Relativistic effects in high-accuracy dynamical modelling of asteroid orbits
Final Report Abstract
In this project, we investigated the relativistic N-body effects in the motion of asteroids, which was motivated by the constant increase in the astrometric observational accuracy. In the first part of the work, we present the results from a rigorous study of the relativistic effects produced by the planets, which we call post-Schwarzschild (PS) effects: we evaluated the impact of these effects on the motion of known asteroids, identified the most sensitive objects and the mechanism responsible for the largest perturbations. An analytical model based on a Fourier analysis was developed to assessing the theoretical post-Schwarzschild perturbations on the orbital elements of main-belt asteroids. A publication in that subject is in preparation. In the second part of the project, we provide a relevant dynamical model to test the Strong Principle Equivalence through the derivation of the Nordtvedt parameter η from high-accuracy asteroid observations. Using realistic simulated data, a variance analysis was performed in the framework of the Gaia mission, which will yield the astrometric positions of more than 250000 asteroids with an unprecedented sub-milliarcsecond accuracy. As other global parameters (relativistic PPN parameters, solar oblateness, variation of the gravitational constant etc.) could be also fitted from Gaia data, the variance analysis was extended to the latter. We evaluated the formal uncertainties and correlations between the parameters, and designed the best strategy to estimate the Nordtvedt parameter along with other global parameters. The previous study also showed that the derivation of the relativistic PPN parameter β and the solar quadrupole J2 are driven by observation of several near-Earth asteroids. The latter are well-known to be sensitive to the non-gravitational Yarkovsky forces, which are difficult to model since physical parameters of asteroids (diameter, thermal inertia, mass etc.) are poorly known. Thus, we used the code already developed for the Gaia mission to investigate the potential of the satellite to detect the Yarkovsky effect. More than 1600 near-Earth asteroids to be observed by Gaia were considered. A list of the most promising candidates was determined. Finally, we have demonstrated that, contrarily to some publications, the stability of the oscillating motion around Lagrange solution of the restricted three-body problem in the post-Newtonian approximation is the same as in Newtonian physics. As expected, utterly small relativistic corrections does not change the qualitative picture known from Newtonian physics.
Publications
- REMAT, Nice, (18–19 June 2009). Relativistic effects in highly-accuracy modelling of dynamics of asteroids
Mouret, S.
- REMAT, Paris (17–18 December 2009). Consequences of the EIH equations on the motion of asteroids
Mouret, S.
- Conference "Systèmes de référence spatio-temporels", (20-22 September 2010). Tests of fundamental physics with the Gaia mission
Mouret, S.
- REMAT, Turin, (3–4 June 2010). Update on relativity in the motion of asteroids
Mouret, S.
- ’Detecting the Yarkovsky effect with the Gaia mission: list of the most promising candidates’. Mon. Not. R. Astron. Soc., 143 (2011)
Mouret, S., Mignard, F.
