A Derivation of the Empirical Anderson Formula for Earth Flyby Anomalies from the ASTG-Model

Following a detailed examination of the flyby anomaly phenomenon, we provide a clear derivation of Anderson et al.’s empirical formula based on the Azimuthally Symmetric Theory of Gravitation (ASTG-model). Our review concentrates on the foundational origins of Anderson et al.’s empirical formula. The ASTG-model, from which we will derive this formula, serves as a logical and natural extension of Sir Isaac Newton’s central gravitational potential theory: $\Phi =\Phi \left(r\right)$ . It proposes a gravitational potential that depends not only on the radial distance ($r$ ) but also on the azimuthal angle ($\theta$ ), i.e.: $\Phi =\Phi \left(r,\theta \right)$ . In the ASTG-model, it is suggested that the observed $\theta$ -dependence in gravitational potential arises from the spin angular momentum of the gravitating body in question. A significant and beneficial result of our derivation of Anderson et al.’s empirical formula is that—to first order approximation—it helps to partially address the ‘nagging’ and ‘bothersome’ free parameter problem that the ASTG-model encounters.