NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Real accuracy of the method of lunar distances
From: Frank Reed CT
Date: 2004 Jan 15, 22:59 EST
From: Frank Reed CT
Date: 2004 Jan 15, 22:59 EST
Jared Sherman wrote:
"My question was and is, how great an effect this tempest in a teapot has on the final result produced by clearing a lunar."
Oh, it's BIG. It could roughly double the error. If my sextant can measure lunar distances to +/- 0.1 minutes of arc and lunar altitudes to +/-5 minutes of arc, this translates to an error of +/-3 minutes of arc in the longitude based on the average rate of change of the "true" lunar distance (where true lunar distance is the geocentri lunar distance --the lunar distance that a hypothetical observer with a sextant at the Earth's center would measure). In cases where the Moon is high, the parallax of the Moon may lead to larger errors in the deduced longitude. Seeing how these differences come about can easily cause confusion, as you've seen on the list recently.
Here's something you can try: open up a copy of the Nautical Almanac to the Moon altitude correction tables (inside back cover usually) and compare them with the star altitude corrections (inside front cover). These altitude corrections are not organized quite right for lunar distance sights, but don't worry about that for now; they include the key corrections. Notice how rapidly the correction changes when the Moon is high... for example, at 80 degrees high. How much change in altitude does it take at 80 degrees to get a 0.1 minute change in the altitude correction? Next look at the altitude corrections when the Moon is 30 degrees high. How much altitude change does it take at 30 degrees to get a 0.1 minute change in the altitude correction? Also check the same for 15 degrees altitude and, just for fun, five degrees altitude. After you've got those pieces of information, take a look at the altitude corrections for a star. How do they compare? This should get you started on the issue that has been vexing some of the other list members (I said it will get you *started*... <g>).
As I noted at the top, this parallax correction is BIG. Just so we're clear, there are a few other issues that have been raised that make only minor differences. For example, the angular distance between the Moon and a planet can change more slowly than the distance angular between the Moon and a star. But that's a small difference (of interest from a strictly theoretical standpoint but irrelevant in practical terms).
Frank E. Reed
[X] Mystic, Connecticut
[ ] Chicago, Illinois
"My question was and is, how great an effect this tempest in a teapot has on the final result produced by clearing a lunar."
Oh, it's BIG. It could roughly double the error. If my sextant can measure lunar distances to +/- 0.1 minutes of arc and lunar altitudes to +/-5 minutes of arc, this translates to an error of +/-3 minutes of arc in the longitude based on the average rate of change of the "true" lunar distance (where true lunar distance is the geocentri lunar distance --the lunar distance that a hypothetical observer with a sextant at the Earth's center would measure). In cases where the Moon is high, the parallax of the Moon may lead to larger errors in the deduced longitude. Seeing how these differences come about can easily cause confusion, as you've seen on the list recently.
Here's something you can try: open up a copy of the Nautical Almanac to the Moon altitude correction tables (inside back cover usually) and compare them with the star altitude corrections (inside front cover). These altitude corrections are not organized quite right for lunar distance sights, but don't worry about that for now; they include the key corrections. Notice how rapidly the correction changes when the Moon is high... for example, at 80 degrees high. How much change in altitude does it take at 80 degrees to get a 0.1 minute change in the altitude correction? Next look at the altitude corrections when the Moon is 30 degrees high. How much altitude change does it take at 30 degrees to get a 0.1 minute change in the altitude correction? Also check the same for 15 degrees altitude and, just for fun, five degrees altitude. After you've got those pieces of information, take a look at the altitude corrections for a star. How do they compare? This should get you started on the issue that has been vexing some of the other list members (I said it will get you *started*... <g>).
As I noted at the top, this parallax correction is BIG. Just so we're clear, there are a few other issues that have been raised that make only minor differences. For example, the angular distance between the Moon and a planet can change more slowly than the distance angular between the Moon and a star. But that's a small difference (of interest from a strictly theoretical standpoint but irrelevant in practical terms).
Frank E. Reed
[X] Mystic, Connecticut
[ ] Chicago, Illinois
