Does the Pope have the authority to baptize aliens (martians)?

I want to contribute to the debate with a different view. According to a recent article in the New Blackfriars (a peer-reviewed Catholic theology journal), entitled "Would St. Thomas Aquinas baptize an Extraterrestrial?":

[t]hrough the philosophical investigation of a hypothetical rational extraterrestrial species, it was established that any species that had radically different matter than humanity could not have a human nature. That the Fall of Humanity transmitted original sin only to those who have a human nature and that the Incarnation pours out grace upon those sharing the nature that was assumed are foundational both to Thomistic soteriology and to Catholic soteriology as a whole. Thus, it was argued that rational extraterrestrial life forms would not participate either in the Fall of Humanity or the Incarnation of Jesus Christ. While this does not exclude the possibility that such a species would have a fall, there are many ways in which St. Thomas holds that God could choose to reconcile them to Himself. The lack of a shared human nature makes the baptism of extraterrestrials improper and multiple Incarnations unnecessary.

The above summarises the idea pretty well. No Original Sin in an alien (which entered into the whole Human race through Adam), ergo no need for Baptism. For more details, check the article.

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.

In the link you cite, the Pope does not say he would baptize aliens. He is using the idea of Martians wanting to be baptized as an analogy to the strangeness Peter experienced when Gentiles wanted to be baptized in Acts 10. It's just a metaphor.