Course / The circle of equal altitude

Part III · The line of position · Page 4 of 4

Two circles make a fix

One circle is not a position. A second body gives a second circle, and you must be on both, so you are where they cross.

Vega overheadArcturus overheadthe other crossingYouN
Two stars at twilight: each altitude gives a circle. Drag "You" and both circles follow.
Vega: altitude, radius
49°00.1', 2,460 nm
Arcturus: altitude, radius
64°55.3', 1,505 nm
The other crossing
2,178 nm away

Two circles cross in two places, usually thousands of miles apart. Your DR is never that wrong, so the crossing near your DR is your position.

These circles are huge: a radius of a couple of thousand miles is normal. You cannot draw them on a chart, and you do not need to. Near your DR, a few miles of the circle is all that matters, and over a few miles it is almost a straight line. That line is the line of position, the next module.