The visual shape and multipole moments of the sun.

Abstract

This thesis describes the 1983 solar shape investigation performed at the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA). Solar diameter measurements, with the North Solar Pole defined as θ = 0° polar angle, have been made between the following polar coordinates: from θ = 0° to θ = 180° (the polar diameter), from θ = 90° to θ = -90° (the equatorial diameter), from θ = -45° to θ = 135° and from θ = 45° to θ = -135°. Expressing the Sun's apparent shape in terms of a Legendre series, these diameters have enabled the calculation of the P₂ (quadrupole) and P₄ (hexadecapole) shape coefficients. The theoretical framework used to provide a relationship between the observed shape of the Sun and the multipole moments of the solar gravitational potential field has been improved to include, in general, the effect of differential rotation in both latitude and radius. Using the shape coefficients and the theoretical framework, the gravitational potential multipole moments, expressed as the P₂ and P₄ coefficients of a Legendre series, have been found to be J₂ = (3.4 ± 1.3)E-6 and J₄ = (1.7 ± 1.1)E-6, respectively. It has been found that the contribution to the perihelion precession of Mercury's orbit, caused by the combined effects from the gravitational quadrupole term and general relativity, was approximately 1σ different from the observed amount after all other known Newtonian contributions had been removed from the observed precession. The total apparent oblateness ΔR (equator-polar radii) found from SCLERA observations is ΔR = 13.8 ± 1.3 milliarcseconds. The surface rotation contribution ΔR' to the apparent solar shape is ΔR' = 7.9 milliarcseconds. The quoted uncertainties represent formal statistical 1σ errors only. Also, it has been shown that large changes in the apparent limb darkening functions were occurring near the equatorial regions of the Sun during the time of the observations. Evidence for periodic shape distortions near the equator have also been found.