While searching for an old post by Dave Lindell I came across a post I had not seen from Dave. It was on 22 July, 2013. "Long Line Inverse Position" He had a form that was on page 68 and said it was Figure 25. Along with wanting to know where it came from (which the poster Melita Kennedy (mkennedy) told him it came from Spheroidal Geodesics, Reference Systems, & Local Geometry). Dave asked the question "why are two distances calculated?
Of the 6 or so posters?ÿNO?ÿone gave the correct answer. It looks like the posters were only guessing at an answer. I would have thought that the poster?ÿbase9geodesy?ÿwould have answered because P.D. Thomas worked for NGS at one time.
So the CHALLENGE is;?ÿ who can be the 1st poster to give the CORRECT answer ?
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JOHN NOLTON
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Damn, I know this was covered in 1 of my classes and I'm forgetting the answer.?ÿ You calculate it going both ways if I remember right, but I forget why.
Forward and backward azimuths are different, but the NGS INVERSE program computes only one distance that is the same if you reverse the points.
From a brief scan of the paper, I think the difference between S12 and S21 has to do with the distance a sub-satellite point would trace on the flattened earth's ellipsoid, as the orbit won't exactly follow a path that makes the sub-surface point the minimum distance.
But I didn't study it enough to be sure of that.
The form says that Position 1 is always West of Position 2. So the form always calculates a West to East line. The second calculation does not retrace the first one in the opposite direction. Instead, it begins at Position 2 and continues in an easterly direction to Position 1.
This is done to see which direction is shorter and thus compute the shortest distance.
Nah, it's not the forward and back azimuth.?ÿ I want to say it was from my coordinate systems class and was related to projections.?ÿ This is probably gonna bug me until I figure what it is that I'm trying to remember even if it's not related to this problem. ????????
Actually, that's not even close to being right.
Two distances are calculated because the normal section method of calculating long lines is used instead of a geodesic.?ÿ The direct and inverse normal sections follow different "paths" along the ellipsoidal surface and are of slightly different lengths.
@bill93?ÿ Your way off Bill93. Looking at page 68 (Fig. 25) there is no S12 and S21. There is S (sub1) and an S(sub2). That's what?ÿDave Lindell wants to know; "why two distances"
@mathteacher?ÿ?ÿMT, the reason for point 1 to be west of point 2 was for the azimuth search.
@frozennorth?ÿ ?ÿSome of what you say is correct?ÿBUT not for this problem.
There are some clues on page 128 where there is a numerical example. It turns out that S2 is the value that closely matches NGS Inverse for the given lat/lon values. It differs from S1 by one additive term of just over 7 meters.
There are some familiar variables, like Q for isometric latitude and the theta latitudes which I've forgotten how they are different from the phi values.
I really don't know why both values are needed.
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@mathteacher?ÿ You are correct about?ÿNOT needing both values. S1 is just a crude check on your final length of S2.
Adding a correction to convert from the great elliptic distance to the true geodesic distance.?ÿ
FWIW, your better copy link gave me a Error 403. I evidently need to update my eyeglass prescription to read the original.
Try searching for the title and look for the Google Books link. It's worth the trouble.
if interested in this topic, have you read Rapp??s Geometric Geodesy parts I and Ii
