1/ What is the lone red star shining low in the south before the Company departs Rivendell? Is it simply Mars/Carnil? Is it an actual star? Or is this supernatural, something to do with Sauron? If so, what is it?

1/ I've been looking at all references to the phase and position of the moon in #LOTR. On Sept 26th (SR), Frodo dreams about Gandalf escaping Orthanc, and "he saw the young moon rising". On that date, it was indeed very close to a new moon. But...