Ytdyklly

I was solving an astronomy problem which said "south of due west."
This could be interpreted in two different ways and I don't know which one is correct. Is 'south of' in that phrase an idiom? Or does it mean southwest?

Look at a compass rose.

Look at W for west. Now move 'southwards', which is anticlockwise¹ in this case, from the point for west. Somewhere in that region is "south of due west". You would expect it to be no nearer south than it is to west, as that would be "west of due south". Conventions vary, but I would tend to interpret "south of due west" WSW, or west-south-west, which is actually due west of south west. It might mean south-west, of course, or if you use a traditional mariner's compass (the compass rose of which has another degree of subdivision, for a total of 32 points), it might mean "west by south" (WbS), the point between W and WSW. Unless you have a clear idea of what the conventions of the text are, it could be any point anticlockwise of west and not anticlockwise of south-west.

¹: In this case it is anticlockwise; 'southwards' from east would be clockwise.

Although it could technically be anywhere between W and S, I would interpret that as being significantly closer to W than S. Probably somewhere between W and WSW.

A more precise expression would be something like "10° south of due west", which would be a heading of 260° (with 0° being due north, 90° due east, 180° due south, and 270° being due west). The less specific "(slightly) south of due west" would indicate a heading just slightly less than 270°, so essentially in a western direction, but a bit south-ish ...

Because it's in an astronomy context, there is a possible reason for this wording over "west-south-west" or "southwest". This could be not just a location, but directions on how to find it. Instead of trying to give a more precise compass direction, the phrase implies that you locate the celestial body in question by first looking due west, then slowly rotating your gaze/binoculars/telescope southwards until you come to the first body that matches the description of the body you're looking for.

So one might write "Betelgeuse is a red star that rises at 9:08 pm local time, South of due West." The intention is if a reader of that sentence wants to find Betelgeuse in the sky, they would go outside on a clear night at about 9:10 pm, locate due West, look in that direction and then start scanning to the South (left) of that point for a red star.

It's actually more helpful to locate stars by intentionally missing to one side and then knowing to look to the left or right of a compass point than it is to try to point at it directly. If you are trying to locate Betelgeuse (for example) by just pointing directly at it, and you don't see it, you don't know whether to scan left or right for it. If you deliberately start off at a point definitely to the right or left of what you're looking for, you always know which direction to scan in. Also, if you don't see it in your scan, you can go back to your reference point and start scanning outwards again, knowing that there's essentially "half the sky" you can ignore.

The same technique is used in some kinds of navigation/orienteering, and I remember seeing a question about that on the Outdoors Stack Exchange.