This comparison implies more than steadfastness. The north star is the star by which sailors have navigated since ancient times, the start that guides them in their voyages, just as Cesar leads the Roman people. The north star is unique in its flexdness; as the only star that never changes its position in the sky.
I got my sources from Spark notes: https://www.sparknotes.com/shakespeare/juliuscaesar/quotes/
