Predicting and Bounding Earth Flyby Velocity Anomalies Using a Minimal Discrete-State Model

Andrew Morton · Public preprint · Exploratory phenomenology

Explores a discrete-step phenomenological description of reported Earth-flyby velocity residuals.

Current program context

Source note: the current abstract describes seven events and an axis-free analysis, while the body retains a six-event analysis with a specified axis. These descriptions require reconciliation before the paper’s quantitative or operational conclusions can be promoted. The deposited abstract is reproduced faithfully below.

Abstract

High-precision Earth gravity-assist maneuvers occasionally exhibit small but systematic discrepancies in post-encounter velocity, known as the flyby anomaly. These Δv offsets, typically at the millimeter-per-second scale, remain unexplained by conventional perturbation models and can affect interplanetary navigation. We revisit the phenomenon with an axis-free, preregistered analysis that treats the anomaly as a phenomenological quantized correction: outcomes are constrained to a discrete ladder {…, −2ε₀, −ε₀, 0, ε₀, 2ε₀, …} with a fixed spacing ε₀.

Using seven well-documented Earth flybys (Galileo I, NEAR, Cassini, Rosetta I, MESSENGER, Rosetta III 2009, Juno 2013) and excluding the drag-dominated Galileo II from the primary fit, a locked spacing of ε₀ = 1.94 mm/s reproduces signs and magnitudes with RMSE = 0.070 mm/s; all declared nulls map to the n = 0 step within the preregistered threshold. A wrapped-phase test scanning ε finds the set is closer to a lattice than expected by chance (best ε⋆ ≈ 1.915 mm/s; FWER-controlled p = 0.002). However, a weighted χ² test using published per-event uncertainties rejects exact quantization at measurement precision (χ² = 17.1 for 4 DoF; p = 0.0018), driven by the high-precision Rosetta I residual. The results suggest discrete structure exists but is not exact at current measurement precision, supporting an operational framework rather than a fundamental quantization law.

We therefore present discrete spacing as an operational bound and falsifiable hypothesis rather than a confirmed law: future Δv measurements should fall on the ε₀ ladder (within registered tolerances) or overturn the model. All code, data, and the analysis specification (with SHA-256 hash) are archived on Zenodo.

Scope

This is an exploratory study of reported residuals. Its shell index is not determined in advance from first principles, so fitted agreement is not a forward spacecraft-navigation prediction.

Paper and supporting files

The deposit includes the paper and Flyby_Anomalies notebook. The source-note discrepancy must be resolved before treating the abstract and notebook as one verified analysis.

Read the current paper and supporting files on Zenodo

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Abstract checked 28 August 2026 · version 4 · public release 19 August 2025.