A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Jan 29, 12:12 -0800
The oblateness is a fixed number: 1/297 is a reasonable value. It's the fractional difference between the Earth's equatorial diameter and its polar diameter. In other words, if the Earth's equatorial diameter is known to be 2970 Galician Leagues (a made-up unit), then the polar diameter is smaller by one part in 297 yielding a polar diameter of 2960 GL. The oblateness correction for lunars is a separate, small correction to the observed lunar distance. It is outside and distinct from the usual math of clearing lunars. The correction it adds is quite small, and in most circumstances, you can ignore it. We can go through the details if you really want. One thing to know in advance is that the oblateness correction to the Moon's altitude (with some details spelled out in the calculation section in every edition of the Nautical Almanac published in the past thirty years), which someone mentioned recently, is not what you're looking for. Yes, that's a piece of the puzzle, but it's not the correct solution for lunars.
Incidentally, the correction for the refractional flattening of the Sun and Moon at lower altitudes is also a type of oblateness correction --in this case the small reduction of the vertical versus horizontal size of the apparent images leading to a direction-dependent semi-diameter, so beware the potential confusion. Naturally both the oblateness and the refractional flattening have been included in the clearing app on my website for many years.