overview of the planetary ephemerides

JPL DE, EPM, INPOP INPOP10a Same modelling expect for 40 the asteroids 35

30 Passive range rely mainly on (Mars) VEX

Viking

25 MGS

% MEX

spacecraft data i

t Stellar occultations

e Optical

Flybys

Lack of Jupiter good i

t 15 VLBI

observations m

I 10 Cassini: good constraints on 5 Saturn 0 e ry s s r e s n u u r e n u u c n a it r n t o r e p tu a p t e V M u a r e lu M J S U N P

1 Poor accuracy of the Jupiter orbit 2 Crucial role of the asteroids

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 4 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Overview of the planetary ephemerides

JPL DE, EPM, INPOP INPOP10a Same modelling expect for 40 the asteroids 35

30 Passive range rely mainly on (Mars) VEX

Viking

25 MGS

% MEX

spacecraft data i

t Stellar occultations

e Optical

Flybys

Lack of Jupiter good i

t 15 VLBI

observations m

I 10 Cassini: good constraints on 5 Saturn 0 e ry s s r e s n u u r e n u u c n a it r n t o r e p tu a p t e V M u a r e lu M J S U N P

1 Poor accuracy of the Jupiter orbit 2 Crucial role of the asteroids

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 4 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Internal accuracies of planetary ephemerides INPOP10A−DE421 INPOP10A−INPOP08 INPOP10A−INPOP06 0 0 0 ] ] ] 1 0 s s s 3 a a a m m m [ [ [

e e 5 0 d d − u u 0 t t i i 0 g g 1 n n

 0 o o 1 0 L L − 1 − 0 0 1 0 2 − −

1900 1940 1980 2020 1900 1940 1980 2020 1900 1940 1980 2020

date date date 0 0 0 0 3 1 2 ] ] ] 0 s s s 0 5 a 0 a a 1 1 m m m [ [ [

e e 0 d d 0 u u t t 0 i i t t 1 a a − L L  5 − 0 0 3 0 0 − 1 2 − −

1900 1940 1980 2020 1900 1940 1980 2020 1900 1940 1980 2020

date date date 0 0 3 0 2 1 ] ] 5 0 1 m m 0 k k 1 [ [

0 e e 0 c c 0 n n 5 a a t t − s s 1 i i − d d 0 2 0 2 − 5 1 −

− Geocentric distance [km]

A. Fienga1900 1940 May1980 4th, 20112020 1900 1940 1980 2020 How1900 GAIA1940 can improve1980 2020 planetary ephemerides ? date date date 5 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz

Planets Umin Umax α δ ρ α δ ρ mas mas km mas mas km Mercury 5 6 1.5 9 4 1.5 Venus83 0.4 8 6 1.0 Mars* 40 15 10 75 30 15 Jupiter 20 30 15 400 200 300 Saturne 0.8 0.43 40 60 100 Uranus 300 120 1200 220 100 1500 Neptune 400 100 3500 160 150 5000 Pluto 3000 1000 80000 6000 2000 140000 long lat ρ long lat ρ Earth3 1.5 0.04 6 3 0.10

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 6 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz INPOP and the asteroids Asteroids are highly important in planetary ephemerides for: Mars with more than 30 years of very accurate (< 5 meters) spacecraft tracking global ﬁt for all the planets: more than 35 % are Mars data

INPOP10a (Fienga et al. 2011) 24635 asteroid orbits (astorb database) integrated in INPOP planets ↔ asteroids, asteroids ↔ asteroids, EIH Kuchynka et al. 2010: List of the most probable perturbers of inner planets (287) + ring Mass estimations with BVLS algorithm Study of correlations

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 7 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz INPOP and the asteroids Asteroids are highly important in planetary ephemerides for: Mars with more than 30 years of very accurate (< 5 meters) spacecraft tracking global ﬁt for all the planets: more than 35 % are Mars data

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 7 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz INPOP10a (Fienga et al. 2011)

List of the most probable perturbers + ring (Kuchynka et al. 2010) Mass estimations with BVLS algorithm Study of correlations → Fixed masses (15)

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 8 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz INPOP and the asteroids

Uncertainties of ≈ 10% on the 3 Big mass determinations

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 9 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz INPOP and the asteroids

324 Bamberga ● ● INPOP10a 94 m Other 3 Juno ● 56 m K11 ● 704 Interamnia INPOP08 34 m 532 Herculina ● 33 m 7 Iris ● 28 m 29 Amphitrite ● 27 m 24 Themis ● 26 m 15 Eunomia ● 22 m 6 Hebe ● 21 m 11 Parthenope ● 17 m 139 Juewa ● 17 m 747 Winchester ● 16 m 8 Flora ● 13 m 41 Daphne ● 12 m 511 Davida ● 10 m 52 Europa ● 10 m 16 Psyche ● 10 m 130 Elektra ● 7 m 107 Camilla ● 5 m 65 Cybele ● 5 m 21 Lutetia ● 5 m 216 Kleopatra ● 3 m 804 Hispania ● 2 m 0 2 4 6 8 10 12 14 Density [g.cm^−3]

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 10 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz How GAIA can help ?

GAIA asteroid mass determinations great improvement in the masses for the biggest improvement for the mass determinations with INPOP

Satellites small Jovian satellites Neptune and Uranus satellites Satellites are not yet implemented in INPOP

Asteroid orbits 24635 asteroids already implemented in INPOP Big picture: mass + orbit + planets

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 11 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz How GAIA can help ?

GAIA asteroid mass determinations great improvement in the masses for the biggest improvement for the mass determinations with INPOP

Satellites small Jovian satellites Neptune and Uranus satellites Satellites are not yet implemented in INPOP

Asteroid orbits 24635 asteroids already implemented in INPOP Big picture: mass + orbit + planets

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 11 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz How GAIA can help ?

GAIA asteroid mass determinations great improvement in the masses for the biggest improvement for the mass determinations with INPOP

Satellites small Jovian satellites Neptune and Uranus satellites Satellites are not yet implemented in INPOP

Asteroid orbits 24635 asteroids already implemented in INPOP Big picture: mass + orbit + planets

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 11 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Do GAIA asteroid observations can give better informations on Jupiter orbit compared to the present accuracy of Jupiter observations ?

Present observation accuracy over 6 years VLBI Galileo observations + Flybys normal points ≈ 10 mas in geocentric (α,δ) and 2 km in geocentric distances ≈ 8 mas in barycentric longitudes and latitudes

impact on the Jupiter orbit over 6 years 10−9 AU for a 10−8 for the angles 10−7 for e

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 12 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz questions: What are the impacts of such uncertainties on asteroid orbits ? Are they observable at the level of accuracy of the GAIA observations ?

method Integrate asteroid orbit with diﬀerent Jupiter orbits Fit of the asteroid orbit to a reference orbit Measurement of the diﬀerences in barycentric longitudes and latitudes of the asteroid

3 cases 1 of the 3 Bigs: 4 Vesta an asteroid with a close approach with Jupiter: 86 Semele a Troyen: 588 Achilles A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 13 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Exploring the ellipsoid of Jupiter orbit uncertainties

For one speciﬁc set of variations of Jupiter IC inducing (δλ, δ b)=(17,5) mas

Impact on Longitudes Impact on Latitudes

● ● 60 4 Vesta ●● 60 4 Vesta ●● ●● ● ● ● 86 Semele ● 86 Semele ● ● ● ● ● ● ● 588 Achilles ● 588 Achilles ● ● ● ● ● ● ● ● ● ● ● ● ● 40 ● 40 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ●●●●● ●●●●●●●●●●● ● ●● ● ●●●●●●●● ●●●●● ●●●●● ● ●● ● ●●● ●●● ●●●● ●●●● ● 20 ● ●● ● 20 ●● ●●● ●●● ●●● ● ● ●● ● ●●● ●●●● ●●● ● ● ●● ● ●●● ●●●● ●●● ●●●●●●●●●● ●● ● ●● ● ●●●●●●●●●●●● ●●● ●●●● ●●●● ●● ● ●● ●●●● ● ●●● ●●● ●●● ●●● ●● ● ●● ●●●●●●●●●●●● ● ●●● ●● ●●● ●● ● ●● ●●●● ●●● ●●●●●●●●●●●●● ●●●●●●●●●● ● ●●● ●● ●● ●● ● ●● ●●● ●●● ●●●● ●●● ●●●●●● ●●●●●●●● ● ●●● ●● ●● ●● ● ●● ●●● ●● ●●● ●● ●●●● ●●●●●● ● ●●● ●● ●● ●● ● ●● ●● ●● ●●● ●● ●●●● ●●●●● ● ●●● ●● ●● ●● ● ●● ●● ●● ●●● ●●●●●● ●●●●● ● ●●●●● ●● ●●● ● ●● ●● ●● ●●● ●●●● ●●●●● ● ●●●● ●● ●●● ●●●● ●● ●● ●● ●●● ●●●●●● ●●●●● ● ●●● ●●●●● ●● ●●● ●●●●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● ●● ●●●●● ●●●●●●●●●● ●● ●●● ●●● ●●● ●●●●●●● ●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● 0 ● ● 0 ● ● 0 ● ●●● ● ● ●●●●●●●● ● ● ●● ● ●●●●●●●●●●● ●●●●●●● ●●●●●●●●●●●● ● ● ● ●●●●●●●●●●●●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ●●● ●●●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●● ●●● ●●● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●●●●● ●●●●●● ●●●●● ●● ● ●●● ●●● ●●● ●●●● ●●●●●● ● ●●●●● ●●●●● ●●●●● ●● ● ●●● ●●● ●●● ●●●●● ●●●●●●● ● ●●● ●●●●●●●● ●●●●●●● ●● ● ●●● ●●● ●● ●●●●●●●●●●●●●●●●●●●● ● ●●●●● ●●● ●●●●●●●●● ●● ● ●● ●●●● ●● ● ●● ●●● ●●● ●● ● ●● ●●●●● ●●●●●● ●● ● ●● ●●●● ●●●● ●● ● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ● ●● ●●●● ●●●● ●● ● ●● ●● ● ●● ●●●●● ●●●●● ●● ● ●● ●● ● ●● ●●●●●●●●●●●●●●●●●●● ●● ● ●● ●● ● ●● ●● ● ●● ●● ● ●● ●● ● ●● ●● ● ●● ●● ● ●● ●● ●● ●● ●● ● ●● ●● ● ● ● ● ● Differences in Latitudes [microseconds] ● ●● ●● ●● ●● ● ●● Differences in Longitudes [microseconds] ●●●●● ●● ●● ●● ●●●●● ●● ●● ●● −20 ● −20 ●● ●● ●●● ●●● ●●● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● ●●●● ●●●● ●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ●●●●●●●●●●●●●●●●●●●●●

0 1 2 3 4 5 6 0 1 2 3 4 5 6

t−t0 [yr] t−t0 [yr]

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 14 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz

For various sets of variations of Jupiter IC inducing (δλ, δ b) up to 6 mas

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 15 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 16 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 17 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz Preliminary Conclusions

On these 3 cases: GAIA asteroid orbits would not be sensitive to small discrepancies (< 6 mas) of the Jupiter orbit But what about looking for speciﬁc close approaches ? what about other planets ? Mars, Earth with NEO, Neptune with TNO ?

Next steps Make a selection of the most perturbed asteroids in order to optimize the results Make the modelling more realistic !

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 18 / 19 GREAT-SSO: Solar System science before and after Gaia tugraz The end

A. Fienga May 4th, 2011 How GAIA can improve planetary ephemerides ? 19 / 19