How does Shakespeare’s use of the specific simile “I am constant as the Northern Star” support the statements he makes in the rest of his speech?

Caesar is pretty arrogant at this point. After defying three warnings that his life is in impending doom, he goes to the Senate and yet again tests his fate. He refuses to repeal the banishment of Publius Cimber and launches into a speech about his invincibility. He compares himself to the brightest star in the sky and adds all kinds of grandiose self-descriptions.