Dear Urban Astronomer

 
I'd like to know the deviation from true north of my compass, here in Johannesburg. I believe that true north is several hundred kilometres from magnetic north. How many degrees is that equivalent to?

Sincerely,

Yoram Bogacz
Highlands North, Johannesburg

Dear Yoram

The magnetic north pole is actually about 1200km from True North, but the exact location of magnetic north varies from year to year (It is currently somewhere North of Canada, and is drifting East at several ten’s of kilometers per year) as the Earth’s magnetic field is dynamic and constantly changing.The angular separation between Magnetic and True North is something like 11 degrees, which means that if you stood on each of these locations and drilled a hole directly down towards the centre of the Earth, the holes would meet at an angle of 11 degrees.  

Now obviously that’s not the same as the deviation your compass needle will show – if you stand directly between them and face North, the compass needle will point exactly behind you, 180 degrees away from the North Pole.  Similarly, if you were to travel far enough along the line that joins them until you’d passed them, the compass needle would be pointing at both poles – the deviation would be 0 degrees.  Unfortunately I’m not very good at spherical geometry, so I haven’t managed to calculate the deviation for your specific location, but the necessary trigonometry is something that navigators of old would have done routinely.

For an easy solution, refer to a table of magnetic declinations.  According to the linked table, the deviation for Johannesburg is -17 degrees (As in, True North is 17 degrees East of your magnetic compass reading).  Or you could always just compare the readings off a magnetic compass with those from a digital compass on a GPS receiver.  Or just use an online calculator like this one, from the National Oceanic and Atmospheric Administration