= Fixed-speed orbital launch-direction error
{title2=$a=R,\quad e=|\sin\alpha|,\quad\Delta r_{\max}=R|\sin\alpha|$}
Launching at the correct circular <orbital speed> but at in-plane <angle> $\alpha$ from the tangent leaves specific <orbital energy> $-GM/(2R)$, hence <semi-major axis> $R$. The specific <angular momentum> becomes $\sqrt{GMR}\cos\alpha$, so $j^2=GMa(1-e^2)$ gives $e=|\sin\alpha|$. The actual periapsis and apoapsis are $R(1\mp e)$, equally far from the intended circular orbit. The maximum geometric radial separation is therefore $Re$. This is not an equal-time separation between two moving satellites.
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