Tomorrow is NOT and adverb. Even it to-morrow or to morrow was once separated - it has now been combined into one word. The one word is tomorrow, a noun. "On tomorrow" is a prepositional phrase. Is "on" needed? No. Is it incorrect to use it? No. If today is Friday and I say "let's meet on Saturday" it is the same as saying "let's meet on tomorrow". I could also say "let's meet Saturday" or "let's meet tomorrow". It may sound funny to some of you but it IS correct. "On tomorrow we will discuss World History 1600 - 1650. On the next day, we will discuss World History 1650-1700. On Monday we will not have class" - On (insert time placeholder) something will happen." There is nothing wrong.