How to center an object in a shaky video...

I recently took video of a SpaceX launch, but I was using a heavy lens and the video is relatively shaky.  Is there any way to edit the video to center the rocket?  I'm an astrophotographer and I use software to superimpose multiple images, but this is not a single point of light I'm trying to track.  It's a dynamic object; it's brightness changes, the trail changes, it's angle and trajectory changes.  I just want to keep the brightest thing in each frame centered.  I can't imagine that's so hard.  I think this is possible with Premiere Pro.  I've seen some videos of soccer balls being centered and what not, but nothing like this.  Any ideas?