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theorem proved term proof high

gravity_uncertainty_comparable

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The inequality shows gravity model velocity uncertainty exceeds one third the typical flyby velocity shift of 5 mm/s. Analysts of spacecraft Earth gravity assists would cite it when checking whether reported anomalies fall inside modeling error bars. The proof is a direct numerical comparison obtained by unfolding the two constant definitions and reducing with norm_num.

claimLet $δv_g$ be the velocity uncertainty arising from gravity model inaccuracies and let $Δv_f$ be the typical flyby velocity shift. Then $δv_g > Δv_f / 3$.

background

Module EA-008 analyzes the flyby anomaly: unexpected velocity changes in spacecraft during Earth gravity assists. The RS verdict is that standard physics suffices once thermal effects and gravity model updates are included. flyby_velocity_shift is the constant 5.0 (mm/s) standing for the observed anomaly magnitude in the 1-10 mm/s range. gravity_velocity_uncertainty is the constant 2.0 (mm/s) quantifying velocity error from current gravity models. The theorem also depends on the meta-realization structure for that supplies the orbit-coherence axioms.

proof idea

The term proof unfolds gravity_velocity_uncertainty and flyby_velocity_shift, then applies norm_num to compare the concrete values 2.0 and 5.0/3.

why it matters in Recognition Science

The result is invoked by ea008_certificate, which declares the flyby anomaly dissolved. It is labeled EA-008.5 and supplies the numerical comparison needed to show gravity-model uncertainty is comparable to the reported shift. Within Recognition Science this step supports the claim that thermal plus gravity-model refinements close the anomaly without new physics.

scope and limits

formal statement (Lean)

  75theorem gravity_uncertainty_comparable :
  76    gravity_velocity_uncertainty > flyby_velocity_shift / 3 := by

proof body

Term-mode proof.

  77  unfold gravity_velocity_uncertainty flyby_velocity_shift
  78  norm_num
  79
  80/-- **THEOREM EA-008.6**: Higher-order multipoles matter for close flybys. -/

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (3)

Lean names referenced from this declaration's body.