# NavList:

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

**Re: Horizons, was Summary of Bowditch Table 15**

**From:**Jim Thompson

**Date:**2005 Jan 31, 08:49 -0400

Trevor and George, Thank you for pointing me on the right path. How does this summary look? Jim Thompson jim2@jimthompson.net www.jimthompson.net -------------------- Outgoing email scanned by Norton Antivirus Where is the center of the earth? Most images in celestial navigation texts and my web pages show the earth as a perfect sphere, placing the terrestrial equator, celestial equator, and celestial horizon through the dead center of that sphere. While this simplicity makes learning easier, and in fact is not far off the truth, the spherical model does not represent the real shape of the earth. The difference is very small, but needs to be considered. See article 204 in Bowditch 2002. The simple spherical model says that a horizon is a curve on the celestial sphere carved by a plane that is perpendicular to a line drawn from the center of the earth through your position on the surface of the earth. It is convenient, and not far off the truth, to think that the local vertical line that you measure with a sextant runs through the center of the earth, but in fact the horizon planes are perpendicular to the direction of gravity (the plumb line), which does not necessarily follow that path. Bowditch 2002: "Horizontal, adj. Parallel to the plane of the horizon; perpendicular to the direction of gravity.". Since you look at the sea horizon to measure the vertical angle to a celestial body with a sextant, and since the sea horizon is very nearly perpendicular to the direction of gravity, except for tiny variations in some parts of the planet, then the vertical angle you measure with a sextant is also perpendicular to gravity. Sextants automatically measure on the local vertical (direction of gravity) from the local visible horizontal (horizon), which is 90? to the local vertical. The local vertical is a plumb line, not the line to the center of the earth. The angular difference between the plumb line (direction of gravity) and the line to the geometric center of the earth is near zero at the equator and poles, but varies to a maximum of about 00? 11' arc at 45? Latitude, because the earth is not a perfect sphere. The difference between the two lines would result in up to about 11 miles of error (11' of arc) in the mid-latitudes if charting was done based on the geometric center of the earth. Modern charting methods use datums and mathematical models that more closely approximate the real shape of the earth, so the difference between the local vertical based on the direction of gravity and the local vertical based on the direction to the center of the charting model is very little. All this is not important for celestial navigators because the angular difference between the plumb line and a line to the center of whatever mathematical model is used to describe the shape of the earth for charting in the navigator's region is not signfiicant enough to cause problems in most practical celestial navigation. Manually obtained CN positions generally are no more precise than 1-2 miles, but the difference between the two vertical lines is much less than that. However mechanical celestial navigation systems that obtain positions to within a few meters do need to consider the difference in angle between the plumb line and the line drawn to the center of the local charting model. For example, that small difference could lead to serious imprecision in a computerized system that uses an automatic star tracking device to precisely measure star altitudes above a visible horizon, if that system was trying to achieve a precision of a few meters. Jim