🔍 Key Concepts

• Circle of equal altitude (COEA) and how it relates to a line of position (LOP) • How the intercept method (Marcq St. Hilaire) approximates a circle by a straight line near the DR position • Why very large observed altitudes (Ho) change the geometry of the LOP near the geographic position (GP) of the body

💭 Think About

• Think about what happens to the radius of the circle of equal altitude as Ho gets closer to 90°. Does the circle get larger or smaller? • At what point does plotting the LOP as a straight line near the DR position stop being a good approximation because you are too close to the GP? • Which of the given angles is commonly used in sight-reduction practice as the cutoff where you switch from a straight LOP to plotting a small circle around the GP?

✅ Before You Answer

• Recall the practical sight-reduction limit often given in textbooks for treating a high-altitude sight as a straight LOP rather than a circle • Check which angle range (low 80s vs mid 80s vs high 80s) is typically cited as the boundary for “too close to the GP” for a normal intercept LOP • Before choosing, be sure you can explain to yourself why that particular cutoff angle makes the LOP better represented by a circle than by a straight line