The mid-plane of the Main Asteroid Belt

We measure the mid-plane of the main asteroid belt by using the observational data of a nearly complete and unbiased sample of asteroids, and find that it has inclination $\bar{I}=0.93\pm0.04$ degrees and longitude of ascending node $\bar{\Omega}=87.6\pm2.6$ degrees (in J2000 ecliptic-equinox coordinate system). This plane differs significantly from previously published measurements, and it is also distinctly different than the solar system's invariable plane as well as Jupiter's orbit plane. The mid-plane of the asteroid belt is theoretically expected to be a slightly warped sheet whose local normal is controlled by the gravity of the major planets. Specifically, its inclination and longitude of ascending node varies with semi-major axis and time (on secular timescales), and is defined by the forced solution of secular perturbation theory; the $\nu_{16}$ nodal secular resonance is predicted to cause a significant warp of the mid-plane in the inner asteroid belt. We test the secular theory by measuring the current location of the asteroids' mid-plane in finer semi-major axis bins. We find that the measured mid-plane in the middle and outer asteroid belt is consistent, within 3--$\sigma$ confidence level, with the prediction of secular perturbation theory, but a notable discrepancy is present in the inner asteroid belt near $\sim2$ AU.