(a) (i) Equinoxes: Refers to two particular days of the year when all parts of the world will experience equal days and nights. These two days are March 21st and September 23rd. During these two days, the sun is vertically overhead at the equator and all parts of the earth will experience equal days and equal nights.
(ii) Great Circles: Any circle which divides a globe into two equal parts (or hemispheres) is a great circle. Examples are the equator, Greenwich meridian, meridian 180°, meridians 10°E and 170°W. 50°E and 130°W. etc. are all great circles. The number of great circles is limitless. It can extend east to west, north to south and so on provided it divides the globe into hemispheres.
(b) The reason(s) why the period of twilight is longer along the Arctic circle than at the Equator;
The brief period between sun set and complete darkness is called twilight. This is caused by the fact that during the period of twilight, the earth receives diffused or refracted light from the sun while it is still below the horizon. Since the sunrises and sets in a vertical path at the Equator, the period during which refracted light is received is short. But at the arctic circle, the sun rises and sets in an obligue path and the period of refracted light is longer. It is much longer still at the poles.