I have Flash handy, so I just utilized the Resources tab in Chrome's Web Inspector to see the video resource Flash was actually streaming.
This approach works for a large percentage of CDN-based streaming video, which rarely has any unique authentication (as sharing any kind of per-user state with the CDN edges would be quite difficult).
Interesting, I tried doing the same thing and couldn't since it was getting it over rtmp from another cdn, which was how i found mine. Apparently NASA has more CDNs for video than others that i've run into.