The word “Planet” is still singular as seen here. Certain word endings change based on what precedes them.
You can read more here about the endings (go to the last paragraph). One example they cite is “Student.” Let’s apply it:
Ich helfe meinem Studenten.
I help my student.
Ich helfe meinen Studenten.
I help my students.
These words largely have to be memorized.
Edit: As @johnl notes, this is also not in accusative. The phrase “on our planet,” which indicates a place, is in this case an example of the dative.
However, some word endings would also change for the accusative. So, the accusative for “Planet” would still have the same ending. At that point, you rely on the case and the article to indicate whether it’s plural or singular. If “Planet” is in the accusative and plural, it would be preceded by “die” and not “den.”
In other words:
Accusative: den Planeten (singular), die Planeten (plural)
Compare this to:
Dative: dem Planeten (singular), den Planeten (plural)
This is why the entire sentence/context needs to be considered.