What is the meaning of "the skies are painted with unnumbered sparks. They are fire, and every one doth shine; but there's but one in all doth hold...

CAESAR: 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.
Act 3. Scene 1

Julius Caesar has behaved modestly and even humbly up to this scene, but Shakespeare evidently wanted to reveal the man as supremely egotistical and arrogant just before he was killed. This would seem intended to justify Cassius, Brutus, and all the other conspirators in the assassination. Caesar is every bit as ambitious as Cassius and Brutus believe, perhaps even more so. Caesar finds no man who can compare with him. He has to look up into the skies as if he is comparing himself with the gods and demigods. 

In Caesar's time it was believed that the earth was stationary and all the stars and planets revolved around it. Even the sun revolved around the earth rather than the other way around. Caesar is saying that all the stars in the heavens, which are all sparks and all fire, are in constant motion except one. That would be Polaris, the Northern Star, which is directly above the North Pole and therefore does not appear to move as the earth rotates. All the other stars appear to move with the earth's diurnal rotation and annual revolution around the sun. Caesar compares himself with the Northern Star in being immovable. He is superior to all other men in begin steadfast, determined, unshakable, strong, self-confident, and always correct in his judgments. He has never spoken this way before. He is becoming intoxicated with the prospect of being crowned king. Ironically, he is just a few steps away from being stabbed to death by the men he so despises.

He obviously has a very high opinion of himself. If he had lived he would not have been satisfied with becoming king. The next step would be to become emperor, and after that he would want to become a god. He would easily become declared a god by the senate because he owns the senate already and would solidify his ownership if he became ruler. His successor Octavius became a god and most of the emperors who followed Octavius also became gods by senate decree and had to be worshiped in Roman temples.

Shakespeare has waited to illustrate Julius Caesar's hubris until just before he is stabbed to death. This is dramatically effective and validates the conspirators' violence. Caesar would have become a tyrant if he had been allowed to live. That is what Brutus is afraid of and what he foresaw. In Act 2, Scene 1, Brutus thinks long and hard about leading the assassination attempt. If he had not agreed to participate, Caesar would probably have lived.

He would be crown'd:
How that might change his nature, there's the question.
It is the bright day that brings forth the adder
And that craves wary walking. Crown him? that;
And then, I grant, we put a sting in him
That at his will he may do danger with.
The abuse of greatness is when it disjoins
Remorse from power, and, to speak truth of Caesar,
I have not known when his affections sway'd
More than his reason. But 'tis a common proof
That lowliness is young ambition's ladder,
Whereto the climber-upward turns his face;
But when he once attains the upmost round,
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend. So Caesar may;
Then, lest he may, prevent. And, since the quarrel
Will bear no color for the thing he is,
Fashion it thus, that what he is, augmented,
Would run to these and these extremities;
And therefore think him as a serpent's egg
Which hatch'd would as his kind grow mischievous,
And kill him in the shell.

It is significant that Brutus says the climber-upward "Looks in the clouds," because that is more or less what Caesar has been doing. He uses the stars as analogies with men in his speech in Act 3, Scene 1--but this is certainly not the first time that he has stood on his balcony at night and gazed up at the stars, planning to be there among them someday--and not just one of them but the principal one, the North Star.

Nicolaus Copernicus, who lived some 1400 years after Julius Caesar, established that the movements of the sun and stars were illusory. They appeared to move as they did because of the earth's rotation on its axis every twenty-four hours and its revolution around the sun every 365 days.