As someone who put in the years required to learn Classical Latin and Attic Greek I can but only heed you to make very, very sure you are willing to invest the enormous amount of time required to learn an ancient language.
If you have a normal job, wife and children, and can't find at minimum 2 hours out of your day to dedicate to language study, then don't bother. You will never read any Sanskrit at a comfortable pace if you can't commit to such an investment. I'm talking about picking up a book and not hitting an unknown word 3 times a sentence. You'll need at minimum 2 years of a full time schedule like before it even becomes fun.
It's the unfortunate and sad reality about the time commitment required in learning ancient languages to the level of fluency.
This is a hoax. The article reproduced there does exist though: it was published in an artificial intelligence journal in 1985 and made no reference to NASA, except for the fact that the author worked at the NASA Ames Research Center. You can find it there: http://www.aaai.org/ojs/index.php/aimagazine/article/view/46...
A quick search on internet for "sanskrit nasa" shows that all occurences are either copies, extracts or translations of this article taken out of its context. The belief that NASA has used sanskrit seems to come from this internet echo chamber.
I could find no reference about it on any NASA website, nor any other articles written by this Rick Briggs. I was able to find only one other article on sanskrit and AI, quoting the one by Briggs, dated to 1987: http://www.cedar.buffalo.edu/~srihari/papers/KRIS87.pdf
I have wanted to learn Sanskrit for a long time, and I think the stuff you could read after learning that would be interesting.
And then there is NASA (apparently) using Sanskrit for AI: http://www.vedicsciences.net/articles/sanskrit-nasa.html