NavList:

Hello, Antoine!

Thanks for your positive post! I remeasured the Moon’s picture and got corrected position fix (some 21  nautical miles from previous fix). I am attaching a picture that ilustrates the new position (Fig.1).

You previously wrote:

“In conclusion - again full agreement here - it can be expected that whatever the method used to solve it, whether 3 D (I can do it again since I have kept all my notes and specific Software), or through by Besselian Elements on the Fundamental plane, or any other method (direct use of Stellarium or equivalent software) there is little doubt that in one specific "direction" on Earth the slightest angular deviation from the Moon limb will generate a quite important displacement on the Earth Surface, which might present [iteration] stability problems.”

Sounds complicated. It would be nice if you could perform your own calculations to compare the results with mine. I know from your posts that you are always very enthusiastic solver of navigational problems. I have no doubt that you will find this navigation problem interesting too. 

My approach was quite easy (it is based on the Frank’s posts on this subject). I am attaching a simple diagram (Fig.2) that ilustrates the process.

1) I chosed some rectangle on the surface of Earth — a region where the Moon is visible at given date and time and where Moon’s altitude is larger than 15°, because compression of the semidiameter in the picture is very little. Initially this rectangle can be choosen larger, and then gradulally smaller. The last step rectangle in my previous post was 1° x 1°. But in the corrected version in this post the rectangle is only 20’x20’. Lets call the corners of the rectangle A, B, C, D (see Fig.2).

2) I calculated lunar far limb distance for all corners. To do this I used Paul Hirose’s excelent tool Lunar4.4. Then I compared these values with the distance from picture.

3) Then I graphically interpolated between the corner points to find a point where position line crosses the corresponding side of the rectangle (on side AB this is a point G; but on side AD: point F). A line through FG is position line. In fact this approach is somewhat similar to original Sumner line construction method.

The concept of 3D cones is not directly involved in these computations. If one has any digital tool that allows to find the lunar distances at any point on Earth at any date and time, it is quite easy to get position fix. But comprehension of 3D cones allows to understand how to choose the best geometry (position among the Moon and stars) that will give the best results.

I am a great fan of this lunar positon fix method. It fascinates me as much as lunars itself.

Modris Fersters