Introduction: If the pope had the authority, would he have posed the question?
Answering from Church Tradition.
What guides the Church in every age is to refer back, through the Church Fathers, to the Apostolic Age [Divine public revelation was closed]. cf. St. Vincent of Lerins: The "Vincentian Canon", AD 434:
(3) Now in the Catholic Church itself we take the greatest care to
hold that which has been believed everywhere, always and by all.
That is truly and properly 'Catholic', as is shown by the very force and meaning of the word, which comprehends everything almost
universally. We shall hold to this rule if we follow universality
[i.e. oecumenicity], antiquity, and consent. We shall follow
universality if we acknowledge that one Faith to be true which the
whole Church throughout the world confesses; antiquity if we in no
wise depart from those interpretations which it is clear that our
ancestors and fathers proclaimed; consent, if in antiquity itself we
keep following the definitions and opinions of all, or certainly
nearly all, bishops and doctors alike.
What comes close to the question asked is the Controversy at Jerusalem [Ac 15:5-7] that led to the Council of Jerusalem [cf. entire Ac 15]. This council is unique among the ancient pre-ecumenical councils in that it is considered by Catholics and Orthodox to be a prototype and forerunner of the later Ecumenical Councils and a key part of Christian ethics.
Thus it appears that the Pope would not have the authority on his own, should such a matter arise. It appears that the matter would have to be settled via a valid Ecumenical Council [vs. say a Synod of Bishops].
Answering from Common Sense.
Moral Authority: A person, group, or organization that has moral authority is trusted to do what is right. cf. Moral - Definition for English-Language Learners from Merriam-Webster's Learner's Dictionary
[A] Nation: a large area of land that is controlled by its own government cf. Nation - Definition for English-Language Learners from Merriam-Webster's Learner's Dictionary
This is Jesus' mandate to baptize:
“All authority in heaven and on earth has been given to me. Go
therefore and make disciples of all nations, baptizing them in the
name of the Father and of the Son and of the Holy Spirit, teaching
them to observe all that I have commanded you; and lo, I am with you
always, to the close of the age.” [Mt. 28:18-20].
To answer whether the Pope has moral authority to baptize martians, one would need to examine whether the Pope is right to determine that Martians can be baptized, i.e. the Martians were in need of Baptism in the first place, and that they were covered in Jesus' mandate.
Nations have always been understood as those belonging to this world (Jesus' on earth). If the Pope were to determine that it was right to baptize Martians, assuming that he had established that Martians were in need of baptism [not sure how he would go about establishing that], it would appear that his determination would be in excess of Jesus' mandate as Martians do not belong to the nations.
Finally, if the pope had the authority, he wouldn't have posed the question.