As far as I can tell from my own research and from reading official sources, there are no physical or theoretical limits on the distance a portkey can take you, unlike brooms, which seem to have a distance cap. While it's not explicitly stated, the limitation is implied when Ron (under the influence of the Veela's charm), claims to have invented a broom that will reach Jupiter.
Officially, almost any inanimate object can be turned into a Portkey, by almost anybody as it appears to be very simplistic and low-level magic. You simply utter the incantation - "Portus" - and once bewitched, the object will transport anyone who grasps it to a predetermined destination, either instantly, or at a specific time.
So, if you knew from Muggle sources what space was like (as we all know, it's a very very very cold vacuum), could you just portkey yourself or your exploration party to an extraterrestrial location?
For example, let's look at Neptune's system. The only activity there was basically what we learned during the Voyager 2 flyby of 1989, and since then, there has been no further Muggle exploration, and neither are there any plans to.
For a particularly adventurous Witch or Wizard, are there any conceivable restrictions - logistically speaking - stopping them from taking a portkey out to one of Neptune's moons, like Triton or Nereid?
I am operating on the assumption that there are more than enough charms and spells in existence to keep the explorer(s) alive, and even comfortable. The bubblehead and warming charms, for example, should conceivably allow the intrepid Magus to not only breathe but stay warm and maintain reasonable mobility, while transfiguration should allow physical constructs to be created or manipulated for extra protection, item storage and/or travel assistance (using Capacious Extremis to create a "broom pocket" for example).
In Canon, the normal requirements for international portkeys are the consent of the authorized person(s) within the governing bodies of both the source and destination. Such was the case for both France and England when Arthur setup his meeting with Bill and Fleur.
However, in Quiddich Through The Ages, there is a note about a referee tampering with equipment in which at least one unlucky sap had his broom turned into a portkey, which dumped him in the middle of the Sahara - a stunt which I doubt was cleared by anybody in Algeria, Chad, Egypt, Libya, Mali, Mauritania, Morocco, Niger, Sudan or Tunisia - all nations whose sovereign land encompasses part of the vast Sahara Desert.
This makes me think that the process of obtaining consent is simply a matter of courtesy, rather than an actual logistical requirement, or functional limitation imposed on the actual portkey, and since going off-planet involves going somewhere without a (human) governing body to authorize incoming travellers, that's just as well.
So from a strictly theoretical point of view, given what I've laid out, is it plausible? Could it be done? And if so, why hasn't it? And also if so, could you add a non-Earth location to the Floo Net (once you get there, that is, presumably by portkey)?
The other "Wizards In Space" questions don't address the plausibility of using portkeys and the Floo Net for extra-planetary exploration and instead only rule out apparition and brooms. Nonetheless, I have modified this question from its original form (asked 6 years ago!) to have it reopened as this topic has come up once again in a fan-group I'm a member of.
