34th Meeting of the AAS Division on Dynamical Astronomy, May 2003
6 Poster Papers
Posters, Monday, May 5, 2003, 8:00pm,

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[6.13] Candidate Asteroids for Discerning General Relativity and Solar Oblateness

J. L. Margot (California Institute of Technology)

Shapiro et al. (1968, 1971, 1972) determined the perihelion precession of Mercury and of asteroid 1566 Icarus to test general relativity and to constrain values in the parametrized post-Newtonian formalism. The perihelion shift of Mercury is now known to about 0.1% (Shapiro 1990, Anderson et al., 1992).

Shapiro (1986) emphasized the need to measure the precession of several bodies in order to separate, based on their heliocentric distance dependence, the general relativistic effects from those due to the gravitational quadrupole moment of the Sun (J2). The J2 of the Sun is now known to be of order 2e-7, at a level where it cannot be detected compared to observational error in the Mercury perihelion shift. The J2 measurements rely on helioseismology, solar rotation data, and oblateness determinations.

The recent near-Earth asteroid discoveries provide better opportunities to detect GR and J2 effects. I computed the predicted perihelion advance for the best candidate asteroids, i.e. those with orbital parameters that minimize a(1-e2) and therefore maximize the sensitivity to J2. About a dozen have long astrometric arcs and perihelion shifts larger than 10''/cy, with the current leading contenders being 2000 BD19 (27''/cy) and 1999 KW4 (22''/cy). These two asteroids and two others (1999 FK21 and 3200 Phaethon) have at least two Earth approaches in the next 4 years during which they will be detectable with the Arecibo radar. The four candidates also have at least five opportunities for radar astrometry before 2020.

With the current best candidate the perihelion precession goes as (1+6e3*J2), assuming that general relativity is correct. A precision of 0.1% or better would be needed to detect the influence of J2. Because obtaining range estimates to the center of mass of asteroids is simpler than contending with the unknown topography of Mercury, this goal may be achievable and may provide the first dynamical measurement of the J2 of the Sun, in addition to probing other potential orbital perturbations.

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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.