Course / The line of position

Part III · The line of position · Page 1 of 3

Close up, the circle is a straight line

Your circle of equal altitude is thousands of miles across. But you only care about the few miles of it near your DR, and over a few miles it is as straight as the edge of a ruler.

YouN
The curved line is the circle of equal altitude; the straight one is square to the Sun's bearing, touching it where you are. Zoom in.
Picture width
about 7,995 nm
Radius of the circle
2,700 nm
Gap between them, 1,999 nm from you
527 nm

From space the circle is plainly a circle.

That straight piece is the line of position (LOP). A circle around the ground position is always square to the line pointing at its center, so the LOP runs square to the Sun's bearing, Zn: at Zn ± 90°.