A Measurement of the Shape of the Solar Disk: The Solar Quadrupole Moment, the Solar Octopole Moment, and the Advance of Perihelion of the Planet Mercury

Abstract

The Solar Disk Sextant experiment has measured the solar angular diameter for a variety of solar latitudes. Combined with solar surface angular rotation data, the solar quadrupole moment ${J}_{2}$ and the solar octopole moment ${J}_{4}$ have been derived first by assuming constant internal angular rotation on cylinders and then by assuming constant internal angular rotation on cones. We have derived values of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for ${J}_{2}$ and $9.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for ${J}_{4}$. We conclude with a discussion of errors and address the prediction of general relativity for the rate of advance of perihelion of the planet Mercury.