= Proper-time normalization of an affine parameter
{title2=$g_{ab}\dot x^a\dot x^b=c^2$}
An <affine parameter> on a <timelike geodesic> can be scaled to <proper time>. With <metric> signature $(+---)$ this fixes the tangent-vector norm to $c^2$. A further constant rescaling preserves the affine <geodesic equation> but changes that norm; conserved <energy> and angular-momentum constants must be rescaled consistently. The unit term in a proper-time-normalized radial <energy> equation is consequently a normalization choice, not a property of every <affine parameter>.
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