10 Spherical geometry Cambridge University Press 1 G

10. Spherical geometry Cambridge University Press 1 G K Powers 2013

Arc length of a circle Arc length is calculated using the following formula. l – Length of an arc θ – Angle at the centre r – Radius of the circle HSC Hint – Arc length of a circle is proportional to the size of the angle at the centre. Cambridge University Press 2 G K Powers 2013

Latitude and longitude q Latitude measures the angular distance north and south of the equator 0° q Longitude measures the angular distance east and west of the Greenwich meridian 0° HSC Hint – Parallels of latitudes run horizontally. Meridians of longitude run vertically. Cambridge University Press 3 G K Powers 2013

Distances along great circle The meridians of longitude and the equator are great circles. Use the formula for arc length. l – Length of an arc θ – Angle at the centre (angular distance) r – Radius of the Earth (approx 6400 km) HSC Hint – Multiply the angular distance by 60 to calculate the distance (nautical miles) between two locations on a great circle. Cambridge University Press 4 G K Powers 2013

Time differences and local time To calculate the local time: Find the time difference by multiplying the difference in longitude (degrees) by 4 minutes. 2. Place the locations on an east-west time line. 1. Find the local time by adding or subtracting the time difference. East of location – Add the time difference. West of location– Subtract the time difference. 3. HSC Hint – Ignore the latitude in time questions. Multiply the angular difference in longitude by 4 to calculate the number of minutes. Cambridge University Press 5 G K Powers 2013

Time zones q Time zones have the same time irrespective of time differences. Positive time zone number ‒ ahead GMT Negative time zone number ‒ behind GMT q Australia has three time zones called the Eastern Standard Time (+10), Central Standard Time (+9. 5) and Western Standard Time (+8). HSC Hint – Time zones are modified by nations to meet their needs. Read the time zone map carefully. Cambridge University Press 6 G K Powers 2013