= Solution
For a <fixed-speed orbital launch-direction error>, the initial radius and <speed> are correct, so the specific <orbital energy> is still $\varepsilon=-GM/(2R)$ and the new <semi-major axis> is still $a=R$. Resolve the launch <velocity> into radial and tangential components, taking $\alpha$ as the in-plane deviation from the intended tangent:
$$
v_r=\sqrt{\frac{GM}{R}}\sin\alpha,\qquad v_\phi=\sqrt{\frac{GM}{R}}\cos\alpha,\qquad j=\sqrt{GMR}\cos\alpha.
$$
For a nondegenerate orbit $\cos\alpha\ne0$, the <orbital eccentricity> follows from $j^2=GMa(1-e^2)$:
$$
e=|\sin\alpha|,\qquad r_{\min}=R(1-|\sin\alpha|),\qquad r_{\max}=R(1+|\sin\alpha|).
$$
The intended circular orbit has radius $R$ everywhere, so the largest radial distance between the orbit curves occurs at either apsis:
$$
\boxed{\Delta r_{\max}=R|\sin\alpha|\simeq R|\alpha|\quad\text{for small }|\alpha|\text{ in radians}.}
$$
This is the geometric separation of the two orbit curves, not the distance between two satellites compared at equal elapsed times. The latter also depends on orbital phase. A purely radial launch is a degenerate zero-angular-momentum trajectory through the central body and requires separate treatment of the collision.
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