During Caesar's famous "I'm the brightest star in the sky" speech, he claims to be the most "constant" (steady) guy in the universe because he can't be swayed by the personal appeals of other men. While this is one of the most arrogant diatribes ever, it's also full of some snazzy literary devices and reveals a lot about Caesar's character. Let's take a look at Caesar's speech so we can think about how his elaborate galaxy metaphor creates meaning in the play:
I am Constant as the Northern Star
I could be well moved, if I were as you;
If I could pray to move, prayers would move me;
But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament.
The skies are painted with unnumber'd sparks;
They are all fire and every one doth shine;
But there's but one in all doth hold his place.
So in the world, 'tis furnish'd well with men,
And men are flesh and blood, and apprehensive;
Yet in the number I do know but one
That unassailable holds on his rank,
Unshaked of motion; and that I am he,
Let me a little show it, even in this;
That I was constant Cimber should be banish'd,
And constant do remain to keep him so. (3.1.7)
The first thing to notice is that when Caesar aligns himself with the "Northern Star," he attempts to elevate himself above all other men. Even though there are other stars (men) in the sky (Rome), "there's but one in all doth hold his place." In other words, Caesar claims that he's the only guy solid enough to rule Rome (as evidenced by his refusal to relent after having banished Cimber).
The irony here is that Caesar delivers this big, fancy speech mere seconds before he's assassinated. Just as our superstar is declaring how "unshak[able]" and immovable he is, the conspirators surround him and stab him to death, unseating him from power.
As a side note, it's not uncommon for Shakespeare's powerful political leaders to align themselves with celestial bodies. Prince Hal, for example, compares himself to the sun in Henry IV Part 1. And Hal's dad, Henry IV, compares himself to a comet.