NavList:

Good day to you Frank,

Thanks for your last insights.

Observer's Lop from visual Satellite pass

From the tools at our hands - heavens-above.com or equivalent - the Observer's Lop is the set of the continuous positions from which at different successive times you see one same satellite passing through the very same point in the sky, or in other words, occulting one same real or fictitious star. It can be seen as the intersection on the Earth surface of a "running straight line" joining such "star" - whether or fictitious - and the Satellite itself.

Your procedure involves just finding 2 such adequately separated points (i.e. not too close and not too wide apart, e.g. 100 nm or so) and drawing the "line" between them to [very] closely fit the local Lop.

Finding such Lop points ?

Trial and error.

Through processing "local geometry" results, it probably should be feasible from one "approximate" first trial to compute an almost exact point of the Lop, if not the full local Lop itself.. Time permitting, I will keep working deeper on this . 

Given the stringent requirements to record UT on one single satellite to achieve a single satellite fix, it is certainly much better to process 2 distinct Lop's which do not require any exacting knowledge of UT.

Also agree with you : as long as we want to obtain on a graph the intersection of both Satellite Lop and Vega Lop already plotted with the appropriate Lat/Long pairs, no need for a specific grid to do the job.

Why Mercator projection then ?

At first, proceeding then here into unknown territory, I decided to use a Projection which - just in case - I could use as a standard and reliable Navigation Map. By the same token I also wanted to cover a rather wide - nonetheless local - area to encompass most of North Carolina + a significant part of the Satellite vertical track over the Earth passing in South Eastern Virginia. Covering such a wide area eventually turned out as being unnecessary.

While I did not need such a wide local area, I did need to draw an Azimuth from my 1st point of the Satellite Lop. I first drew a line parallel to the ground track of the Satellite (@140°) and from its intersection with Parallel N36°, I had to verify that I was not too far off the Satellite Lop, which was indeed the case. Then with 2 such different points of the Satellite Lop, and with the Vega Lop I drew the Lop's intersection, which put me inside the Scotland Neck (NC) territory.

In other words, given the method I used, I did need a conformal Navigation Chart since I had to draw an Azimuth oriented line from my 1 St Satellite Lop point. Hence my choice for a local Mercator chart.

The procedure you are advocating - i.e. drawing a line on any grid between 2 adequately separated points of the Satellite Lop - is certainly as good if not definitely better in marginal cases than the procedure I have used here (1 point only + a parallel to the Satellite ground track).

Anyway, it has been a great exercise and thank you very much, Frank, for having brought this example to our attention.

Antoine M. "Kermit" Couëtte