# How do I express magnetic latitude as geographic latitude/longitude?

1. ### erotavlas

26
For a circle of latitude on the earth centred on the magnetic pole, how do I represent that in geographic coordinates (lat and long), centred on the geographic pole?

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3. ### SteamKing

9,113
Staff Emeritus
It's not clear why you want to do this. The magnetic pole location is subject to wandering w.r.t. the geographical coordinate system over time.

4. ### erotavlas

26
I understand that it wanders, and I have the model to calculate the correct position of geomagnetic pole at a given time.

WHat i need to do it plot the points of magnetic latitude and longitude on a map. So I'm trying to transform them into geographic coordinate system.

Anyway I found the transformation in this paper (page 3)
http://kho.unis.no/doc/Sigernes_Oval.pdf

But I'm stuck on the magnetic longitude calculation

5. ### abitslow

140
You may be misunderstanding what SK was saying. Look at this:http://en.wikipedia.org/wiki/Magnetic_Declination#Change_of_declination_over_time_and_space
Looking at the illustrations, it should be obvious to you that there is no 1-to-1 mapping between magnetic coordinates and geographical ones. That is two people thousands of miles apart may measure the same magnetic latitude. It isn't a good predictor of where you are, in general. It is best used locally.
I am not motivated to actually do the algebra to give you the answer, but this tells you how to get the answer.
Any point on the surface of a sphere can be represented by two coordinates which are transformed in a two by two matrix into any other (arbitrary) pair of coordinates. In 3 space, R is constant (approx) so what I would do to solve this problem is convert figure out the two matrices which convert geographical coordinates to spherical φ and θ, and do the same with your magnetic coordinates. Then figure out the inverses and multiply the Inverse of one by the other and you'll have the two transformation matices.
In other words given (lat, long) there is a 2x2 matrix which will convert them to (θ,φ). And there is a matrix which will convert (θ,φ) to (mag_lat,long) ((hint the final matrix will have for long (assuming geograph and geomagnet are the same) the row 0...1)). So, all you need figure is the values of lat and long which will transform to mag_lat. It will be composed of sin() and cos() functions of the (θ,φ) coordinates.