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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Question about LoP's and Intercepts on a Mercator Chart
From: David Iwancio
Date: 2021 Jan 20, 22:23 -0800

Am I right in thinking that LoP's do not strictly cross intercepts at right angles?

Here's my train of thought.  Please point out where I've jumped the rail.

• Plotting is typically done on Mercator projections (or something "close enough")
• A (small) circle on the earth's surface is still a circle on a Mercator chart (generally), i.e. they don't turn into ovals
• (I'm assuming a spherical earth without flattening)
• A great circle on a Mercator chart is not a straight line (generally)
• Intercepts are drawn from the AP along the great-circle direction towards the geographic point
• Because intercepts aren't "straight" (i.e. rhumb) lines on the Mercator chart, they aren't pointing "directly" at the center of the small circle
• Therefore, an intercept doesn't cross a line of position (an arc of a small circle) at a right angle (generally)

This would explain why some of the math of a project of mine isn't quite working out.  I'm guessing it would be "more correct" to rotate the LoP slightly by an amount equal to the conversion angle.

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