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

[erotavlas]

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?

 

[SteamKing]

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.

 

[erotavlas]

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

 

[abitslow]

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.

 

[LudusRex]

Magnetic latitude is a measure of the angle between the Earth's magnetic field lines and the geographic equator at a specific location. It is typically expressed in degrees, with positive values representing locations north of the equator and negative values representing locations south of the equator.

In order to express magnetic latitude as geographic latitude and longitude, one must first understand the relationship between the Earth's magnetic field and its geographic coordinates. The Earth's magnetic field is not aligned with its geographic axis, which means that the magnetic poles are not in the same location as the geographic poles.

To convert magnetic latitude to geographic latitude, one must use a mathematical formula that takes into account the angle between the magnetic field and the geographic equator at a specific location. This formula is known as the magnetic inclination or dip, and it can be calculated using the Earth's magnetic field model.

Once the magnetic inclination is determined, it can be added to or subtracted from the geographic latitude, depending on whether the location is north or south of the equator. This will result in the corresponding geographic latitude for the given magnetic latitude.

To represent a circle of latitude on the Earth centred on the magnetic pole in geographic coordinates, one must first locate the geographic pole and then determine the magnetic inclination at that location. This inclination can then be applied to the circle of latitude to determine its corresponding geographic latitude.

In terms of longitude, the geographic longitude of a location is not affected by its magnetic latitude. Therefore, the longitude for a circle of latitude centred on the magnetic pole would remain the same as its geographic longitude.

In summary, converting magnetic latitude to geographic latitude and longitude involves using the magnetic inclination to adjust the geographic latitude and keeping the longitude unchanged. This method allows for a representation of magnetic latitudes in geographic coordinates and can be useful for comparing and analyzing data from different locations on the Earth's surface.