Geodetic coordinate of Intersection Point

Arman; Your description is not real good for this problem. You have 2 points with geodetic coordinates; is that correct??ÿThen you say you have 2 bearings for these 2 points?

Well if you have 2 points with geodetic coord. on them you will have a forward azimuth and a reverse geodetic azimuth.

What I am missing from you is where are these 2 points going to intersect?

If you extend the forward azimuth or the reverse azimuth you are going to get a geodetic arc. It will not close on itself unless its the equator or a meridian.

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Can you give me the coordinates of your 2 points and a better description of what you want from my above?ÿ

information?

JOHN NOLTON

I think he has geodetic coordinates for two points, and bearings from each of them (probably derived from angles) to a third unknown point.?ÿ He wants to solve for geodetic coordinates of the 3rd point and distances from the known points.

Since you have the grid coordinates of the intersection point, just convert to lat/long

actually, to answer your original question, you have a spherical triangle with three knowns...the distance (and azimuth, but that is not needed to solve the triangle) between the known points, and the two angles, so two angles and the included side. With that information you can solve for the other two sides. Then you can use those distances to solve for the intersection point by geodetic direct computation.?ÿ

Bomford has formulas for solving spherical triangles on pgs 123-125 and 563-564 (Third edition)

@bill93?ÿ ?ÿYou think, or you infer or you assume. Lets find out exactly what he has and wants and then help him with his problem!

?ÿ

JOHN NOLTON

Someone with Carlson can give you the answer in a minute. I would offer, but I temporarily don't have access.

Youwill have to explain what type of bearings you have.?ÿ

?ÿ

If you aren't comfortable solving spherical triangles, this approximate method may work.

Solve the problem in plane coordinates to find distances.

Find the FORWARD?ÿ program in the NGS Toolkit at www.ngs.noaa.gov.

Use the distance and bearing from one known point to the new point with the FORWARD program to find geodetic coordinates for the new point.

Repeat starting from the other known point and using FORWARD.

Compare the solutions to see if they agree well enough. Or take an average if slightly different.

This is not theoretically correct but will get you very close unless the distances are large.

Check by finding the geodetic distances and bearings using the program INVERSE. Note that those programs work with points and distances on the ellipsoid model of the earth and not ground distances.

Posted by: @john-hamilton

Since you have the grid coordinates of the intersection point, just convert to lat/long

His plane solution may not be on any standard grid projection.

Posted by: @john-hamilton

Should work if he can figure out spherical trigonometry, and if the distances are not so large that an ellipsoid solution is needed.

@john-nolton I hope this pic represents the problem more clearly.

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@bill93 Yes, you are correct. I hope this pic represents the problem more clearly.

@john-hamilton I have access to the Fourth Edition of Geodesy by Bomford. I will look in to it.

@bill93

Sadly, I do not have the distance between the known points and the unknown point.

@bill93?ÿ

Its still not clear what kind if bearing he has. If he is looking for a geodetic solution he may already have true mean bearings, or he could have some sort of plane bearings, or.... Your solution assumes geodetic forward bearings.?ÿ

Most surveyor's software of choice can easily?ÿ give him a precise answer isn't if he?ÿ knows wha type of bearings he has (except for Civil3D).?ÿ

If I understand the problem correctly, I would covert to plane, manually adjust the bearings by guess until they match his geodetic bearings, solve and covert back to geodetic.?ÿ The only way I have to calculate spherical triangles are by worksheet and an hour of quiet time.?ÿ

Don't let spherical trigonometry scare you.?ÿ It's just like regular trigonometry, except the formulas have more terms which are easy to understand and the answers are all angles.

arman.zmn?ÿ has not got back to me yet to clear up his wording of his problem. Breaking it apart (his post)

line by line I get the following;

#1)?ÿI have a two-point coordinate in Lat-Long,

This I think he means he has 2 points, P1 and P2?ÿ with a geodetic coordinate on each one.

#2) and I also have two bearings for these two points.

Here I think he means that for some point?ÿP3 he has a bearing from P1 to P3 and P2 to P3,

what type of bearing would be nice to know.

#3)?ÿthe geodetic line drawn out from these 2 points will intersect a point.

So if we have point?ÿP1 and P2 we can intersect to point P3.

This problem can be solved geodetically?ÿ, and has been solved by many.

Question to the people that have posted: What do you think that he wants? I hate to post and answer when I don't have all the information or have to guess at what a poster wants. It takes too long to type up something just to find out the poster wanted something else or left out something.

JOHN NOLTON

@arman-zmn?ÿ ?ÿOK we are getting close to being able to give you a solution.?ÿYou are still missing a very important part to tell us;?ÿ Do you want this to be on a "sphere"?ÿ or an?ÿ ?ÿ"ellipsoid".

?ÿ

JOHN NOLTON

Posted by: @arman-zmn

Sadly, I do not have the distance between the known points and the unknown point.

The INVERSE program I mentioned in another reply in this thread will compute the geodetic distance on the ellipsoid model of the earth, given latitude and longitude of the points.