I don't really get the meaning of this line 'すれ違う赤の軌道' Could it mean 'Crimson path crossed' or 'The crimson path i crossed' ?
I was looking for some more context and I found out that the sentence you are asking about is probably part of the lyrics of a song called "Brave Shine". I have found a full translation of the lyrics here: leirion63.blog.fc2.com/blog-entry-21.html The whole translation is not perfectly literal though, but I think in general it makes sense and it might put you on the right direction.– TommyMay 29, 2016 at 12:49
すれ違う: Two things passing or missing one another. In my opinion this can have a romantic or at least emotional connotation, as in "so close, but so far!"
軌道: orbit, often the orbit of a planet or other celestial body
The link given by Tommy (converted to a comment) is a good start, but the translation is somewhat non-literal.
A slightly more literal translation of this part could be:
Red orbits, passing either other by