The Universe is the cosmos, all space and everything in it. Space is the empty space the things in the universe move through. Are you sure the sentence isn't: The Earth and all other celestial bodies of the boundless Universe move in space with the ease of birds in flight and to the rhythm of __ song. I removed "its" because it didn't clearly indicate "song of the Universe". But I stopped short of further editing because maybe this is not what you intended at all.

Earth and all what is IN Universe is moving around the space IN the same Universe. In this sentence, Universe would mean planets, stars or simple dust.

Universe means star, planet and all physical matters those exist. Space is where they all exist.