20–27 Mar 2026
Wild View Resorts
Africa/Gaborone timezone

On a General Equation of Motion in the Case of an Azimuthally Symmetric Gravitational Field

Not scheduled
20m
Wild View Resorts

Wild View Resorts

Plot 80 President Avenue, Kasane, Botswana
In-person - Poster Presentation 10 S&E poster Science & Engineering

Speaker

Praise Nesvinga (National University of Science and Technology)

Description

This multiphase, ongoing study offers a data-driven theoretical analysis of the Earth flyby anomaly using the Azimuthally Symmetric Theory of Gravitation (ASTG). We create minute-resolved trajectories for seven flybys and calculate the asymptotic velocity change predicted by ASTG using high-resolution Horizons ephemerides combined with IERS Earth orientation characteristics. The possibility for ASTG is expressed as $\Phi(r,\theta) = -{GM/r}\left[1+\sum_{\ell=1}^{\infty}\lambda_\ell\left(R_s/2r\right)^\ell P_\ell(\cos\theta)\right]$, producing a noncentral polar acceleration component $a_\theta$ that breaks spherical symmetry. Starting from the Poisson equation $\nabla^2\Phi=4\pi G\rho$ we retain the leading polar perturbation $\ell=1$ and derive the modified equations of motion. Retaining the leading $\ell=1$ term yields the approximation $\Delta v_\infty/v_\infty\approx (R_s/\ell)(\cos\delta_{\rm in}-\cos\delta_{\rm out})$, which reproduces Anderson et al.'s empirical formula $\Delta v_\infty/v_\infty=\kappa_A(\cos\delta_{\rm in}-\cos\delta_{\rm out})$ and links $\kappa_A$ to ASTG parameters via $\kappa_A=\lambda_1(R_s/\ell)$. Using a least-squares method and bootstrap error estimates, we fit the limited model using flyby Doppler data that has been archived in order to evaluate the robustness of the parameters.

The findings indicate that the ASTG-derived expression predicts a small extra perihelion precession ~1 mas $cy^{-1}$ for planetary orbits, while matching the sign and amount of measured asymptotic variations within observational error for several examples. We discuss consistency with Pioneer deceleration bounds, noting the reported value $a_P\approx(8.74\pm1.33)\times10^{-10} \mathrm{ms^{-2}}$ and delineate allowed $\lambda_1$ ranges that satisfy both spacecraft and planetary constraints.

Within a spin-dependent modified gravity framework, this study offers a tangible physical foundation for Anderson's empirical rule and suggests precise observational testing, such as high-precision planetary ephemeris analysis and targeted flyby geometry selection.

Key references:
1. Anderson, et. al, 2008. Anomalous orbital-energy changes observed during spacecraft flybys of Earth. Physical Review Letters, 100(9), p.091102.;
2. Nyambuya, 2010. Azimuthally symmetric theory of gravitation–I. On the perihelion precession of planetary orbits. Monthly Notices of the Royal Astronomical Society, 403(3), pp.1381-1391.

Stream Science or Engineering

Primary author

Praise Nesvinga (National University of Science and Technology)

Co-author

Golden Gadzirayi Nyambuya (National University of Science and Technology)

Presentation materials

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