added these to the 300 already integrated in INPOP06 and thus there are in total 303 asteroids integrated individually in INPOP08. More details on the methodology used for obtaining the most probable list of the top 300 perturbing asteroids can be found in (Kuchynka et al. 2009).

[Figure: Fig. 1. Differences (in nanosecond) between TE405 (corrected from the 6.55 × 10−5 second offset) and the (TTTDB) integrated in INPOP08. X axis is Terrestrial Time, expressed in years from J2000.]

3.2. The ring In the former version of INPOP (Fienga et al. 2008), perturbations of asteroids on planets were modeled with 300 individual asteroids and a static circular ring at 2.8 AU. Five asteroid masses, 3 taxonomic densities (attributed to the remaining 295 asteroids) and the mass of the ring were fitted to observations.
per year between TT and TDB). These small discrepancies could be surprising because TE405 does not take into account the terms in 1/c4. Neglecting them in eq. (10) induces an important drift of 346.0 ns/cy , close to the value ∆L(P N)
After the integration of such a model on a 100-years time interval, it appeared that the asteroid ring induced a drift of several meters in the position of the Solar System barycenter (Fig.2). The static ring was then replaced by a more realistic implementation that now conserves the total linear and angular momenta of the system: the ring interacts fully with the planets and is no longer assumed to act only in their ecliptic planes. Its center is attached to the Sun and its orientation is an integrated parameter which evolves with time. The ring’s interaction with other objects is actually identical to the interactions of an asteroid on a circular orbit averaged over the asteroid’s mean orbital motion. Besides eliminating the barycenter drift, the advantage of the new implementation is that the ring is taken into account in a more realistic way and its presence in the model is more meaningful. The ring’s radius was chosen at 3.14 AU.
= 346.2 ns/cy from (Irwin & Fukushima, 1999). But this drift can be compensated by a change of the constant LB or LC. Now that TDB is defined as a conventional and fixed linear function of TCB (see eq. 9) and LB is fixed to the value given by the IAU 2006 resolution B3, terms in 1/c4 are thus essential. Because discrepancies are small, no impact is noticeable in the differences between observed planet positions and positions computed with TE405, the relation of Fairhead and Bretagnon (1990), or with the Chebychev polynomials representing the INPOP TT↔TDB. No additional iteration is then necessary, even if at each step of the adjustment of INPOP to observations, the computation of TT↔TDB coefficients is automatically iterated.
C
3. New constraint on asteroid modeling
Another novelty is that the mass of the ring is not fitted to observations but estimated independently. This estimation is made by calculating the amplitude of the perturbation on the Earth-Mars distance exerted by all main-belt asteroids but the 303 most perturbing ones determined previously. 24635 asteroids are considered as a model of the main belt and a simple scheme based on the Statistical Asteroid Model (Tedesco et al. 2005) is used to assign each asteroid with a reasonable distribution of masses. A Monte Carlo experiment where asteroids are assigned random (but reasonable) masses allows to calculate the corresponding perturbation from all the asteroids but the 303 most perturbing ones. For each random set of masses, a ring’s mass is determined so as to fit the perturbation of the ring to the global effect. This leads to the estimation of the ring’s mass at Mring = (1 ± 0.3) × 10−10M�for a ring at 3.14 AU
3.1. Supplementary selection of asteroids For INPOP08, we also slightly revised the INPOP06 selection of asteroids perturbing Mars and the inner planets. This was done with the same method as the estimation of the mass of the ring described in the 2 section : 24635 selected asteroids are assigned with reasonable distribution of masses according to available data and the Statistical Asteroid Model (Tedesco et al. 2003). A Monte Carlo study allows to assign to each asteroid the probability of being among the 300 most perturbing asteroids in terms of amplitude of the perturbation on the Earth-Mars distance between 1969 and 2010: For each of the 24635 asteroids, two integrations have been done between 1969 and 2010: one with the asteroid i and one without the asteroid i, i varying from 1 to 24635. The differences between the two integrations give the impact induced by the asteroid i. To built our list of asteroids, we have studied the impact not only on the Earth-Mars distances, but also the Earth-Venus and Earth-Mercury distances. We are thus able to compile the most probable list of the 300 most perturbing asteroids and compare it to the INPOP06 selection used
(Kuchynka et al. 2009).
1 the list of asteroids integrated individually in INPOP06 or DE405 is given in (Standish and Williams 2001)