Is there a Catholic bishop with jurisdiction over space?

The short answer is yes: the pope.

Here is another way of possibly looking at this question.

Our Lord Jesus Christ is King of the entire Universe.

Pope Pius XI instituted the Feast of Christ the King in his encyclical Quas primas of 1925, in response to growing secularism and nationalism, and in the context of the unresolved Roman Question.

The title of the feast was "Domini Nostri Jesu Christi Regis" (Our Lord Jesus Christ the King), and the date was established as "the last Sunday of the month of October – the Sunday, that is, which immediately precedes the Feast of All Saints". In Pope John XXIII's revision of the Calendar in 1960, the date and title were unchanged but, according to the simplification of the ranking of feasts, it was classified as a feast of the first class.

In his motu proprio Mysterii Paschalis of 1969, Pope Paul VI amended the title of the Feast to "D. N. Iesu Christi universorum Regis" (Our Lord Jesus Christ King of the Universe). He also moved it to the new date of the final Sunday of the liturgical year, before the commencement of a new liturgical year on the First Sunday of Advent (the earliest date for which is 27 November). Through this choice of date "the eschatological importance of this Sunday is made clearer". He assigned to it the highest rank of "solemnity".

The liturgical vestments for the day are colored white or gold, in keeping with other joyous feasts honoring Christ. - Feast of Christ the King (Wikipedia)

The Supreme Pontiff of the Roman Catholic Church is also know as the Vicar of Christ.

(Latin Vicarius Christi).

A title of the pope implying his supreme and universal primacy, both of honour and of jurisdiction, over the Church of Christ. It is founded on the words of the Divine Shepherd to St. Peter: "Feed my lambs. . . . Feed my sheep" (John 21:16-17), by which He constituted the Prince of the Apostles guardian of His entire flock in His own place, thus making him His Vicar and fulfilling the promise made in Matthew 16:18-19. - Vicar of Christ (Catholic Encyclopedia)

Thus if the pope is the Vicar of Christ and according to the Catholic Church, Jesus is the King of the Universe, the pope thus has total spiritual jurisdiction over space and is in fact its’ bishop.

Is there a Catholic bishop with jurisdiction over space?

The short answer is yes and no.

There is at least one bishop who claims jurisdiction over the moon and that is in space.

An obscure law from 1917 places the moon under the purview of the Diocese of Orlando, Florida.

The Diocese of Orlando, Florida, covers much of the greater central Florida area. It encompasses nine counties, hundreds of cities, nearly 401,000 Catholic residents, and, strangely enough, the moon. nearly 401,000 Catholic residents, and, stran UCatholic explains the unusual circumstances that led to the moon’s spiritual jurisdiction landing with the diocese that ministers to Disney, Universal, and Cape Canaveral:

The Apollo 11 space mission began with the launch from Cape Canaveral on July 16, 1969. The mission fulfilled the national goal proposed by President John F. Kennedy in 1961 of “landing a man on the Moon and returning him safely to the Earth, before this decade is out.” However, when Apollo 11 made its famous flight from Cape Canaveral to ultimately fulfill that goal, they inadvertently made Bishop Borders the first Bishop of the Moon thanks to an obscure rule from the 1917 Code of Canon Law in effect at the time.

In 1968, William Donald Borders was named the first bishop of Orlando. When Apollo 11 launched, one year later, there was still a law in the books that stated that any newly discovered territory would fall under the bishopric from whence the discovering expedition departed. Since Cape Canaveral was under the purview of the Diocese of Orlando, Bishop Borders was effectively the first bishop of the moon.

UCatholic notes that, if taken seriously, the Diocese of Orlando would become the largest, at fourteen and half million square miles, although it would be hard to call it the largest diocese in the world.

Father John Giel, chancellor for Canonical Affairs for the Diocese of Orlando, commented that being able to boast the moon is ultimately fruitless since it “means nothing if there is no one to have jurisdiction over.” Father Giel did, however, commend Bishop Borders for the gig:

“Since we have yet to find any life on the moon, the story only emphasizes Bishop Border’s good and humorous nature that allowed him to be such a good first bishop for central Florida.”

Yes, the moon has its own Catholic bishop

Short answer

The local ordinary of the outer space is the pope alone.

Rite disclaimer

The following answer is written with respect to the laws of the Latin Church esp. the CIC. Most parts will apply also to Eastern Catholic Churches and the CCEO (just with a role for the Patriarchs).

Long Answer

That the pope has ordinary jurisdiction over the whole Church wherever it is, so also in outer space, is generally known.

can. 331 CIC The bishop of the Roman Church, in whom continues the office given by the Lord uniquely to Peter, the first of the Apostles, and to be transmitted to his successors, is the head of the college of bishops, the Vicar of Christ, and the pastor of the universal Church on earth. By virtue of his office he possesses supreme, full, immediate, and universal ordinary power in the Church, which he is always able to exercise freely.

That there is no diocese for the outer space is also no suprise. I cannot prove absense, but you wont find such a diocese (and someone else would have found one before and answered the question). So the question comes down to: How is a Latin Catholic ruled at a place without a Latin Catholic hierarchy?

This question is not new, but very old. The high seas have no bishop and there was a time when nearly the whole world had no Catholic hierarchy. In the last century in most parts of the world at least a apostolic prefecture was errected. Maybe the last land place without a hierarchy is Antarctica (at least I never heared of a hierarchy for it). The only country without a Latin hierarchy is Eritrea. It only has the Eritrean Catholic Chruch.

There are two aspects of jurisdiction to look into: What particular law (local law) is applicable to someone living in area without jurisdiction? Who is the local Ordinary for the such a place?

In cann. 102-106 CIC the concept of a domicile is defined. This domicile is a dioecese and a parochy (or only a diocese). If one has no domicile or quasi-domicile in any diocese he is a transient (vagus, can. 100 CIC). So there is no bishop who could make particluar laws for him, but if he is (even for a short time) at a territory whithin a diocese he is bound to all laws of this place (can. 13 § 3 CIC). [1]

In some cases the local Ordinary of a place is needed. For example only the local Ordinary and pastor can ordinarily assist in a marraige (can. 1108 f. CIC). The term local Ordinary is defined in the CIC:

can. 134 §1. In addition to the Roman Pontiff, by the title of ordinary are understood in the law diocesan bishops and others who, even if only temporarily, are placed offer some particular church or a community equivalent to it according to the norm of can. 368 as well as those who possess general ordinary executive power in them, namely, vicars general and episcopal vicars; likewise, for their own members, major superiors of clerical religious institutes of pontifical right and of clerical societies of apostolic life of pontifical right who at least possess ordinary executive power.

§2. By the title of local ordinary are understood all those mentioned in §1 except the superiors of religious institutes and of societies of apostolic life.

As nobody else is the local Ordinary for a place without own hierarchy only the Pope is the local Ordinary for such a place. A marriage in space can only be held with the Pope in person or someone delegated by him. Note that the Roman Pontiff is local Ordinary and not the Apostolic See which would include the whole Roman Curia.[2]

As stated before in the outer space is the same situation as in the high seas. For Pastoral Care for the People of the Sea the Pope made extra laws esp. the Motu Propio Stella Maris in 1997. The responsible authority in the Roman Curia is the Pontifical Council for the Pastoral Care of Migrants and Itinerant People. As the Pope did nothing like this for space missions there are no special rules and only the Pope has ordinary authority over the outer space.

The Pope makes also regularly rules for the Catholics who live in terretories without a hierarchy of their Church sui iuris, but with a hierarchiy of an other Catholic Church. As there is no Catholic hierarchy in space at all this does not help us anyway.

[1]: Klaus Lüdicke (Editor): Münsterscher Kommentar zum Codex Iuris Canonici unter besonderer Berücksichtigung der Rechtslage in Deutschland, Österreich und der Schweiz. 53. Lieferung April 2017. Ludgerus Verlag. Essen, can. 107 Rn. 6 [most important German commentary on the CIC]

[2]: ibid., can. 1109 Rn. 3

The 28th Canon of the 4th Ecumenical Council at Chacedon in 451 ceded jurisdiction of all Dioceses "among the barbarians" to the See of Constantinople. The text of the Canon reads:

Following in all things the decisions of the holy Fathers, and acknowledging the canon, which has been just read, of the One Hundred and Fifty Bishops beloved-of-God (who assembled in the imperial city of Constantinople, which is New Rome, in the time of the Emperor Theodosius of happy memory), we also do enact and decree the same things concerning the privileges of the most holy Church of Constantinople, which is New Rome. For the Fathers rightly granted privileges to the throne of old Rome, because it was the royal city. And the One Hundred and Fifty most religious Bishops, actuated by the same consideration, gave equal privileges to the most holy throne of New Rome, justly judging that the city which is honoured with the Sovereignty and the Senate, and enjoys equal privileges with the old imperial Rome, should in ecclesiastical matters also be magnified as she is, and rank next after her; so that, in the Pontic, the Asian, and the Thracian dioceses, the metropolitans only and such bishops also of the Dioceses aforesaid as are among the barbarians, should be ordained by the aforesaid most holy throne of the most holy Church of Constantinople; every metropolitan of the aforesaid dioceses, together with the bishops of his province, ordaining his own provincial bishops, as has been declared by the divine canons; but that, as has been above said, the metropolitans of the aforesaid Dioceses should be ordained by the archbishop of Constantinople, after the proper elections have been held according to custom and have been reported to him.

In 1995, Pope John Paul II affirmed in his encyclical Ut Unum Sint declared, that "the Church must breathe with her two lungs" and recalled the "unity which, in spite of everything, was experienced in the first millennium." This might be interpreted to mean that the same authority granted to the Patriarch of Constantinople in the first millennium (i.e. prior to the 1054 Schism) still exists in some semblance today.

Given the above, it would seem to me that the one bishop with any sort of claim of ecclesiastical authority over space with at least tentative assent by the Roman Catholic Church might be the current Eastern Orthodox Patriarch of Constantinople, Bartholomew I.

Given, however, the number of Russian Orthodox cosmonauts that have been and are currently in space, such authority might be disputed by the current Patriarch of Moscow, Kirill I, who has lately himself improved relations with Pope Francis. (Interestingly, the Patriarch of Moscow himself was once under Constantinople's jurisdiction, since the Russians were considered to be "among the barbarians" until 1589).

It may be that ceding jurisdiction over space to the Orthodox Patriarch of Constantinople - something that seems proper under the ancient canons of the Church - may end up being the first small step on the long path to full re-unification with Rome.