Preliminary Determination of the Sun's Gravitational Quadrupole Moment from Rotational Splitting of Global Oscillations and its Relevance to Tests of General Relativity

The sun's internal angular velocity is estimated from observations of rotational splitting of low-order, low-degree global oscillations detected as fluctuations in the limb-darkening function. The inferred rapid rotation implies a unitless grativational quadrupole moment, $J_2$, of (5.5±1.3)×${10}^{-6\mathrm{}}$. When this result is combined with two published planetary radar results, values of 0.987±0.006 and 0.991±0.006 are obtained for $\frac{1}{3}(2+2\mathrm{}\gamma -\beta )$, a quantity equal to 1 in the general theory of relativity.