After PhD in Aerospace Engineering, could I be admitted into a top university for a second PhD in Computer Science? I currently work as an Aerospace Engineer for the Department of Defense for nearly 6 years now, and I have a PhD in Aerospace Engineering from a top-10 university in the United States. I am seriously thinking of doing a 2nd PhD in Computer Science, because I want to eventually own an Algorithmic Energy Trading Firm and need to become an expert in Machine Learning algorithms.

As of now, I am working on a few journal papers to publish and I am not going to have any problems getting strong letters of recommendation from my employer and professors on campus.  I ought to be able to get a letter from the Dean of my college as well.  So, I am thinking of a second PhD in Computer Science because I really want to immerse myself in Machine Learning and figured a PhD was the way to go.

Question for everyone:  Would it be a challenge for me to acquire entrance into a top 5 school in Computer Science for a PhD?

I ought to mention that my PhD research was in Computational Fluid Dynamics, Turbulent Flow and I had to develop my numerical solver and turbulence models in Object-Oriented C++.
A major part of doing a PhD is learning how to do research and handle working on problems which sit on the edge of what is known. You've done that already. Doing it a second time is unnecessary, expensive and time consuming.

If you've been doing aerospace engineering then you almost certainly have the necessary calculus under your belt already. And if you have a PhD you can teach yourself stuff. Buy a few good textbooks - I recommend "Pattern recognition and Machine Learning" by C.M. Bishop; "Information Theory, Inference and learning Algorithms" by D.J.C. Mackay (this one is free to download on the author's website because he's nice like that). Look up material universities and other insitutions put online - e.g. https://www.coursera.org/course/ml is a free course, whose description sounds like it covers a lot of the necessary basics.  A lot of machine learning conferences make their proceedings available for free - ICML and NIPS I think both do this, and the work is good quality.

Start getting up to speed on all this stuff. If it still interests you and you want to go the academic route, go looking for postdoc positions and then try to find a couple of talented people you can form a startup company with.