"Discuss astronomy" or "talk about astronomy" are correct, grammatically-speaking. But native English speakers (especially in the US) are always finding creative ways of omitting words, or using one part-of-speech as another (adjectives as nouns, for example), and these alterations become part of the culture. So they're understood within the culture even though they're not correct according to the language. Changing "to talk about astronomy" to "to talk astronomy" is one such example.

As a native US speaker, I feel that the construction "to talk X" is perfectly correct... but perhaps only in US English. It's simply that one of the possible meanings of "talk" IS "discuss." "Discuss" is only a transitive verb, so we say "he wanted to discuss astronomy with the students," and we cannot say "he wanted to discuss about astronomy with the students." "Talk" is an intransitive verb, and can be used in a phrase like "he wanted to talk about astronomy with the students." But at least in US English it can also be a transitive verb, synonymous with "discuss," which can be used correctly in a phrase "he wanted to talk astronomy with the students." The American Heritage dictionary confirms this: talk, v.tr. 2a. To speak about or discuss (something) or give expression to (something): talk business; talk treason. Oxforddictionaries.com does not, so it might be a US-specific usage. A search of www.gutenberg.org for "talk business with" turns up four hits... all US.

I think "he wanted to talk about astronomy" is correct. And I think it's not "what that sentence correct?" but "is that sentence correct?" I'm still learning too. Correct me if I'm wrong.