Using astronomy software I realized it was impossible for the events in The Hobbit to have happened in 2941 T.A. and still have the phases of the moon be in alignment with that of LOTR. However, it fits perfectly if you move it back one year. Was there a missing year?
I found one year from about 6,000 years ago(as Tolkien implied in one of his quotes) that squares the seasons, venus and moon phases for 3019 T.A. I just couldn’t get The Hobbit to fit.