https://arstechnica.com/science/2016/02/the-audacious-rescue...
It would have been barely on the brink of possible, but with huge risks of its own. Going through the exercise though reveals a lot of details of the shuttle, being in orbit, and our capabilities at the time. It's been discussed a few times over the years on HN, the biggest one being 8 years ago when it was first published [0], but seems timely along with this article.
I'm very glad though going forward that entire class of failure modes is gone for good and that particular possibility for heroics will not be needed. Side mounting the shuttle was always one of the worst design choices amongst many, many bad decisions that went into the STS. Also created one of the worst launch abort profiles of any system ever. Nobody will do that again though.
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