Gravitational Spectral Shift Exterior to the Sun, Earth and the Other Oblate Spheroidal Planets

Here, we use our new metric tensor exterior to homogeneous oblate spheroidal mass distributions to study gravitational spectral shift of light in the vicinity of the Sun, Earth and other oblate spheroidal planets. It turns out most profoundly that, this experimentally verified phenomenon holds good in the gravitational field exterior to an oblate spheroid using our approach. In approximate gravitational fields, our obtained theoretical value for the Pound-Rebka experiment on gravitational spectra shift along the equator of the Earth ($2.578 x 10^{-15}$) agrees satisfactorily with the experimental value of $2.45 x 10^{-15}$. We also predict theoretical values for the Pound-Rebka experiment on the surface (along the equator) of the Sun and other oblate spheroidal planets.