When Krishna spoke the Gita to the sun-god, was that Gita exactly the same as was spoken to Arjuna?

From: ankush

I read in Bhagavad Gita that it was spoken in the begining of treta yuga to sun god. But how could those verses where Lord Krsna addresses Arjuna be there that time in it? Since there was no Arjuna present that time. How do you explain this?