(a) What is a Great Circle? (b) Outline three characteristics of a Great Circle. (c) If the time at longitude 100°E was 5 a.m on Monday, 11th April 2011, wh...

(a) What is a Great Circle?

A Great Circle is any circle drawn on the surface of the earth whose plane passes through the centre of the earth, thereby dividing the globe into two equal halves (hemispheres). It has the same circumference as the earth. Examples are the Equator and every pair of opposite meridians of longitude.

(b) Three characteristics of a Great Circle

• Its plane passes through the centre of the earth and divides the earth into two equal halves.
• It has the largest circumference possible on the globe, equal to that of the earth.
• The arc of a Great Circle gives the shortest distance between any two points on the earth's surface (used in air and sea navigation).

(c) Time calculation

Given time at 100°E = 5 a.m. on Monday, 11th April 2011. Find values at 10°W.

Difference in longitude \( = 100^\circ + 10^\circ = 110^\circ \).

Since \( 1^\circ = 4 \) minutes of time:

\[ 110 \times 4 = 440 \text{ minutes} = 7 \text{ hours } 20 \text{ minutes} \]

Because 10°W lies west of 100°E, its time is behind, so we subtract:

\[ 5{:}00 \text{ a.m. Monday} - 7\text{h }20\text{m} = 9{:}40 \text{ p.m.} \]

(i) Time at 10°W: 9:40 p.m. (21:40 hours).

(ii) Day at 10°W: Sunday.

(iii) Date at 10°W: 10th April 2011.