It’s confusing because the latitude line 66° south looks like a straight line on a globe. But to sail in a “straight line”, which means keep your steering centered forever, you will travel in a great circle.
All great circles lie on a plane that intersects the sphere (earth) through the center of the sphere. You can see that the only latitude line that’s on a plane intersecting the center of the earth is the equator, and that 66° south doesn’t. This also means that all straight line paths on earth touch the equator at 2 opposing points. Or said another way, you can start with the equator, pick any one point on the equator and rotate it around that point to get a new great circle.
So in order to stay sailing along 66° south, you’d have to have your steering turned constantly just a little bit south.
It sure does, you’re right. So does any “straight line” great circle too, so that isn’t super helpful. The equator has the same circle projection that 66° does.
Look at it from the side and it looks straight. If you’re sitting in the plane of 66°, the projection is straight.
I was trying to be supportive of @dbatten while explaining. It’s easy to get confused about what straight means on a sphere, since nothing is actually straight.
May apologies if I sounded knee-jerky. The intention was to show that a picture was a better answer to @dbatten's very legitimate comment.
The idea is to demonstrate that a "straight" line on a surface needs to be viewed along a normal to that surface at the point of the line you are concerned with, assuming the definition of "straight" is "don't have to turn when travelling along line on the surface". That makes great circles look straight, and non-great circles not.
All great circles lie on a plane that intersects the sphere (earth) through the center of the sphere. You can see that the only latitude line that’s on a plane intersecting the center of the earth is the equator, and that 66° south doesn’t. This also means that all straight line paths on earth touch the equator at 2 opposing points. Or said another way, you can start with the equator, pick any one point on the equator and rotate it around that point to get a new great circle.
So in order to stay sailing along 66° south, you’d have to have your steering turned constantly just a little bit south.