The applause that the speaker hears is a response to the supposed "greatness" of science.  The astronomer has reduced the magnificence of the universe to a few complicated-looking formulas upon the blackboard:  "the proofs, the figures"  "the charts and diagrams."

The students are impressed and break into applause, but not  the speaker.  For him, there is no comparison to the awe that is in the skies.  Man, for all his learning, can never produce anything as magnificent as a single star.

Whitman, like many of the Romanticists and Transcendentalists, shunned the new and growing schools of science, those who, like the "learn'd astronomer" sought to explain the majestic and the unknowable.  For Whitman and many of his contemporaries, the natural world is its own reward and true learning takes place not in a lecture hall, but on hillsides and vistas. 

The lecturer in the poem is making a scientific presentation on some aspect of astronomy. He provides his audience with mathematical proofs, figures, charts, and diagrams. His lecture is rooted in scientific reason and logic.

The reader can infer from the second line of the poem that the astronomer fills a blackboard with complex notes to support his presentation because his information is "ranged in columns" before the poem's narrator. Apparently no detail is omitted from his lecture.

The audience in the lecture room applauds the astronomer for his great knowledge and detailed scientific presentation. He is a "learned" astronomer indeed.