Reposting as a question.
Uhoh's answer allows us to compute the velocity at a given r.
Let's see what velocity is at $r=100000 \text{ km}$:
\begin{align}\mathscr{E}_{tot} &= {1\over 2}v^2 - {GM\over r}\\ -0.7\text{ kg}\cdot \text{m}^2 /\text{s}^2 /\text{kg} &= {1\over 2}v^2 - {4e8\text{ m}^3 /\text{s}^2\over 1e8\text{ m}}\\ -0.7\text{ m}^2/\text{s}^2 &= {1\over 2}v^2 - 4\text{ m}^2/\text{s}^2\\ 3.3\text{ m}^2/\text{s}^2 &= {1\over 2}v^2\\ 6.6\text{ m}^2/\text{s}^2 &= v^2\\ v &= 2.6\text{ m}/s\end{align}
At 100,000 km from Earth the CSM would be traveling at 2.6 m/s... And that's not even halfway to the moon.
I think somebody said the math was wrong, but... how?
So is this bad news?