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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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Re: Scope Center Field
From: Frank Reed
Date: 2012 Oct 9, 11:42 -0700

Greg, you wrote:
"This mornings exercise was to observe Sun and Venus lunars using the perimeter field of the scope. I was surprised at how much deflection there was in my reductions when compared to center scope field observations. Nearly a full minute of arc. To verify this effect the sextant was set to zero and the Sun images were adjusted to touch limb to limb. The Sun images were then observed spreading apart as the field of view was shifted to the perimeter."

The first observation is definitely true, and it applies to normal altitudes as well as lunars. It's line of sight "collimation". The observer's line of sight should be as nearly as possible parallel to the frame of the instrument (or in the case of a Bris sextant, parallel to the imaginary plane that is perpendicular to both mirrors). The resulting error is T^2*tan(h/2) where T is the tilt of the line of sight away from the frame and h is the altitude (or other angle) being measured. With the Sun or Moon in the field of view, T is visually measurable since you have the Sun/Moon as a scale. If you're making contact one Sun semi-diameter away from the center of the field, then T is just about 16'. The error equation assumes T is a pure angle (in "radians") and also gives the result as a pure angle. For practical use, it's easier to give T in degrees and a result in minutes of arc. Then error=(pi/3)*T^2*tan(h/2). The factor pi/3, of course is nearly equal to one. The error increases quadratically with T, so it becomes really noticeable when you're right near the edge of the field of view. It also clearly increases with higher angles.

It's worth noting that this is a visible error. So even if you're not entirely sure that the sextant's telescope is aligned with the center of the field of view in the right place, you can detect the center by observing a very large angle and slowly rotating the sextant keeping the objects aligned "vertically" in the field of view. A noticeable gap will develop on the left and right sides of the field of view with contact or minimum distance near the middle. If the minimum is too near the edge of the field of view or even beyond the edge, the telescope needs to be re-aligned. With modern sextants, this is rarely a problem.

Although the error is visible, and so it should be easy to eliminate, there's a catch. Observers tend to systematically place the Moon or especially the Sun off-center in a consistent direction usually because the shades aren't quite right. So rather than averaging out in the long run, you get a systematic error.

Some practical rules... Errors that are smaller than your eye's resolution (accounting for magnification), and errors that are smaller than your minimum error level for the whole process, don't matter. Let's say we're using a 3x telescope. The eye's unaided resolution is about a minute of arc. With a three power telescope, you can resolve angles of about 0.3'. Navigators usually (excluding lunars) hope for a result accurate to a minute of arc, and that generally means that we like to keep errors at individual steps smaller than 0.2'. Given that condition, for an altitude of 20 degrees, T should be less than 1 degree (the CENTER of the Sun should be less than TWO full Sun diameters from the center of the field of view). At 40 degrees altitude, T should be less than 3/4 of a degree. At 60 degrees, T should be less than about 34 minutes of arc (the center of the Sun should be less than ONE full Sun diameter from from the center of the field of view). At 80 degrees, T should be less than about 28 minutes of arc. Finally, at 100 and 120 degrees (not normally relevant for altitudes but important in lunars and also a.h. sights), T should be less than 24' and 19' respectively. For lunars, reduce all of the T limits by a factor of two, which reduces the potential error by a factor of four. A generously safe rule for nearly all altitudes and circumstances is that the Sun or Moon should never be further than one semi-diameter away from the center of the field of view, or, visually, the Sun or Moon's image should always overlap the exact center of the field of view (or the center of collimation if it's been determined). That's not difficult in practice.

One little puzzler here. Greg, you said you tested this with the Sun limb-to-limb. But the error is quite small when h is one degree.

-FER

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