The first commandment of the Torah is to be fruitful, multiply, and fill the earth/land (הָאָ֖רֶץ).
The question is whether Mars (and other terrestrial planets and moons) should be included in the definition of הָאָ֖רֶץ.
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G-d did not command man to fill any specific geographic area, so colonizing additional area (on earth or elsewhere) does not directly fulfil any commandment.
Ramban explains "fill the earth" (וּמִלְא֥וּ אֶת־הָאָ֖רֶץ) as G-d's blessing to mankind to increase in numbers and populate vast areas; and "and subdue it" (וְכִבְשֻׁ֑הָ) as G-d's gifting mankind the power to dominate the rest of His creation.
Welcome to Mi Yodeya and thank you for sharing your fascinating question, Doug! Rav Moshe Heinemann says in the name of his Rosh Yeshiva, Rav Aharon Kotler zt"l, that we are not supposed to travel outside of earth based on the verse in Tehillim (115:16):
הַשָּׁמַיִם שָׁמַיִם לַה' וְהָאָרֶץ נָתַן לִבְנֵי־אָדָם׃ The heavens belong to the LORD, but the earth He gave over to man.
Hashem gave this earth to us to inhabit, but outer space is His. Accordingly, it is a commandment for us to inhabit THE earth, the only one we are allowed to inhabit.