Could astronomic equations be “patented” as a theoretic property of this student, or anyone?
Other things, such as tomes of fiction or pieces of music can be attributed to a particular source.
No. Mathematical methods and scientific theories are two of a number of things expressly excluded from patentability by every patent code on earth.
No.
Or anyone?
That's tougher. Have to ask the legal minds here. But I don't think so. If you invent something as a result of some equations you've derived, I think only the device you've invented (not the equations) is protected. So someone could take your equations and fly with them; i.e., develop them further, and invent something based on them that's completely different than your original device, if you had one, and you've got no recourse.
Also, if you invent something the government wants (anything to do with encryption, weapons, etc.), they can shut you down completely. You can't publish your results or manufacture anything that incorporates your ideas without their approval. Don't worry. I think they are pretty good about giving discoverers, inventors, etc., a nice little cut or a nice little contract, to manufacture things that have to do with national security. Anyone would love to be in such a position.
Again, this is a math major, definitely not a lawyer, speaking.
Doesn’t the Church of $cientology proclaim that some of the secrets they share with clients after extensive/expensive “auditing” are “trade secrets” (which blows the notion that it is a RELIGION)?