"Our planet is Earth."
Translation:Nasza planeta to Ziemia.
That's "Earth is our planet", so you start with the knowledge about "the Earth".
Here we have a sentence that says what is the planet we live on called.
I wonder why not: "Nasza planeta jest Ziemią" - how do you decide which half is the predicate?
Maybe just because it's a proper noun. Your sentence is like saying that "our planet" is "an Earth".
To show it even more clearly, "Paweł jest lekarzem" (Paul is a doctor) and not "Lekarz jest Pawłem" (The doctor is a Paul).