2. Great circle distances
Any circle that has the centre of the earth as its centre is a great circle.
We saw in M5 (ch 2) that the circumference of a circle is found by:
A =
We also saw that the length of an arc is found by:
l =
If two locations are on the same great circle we can use this formula.
First we need to work out the angle between the two locations.
The angle should be less than 180º.
The radius of the earth is approximately 6400km.
If the locations are on the same side of the equator or prime meridian,
subtract the latitudes or longitudes.
If the locations are on the different sides of the equator or prime meridian, add the latitudes or longitudes.
ie Same Side Subtract
2πr
θ/360 × 2πr

3. Example 1
Kojabbi (20ºS, 150ºE) is in NW QLD. Corraweena (29ºS, 150ºE) is in SA. What is the distance between the 2 towns?
Both towns are on 150ºE
Both are on the same side of the equator, so subtract.
Angle =
= 29  20
= 9º
l = θ/360 × 2πr
l =
= 9/360 × 2 × π × 6400
= 1005km
Lake George (0º, 30ºE) is in Uganda. Macapá (0º, 51ºW) is in Brazil. What is the distance between the 2 locations?
Both towns are on the equator.
Locations are on opposite sides of the prime meridian
Angle = =
= 81º
l = θ/360 × 2πr
l =
= 81/360 × 2 × π × 6400
= 9048km

4. Today’s work Monday’s work Exercise 7-02 Page 256 → 257 Q3, 5 → 12