1.1 The geoid, latitude and longitude
Earth isn't a perfect sphere: because it spins, it is flattened at the poles and bulges at the Equator. This unique shape is called the geoid. The equatorial radius is about 6378 km and the polar radius about 6357 km. Because of the flattening, gravity is slightly stronger at the poles, and one degree of latitude gets very slightly longer towards the poles.
Latitude is a place's angular distance from the Equator (0°–90° N/S); two neighbouring parallels are about 111 km apart. Latitude controls temperature, differences in day length and climate belts. Longitude is the angular distance from the Prime (Greenwich) Meridian (0°–180° E/W). Earth turns 360° in 24 hours, so each 1° of longitude means 4 minutes of local time; places to the east see the Sun first and are ahead in time.
FormulaLocal time difference = longitude difference × 4 minutes (east ahead, west behind)
1.2 Time zones and the date line
If every place used its own local time there would be chaos, so the world is divided into zones, usually 15° (one hour) wide. Countries pick a common time that suits their borders. Since 2016, Türkiye has used the time of the 45° East meridian (UTC+3) all year, so in western Türkiye the Sun rises and sets late by the clock.
At the International Date Line, which roughly follows the 180° meridian, the date changes: crossing it from west to east you go back a day (living the same day twice); crossing east to west you jump a day ahead. The line zigzags so as not to split countries.
1.3 Axial tilt and the seasons
Earth's axis is tilted about 23°27' from the perpendicular to its orbit and points the same way all year. So the latitude where the Sun's rays strike vertically (the declination) moves during the year between 23°27' N (the Tropic of Cancer) and 23°27' S (the Tropic of Capricorn). The seasons are caused by this tilt, not by Earth's distance from the Sun: during the northern summer, Earth is close to its farthest point from the Sun.
On 21 June the rays are vertical over the Tropic of Cancer; the Northern Hemisphere has its longest day and north of the Arctic Circle (66°33' N) the Sun doesn't set. On 21 December they are vertical over the Tropic of Capricorn. On 21 March and 23 September (the equinoxes) they are vertical over the Equator and day equals night everywhere.
FormulaSun's noon altitude: h = 90° − |latitude − declination| (use the sum when they are in different hemispheres) · Shadow length = object height ÷ tan h
Key terms
- Geoid
- Earth's own shape, flattened at the poles.
- Declination
- The latitude where the Sun's rays are vertical.
- Equinox
- A date when day and night are equal everywhere (21 March, 23 September).
- Local (solar) time
- Time set by the Sun's position, depending on longitude.
End-of-unit problems
Solve each one yourself first, then open the solution.
Istanbul is at about 29° E and London at 0°. When it is 12:00 local time in London, what is local time in Istanbul? Since Türkiye uses UTC+3, at roughly what official time is the Sun highest in Istanbul?
Show the solution
The longitude difference is 29°; 29 × 4 = 116 minutes = 1 h 56 min. Istanbul is to the east, so local time is 13:56. Official time is set to 45° E; Istanbul is 16° west of it: 16 × 4 = 64 minutes. The Sun is highest at about 12:00 + 1 h 4 min ≈ 13:04 official time (ignoring small seasonal variations).
Calculate the Sun's noon altitude at latitude 41° N on 21 June, 21 March and 21 December (take the tilt as 23.5°).
Show the solution
21 June: declination 23.5° N → h = 90 − (41 − 23.5) = 72.5°. 21 March: declination 0° → h = 90 − 41 = 49°. 21 December: declination 23.5° S (other hemisphere) → h = 90 − (41 + 23.5) = 25.5°. The range (47°) is twice the axial tilt.
At noon on 21 December, roughly how long is the shadow of a 1 m vertical stick at 41° N? (tan 25.5° ≈ 0.48)
Show the solution
Shadow = 1 ÷ tan 25.5° ≈ 1 ÷ 0.48 ≈ 2.1 m. The lower the Sun, the longer the shadow — which is why south-facing walls matter so much in winter.
A ship in the Pacific sails east from 175° E to 175° W and crosses the date line on Tuesday 3 March. What is the date on board after crossing? Why?
Show the solution
Crossing west to east, you go back a day: the date becomes Monday 2 March. The western (Asian) side sees the Sun first, so it is a day ahead on the calendar.