Earendil wrote:Did Tolkien ever actually say that Aragorn travelled beyond the Equator, or is that just a supposition based on people's intepretation of his line about "where the stars are strange"?
Well, most of the relevant passages all seem to be in "The Tale of Aragorn and Arwen" from Appendix A. First we have this, which includes Aragorn's first few years of wandering plus his period of great journeys and errantries:
'Then Aragorn took leave lovingly of Elrond; and the next day he said farewell to his mother, and to the house of Elrond, and to Arwen, and he went out into the wild. For nearly thirty years he laboured in he cause against Sauron; and he became a friend of Gandalf the Wise, from whom he gained much wisdom. With him he made many perilous journeys, but as the years wore on he went more often alone. His ways were hard and long, and he became somewhat grim to look upon, unless he chanced to smile; and yet he seemed to Men worthy of honour, as a king that is in exile, when he did not hide his true shape. For he went in many guises, and won renown under many names. He rode in the host of the Rohirrim, and fought for the Lord of Gondor by land and by sea; and then in the hour of victory he passed out of the knowledge of Men of the West, and went alone far into the East and deep into the South, exploring the hearts of Men, both evil and good, and uncovering the plots and devices of the servants of Sauron.'
What is especially interesting here is that it places his great journeys after his service to the Steward Ecthelion of Gondor, which would also place those journeys after the year 2980 unless, when he wrote this, Tolkien meant for Aragorn's errantry in Gondor to end earlier than indicated elsewhere. A couple of paragraphs later the Ranger comes to Lothlórien:
'It came to pass that when Aragorn was nine and forty years of age he returned from perils on the dark confines of Mordor, where Sauron now dwelt again and was busy with evil. He was weary and he wished to go back to Rivendell and rest there for a while ere he journeyed into the far countries; and on his way he came to the borders of Lórien and was admitted to the hidden land by the Lady Galadriel.'
This is when Aragorn is reunited with Arwen. They spend a season together before plighting their troth upon the hill of Cerin Amroth. Again, the implication is that he has not yet embarked upon the greatest of his early journeys, farther East than Rhovanion and beyond the borders of Umbar. The exact quote from Aragorn regarding the stars is from the Council of Elrond:
'I have had a hard life and a long; and the leagues that lie between here and Gondor are a small part in the count of my journeys. I have crossed many mountains and many rivers, and trodden many plains, even into the far countries of Rhûn and Harad where the stars are strange.'
So, as you say, we cannot say for certain that Aragorn ever crossed the Girdle of Arda, but we can guess that he at least came fairly near to it.
A final note: Both Appendix A and Appendix B (The Tale of Years) agree that the year 2980 saw both the end of Aragorn's service to Gondor (as Thorongil) and his reunion with Arwen, with some time in between scouting along the Mountains of Shadow. Missions for Gondor or Rohan might have taken Aragorn to distant lands, but it looks as though he still traveled extensively after that time before taking his place as the sixteenth and last Chieftain of the Dúnedain.