Which Way to Mecca?

Knowing the direction to Mecca is important to all Muslims.  This post goes into the best way to find it. (Updated May, 2019 to take compass variation into account.)

Today is Friday and all over the world, Muslims will join together for Friday prayers, like a wave washing over the world from east to west.  By some estimates there are over 1.8 billion Muslims in the world and one of the many things that binds them together is prayer, or Salat.  Most people are aware that Muslims pray five times a day but not everyone is aware that when they pray, they all face the same place, Mecca, and more precisely, the Ka’aba, a squarish shrine of black marble that sits in the centre of the Great Mosque of Mecca.

(For the pedantic amongst you (meaning me), a better transliteration would be Makkah).  This direction is known as the Qibla.  Most mosques will be oriented along that direction, with an alcove inside (the mihrab) to indicate that direction.  That forms quite a picture in my head of a worldwide practice – and must add greatly to a sense of unity.

Disclaimer: I am not a Muslim but I did live for two years in a very conservative Muslim country and learned quite a lot about Islam.  I won’t claim to be an expert on Islam but I think I have a good familiarity.  I’ll ask for forgiveness in advance if I’ve gotten something wrong here- and am more than happy to be better educated on this.  Please!

Recently, a friend asked me to help with determining that direction for a gathering they were organising.  Off the top of my head, I thought that it has to be either roughly northeast or northwest depending on which way is shorter.  Here’s a map similar to the one in my head that was behind my reasoning:

Based on that, I figured it’s probably northwest from here.  This was important and I wanted to be sure – so I consulted the internet (as you do).  A issue like this is quite common for Muslims, especially when travelling.  I can recall visiting countries in Asia and the Middle East where the qibla was shown as an arrow painted on the ceiling of hotel rooms.  (This guy has some special issues.)  It should come as no surprise that there are apps and websites that provide this service.  The first website I consulted was Hamariweb.com which listed most New Zealand cities – here’s what they said was the qibla for Christchurch:

Hang on – that’s really messing with my schema, thank you very much.  West southwest?  Zooming out I get this:

Okay, so, yes, this does end up at Mecca, but is this correct?  Better check somewhere else:

And note how Musjid Al Noor is oriented in this direction:

These are all consistent, yes, but clearly I’m not understanding this.  Does this have to do with great circles?

Great Circles

With  reading most maps, the curvature of the earth doesn’t come into play very much, particularly if you’re looking at relatively small areas.  But say you take an overseas trip – perhaps it’s your year to make the pilgrimage to Mecca (the Haj).  When travelling long distances by air, planes take the most direct route, to save on fuel and time.  When plotted on most world maps, these end up being curved lines rather than straight.  These curved lines are referred to as Great Circles and occur when a plane (not an airplane…a geometric plane) intersects a sphere and passes through the centre of that sphere.

This represents the shortest distance between two points on the sphere’s surface.  When we project the three dimensional nature of the earth’s surface into a flat, two dimensional space, distortions occur, so these are really problems with how well our 2D maps represent a 3D object.  The straight line an airplane would follow becomes curved because the earth is relatively spherical.  As shown in the map below, the shortest path an airplane would fly going from New York to Madrid is not the straight line drawn between them, but the curved great circle route above.

I did manage to find a great circle mapper and plugged in the airport codes for Christchurch (CHC) and Mecca (OJEN).  Here’s what they came back with:

So, putting all this together, I’ll suggest to my friend that the qibla for Christchurch is on a compass bearing of 256 degrees West.

Correcting for compass variation

We’re not quite done yet.  Those of you who are marine inclined might be inclined to ask – is that bearing true or magnetic?  Due to variations in the earth’s composition, there is usually a difference between true north (to the north pole) and magnetic north (the direction your compass points to) which need to be taken into account.  The bearing to Mecca from the sites above are with respect to true north so to be accurate we need to correct the bearing based on the compass variation here.  This turns out to be 24 degrees 1 minute East.  One of many nautical sayings helps us know how to take this into account: “Variation east, compass is least” or less, so I need to subtract 24 from 256 to get the magnetic bearing – which is (let’s see, where’s that calculator…) 232 degrees.  So to find the proper bearing to read of my compass, this is what I’ll use to find the direction to Mecca.

While this is always an important thing for Muslims to be aware of, it is especially so now as Ramadan, the Muslim month of fasting is about to begin.  The sighting of the new moon will make it official but it should be sometime around Sunday the 5th.  To all our Muslim brothers and sisters, Ramadan Kareem!

C