The Earth's Rotation and Revolution – The Universe and the Solar System (Senior 5 Geography) | Ganzaa

The Universe and the Solar System

Lessons

Senior 5 · Geography

The Universe and the Solar System

3 lessons

Lesson 2 of 3

The Earth's Rotation and Revolution

25 min

Why the sun rises at six in Kigali all year

In Kigali the sun rises close to six o'clock in the morning and sets close to six in the evening in every month of the year. In Oslo, Norway, it rises before four in June and after nine in December. Both facts follow from two movements of the Earth, its spin and its journey round the Sun, together with the tilt of its axis. This lesson works out their effects, including the calculations the A-level examination asks for.

What makes the Earth special

Liquid water covers about 71% of its surface. It is the only planet known to have stable liquid water on its surface.
An atmosphere rich in nitrogen and oxygen, which supports life, burns up most meteoroids and keeps the surface temperature moderate (a mean of about 15 °C).
The right distance from the Sun: close enough for warmth, far enough for water not to boil away (the "habitable zone").
A magnetic field, generated in its liquid outer core, that deflects charged particles streaming from the Sun.
Life: it is the only body on which life is known to exist.

Definition

Rotation: the spinning of the Earth on its axis, from west to east, once in about 24 hours (one solar day). Axis: the imaginary line through the North and South Poles about which the Earth spins. Example: because the Earth spins eastwards, the Sun appears to rise in the east.

Effects of rotation

Day and night. One half of the Earth faces the Sun at any moment. The line between the lit and dark halves is the circle of illumination.
Differences in local time. The Earth turns through 360° in 24 hours, which is 15° of longitude per hour, or 1° every 4 minutes. Places to the east see the sun reach its highest point first.
Deflection of winds and ocean currents (the Coriolis effect): moving air and water are turned to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
A daily rhythm of heating and cooling, and the land and sea breezes that follow it.

Worked example 1: local time from longitude

Problem. It is noon by the sun in Kigali (30° E). What is the local solar time in Accra, Ghana (0°), and in Lima, Peru (77° W)?

Solution. Accra: the difference in longitude is $30^\circ$ , and $30 \times 4 = 120$ minutes, 2 hours. Accra is west, so its time is earlier: 10:00.

Lima: the places are on opposite sides of the Greenwich meridian, so add the longitudes: $30^\circ + 77^\circ = 107^\circ$ . $107 \times 4 = 428$ minutes $= 7$ h 8 min. Lima is west, so earlier: $12 : 00 - 7 : 08 =$ 04:52.

Rule: east gains, west loses. Same side of the prime meridian: subtract the longitudes; opposite sides: add them.

Standard time. If every town kept its own solar time, clocks in Rubavu and Kirehe would differ by several minutes. Countries therefore adopt one standard time for a whole zone, usually a whole number of hours from Greenwich Mean Time (now Coordinated Universal Time, UTC). Rwanda keeps Central Africa Time, two hours ahead of UTC (IANA time-zone database, zone Africa/Kigali). Because 2 hours equals 30° of longitude, and Kigali lies almost on 30° E, the sun in Kigali is highest very close to 12:00 by the clock. The International Date Line, roughly along 180°, is where the date changes: crossing it eastwards, you go back one day; westwards, forward one day.

Definition

Revolution: the movement of the Earth in its orbit around the Sun, once in about 365¼ days. The orbit is a slightly flattened circle (an ellipse): the Earth is closest to the Sun (perihelion, about 147 million km) in early January and farthest (aphelion, about 152 million km) in early July. Example: the extra quarter day each year is collected into a 29 February every fourth year, a leap year.

Effects of revolution with a tilted axis

The Earth's axis is tilted 23.4° from the perpendicular to its orbit and always points the same way in space. So for half the year the Northern Hemisphere leans towards the Sun, and for the other half the Southern Hemisphere does. The effects are:

Seasons in middle and high latitudes. They are caused by the tilt, not by the distance from the Sun: the Earth is nearest the Sun in January, during the northern winter.
The apparent movement of the overhead sun between the Tropic of Cancer (23.4° N, about 21 June) and the Tropic of Capricorn (23.4° S, about 21 December). It crosses the equator at the equinoxes (about 20 March and 23 September), when day and night are equal everywhere. The rain belt of the tropics follows it, which is why Rwanda has two rainy seasons, around March to May and September to December (Meteo Rwanda climatology).
Changing day length: at the equator it stays near 12 hours all year; towards the poles the difference grows, until inside the Arctic and Antarctic Circles (66.6°) there is at least one day of 24-hour daylight and one of 24-hour darkness each year.
Changing altitude of the midday sun, which controls how strongly the ground is heated.

Worked example 2: the altitude of the noon sun

Problem. Find the altitude of the midday sun at Kigali (1.9° S) on 21 June and on 21 December.

Solution. The midday sun's altitude is $90^\circ$ minus the angular distance between the place and the latitude where the sun is overhead.

21 June: the sun is overhead at 23.4° N. Kigali is south of the equator, so the distance is $23.4^\circ + 1.9^\circ = 25.3^\circ$ and the altitude is $90^\circ - 25.3^\circ = 64.7^\circ$ , in the northern sky.

21 December: the sun is overhead at 23.4° S, on the same side, so the distance is $23.4^\circ - 1.9^\circ = 21.5^\circ$ ; altitude $90^\circ - 21.5^\circ = 68.5^\circ$ , in the southern sky.

The sun is directly overhead at Kigali twice a year, when it passes 1.9° S on its way south (in late September) and on its way north (in mid-March).

Warning

Common mistakes

"Seasons come from distance to the Sun." The Earth is closest in January, yet that is winter in the north. The tilt causes seasons.
Adding or subtracting longitudes wrongly. Opposite sides of 0°: add; the same side: subtract.
East and west reversed. Places east of you are ahead in time.

Tip

Exam technique. In time questions, write the four steps every time: difference in longitude, × 4 minutes, convert to hours and minutes, then add (east) or subtract (west), and state the day if midnight is crossed.

CrashCourse: "Cycles in the Sky: Crash Course Astronomy #3". Watch the part on the seasons and note how the tilt of the axis, not the distance to the Sun, changes the angle of sunlight.

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Practice

Give three effects of the Earth's rotation.
How many minutes does it take the Earth to turn through 1° of longitude? Show why.
When it is 14:00 local time at 30° E, what is the local time at 45° E?
A football match starts at 18:00 local solar time in Lagos (3° E). At what local solar time does it start in Kigali (30° E)?
A ship crosses the International Date Line sailing westwards at noon on Monday. What day is it immediately after crossing?
Explain why the Northern Hemisphere has its summer in July even though the Earth is then farthest from the Sun.
Calculate the altitude of the noon sun at Nairobi (1.3° S) on 21 June.
Explain why day length in Rwanda varies so little during the year.

Show answersHide answers

Any three: day and night; differences in local time (15° per hour); the Coriolis deflection of winds and currents; a daily rhythm of heating and cooling.
4 minutes: 24 h × 60 = 1,440 minutes for 360°, and 1,440 ÷ 360 = 4.
15° east, 15 × 4 = 60 minutes later: 15:00.
27° difference, 27 × 4 = 108 minutes = 1 h 48 min; Kigali is east, so 18:00 + 1:48 = 19:48.
Tuesday (crossing westwards, the date moves forward one day).
In July the Northern Hemisphere is tilted towards the Sun: the sun is high in the sky, its rays strike more directly, and days are long. The tilt matters far more than the 3% change in distance.
Distance = 23.4° + 1.3° = 24.7°; altitude = 90° − 24.7° = 65.3°, in the northern sky.
Rwanda lies only about 2° from the equator, where the circle of illumination always cuts the latitude roughly in half, so day and night stay close to 12 hours each all year.

Summary

Rotation (24 h, west to east): day and night, 4 minutes of time per degree of longitude, Coriolis deflection.
Revolution (365¼ days) with a 23.4° tilt: seasons, the overhead sun moving between the tropics, changing day length and noon-sun altitude.
Noon-sun altitude = 90° − (angular distance between the place and the overhead sun).

Sources and credits

Written by Ganzaa. Earth data (tilt, perihelion, aphelion, water cover): NASA Earth Fact Sheet and NASA Science. Rwanda's time zone: IANA time-zone database (zone Africa/Kigali, UTC+2). Rainy seasons: Rwanda Meteorology Agency (Meteo Rwanda). Figures 2 and 3 were drawn by Ganzaa.

Video: "Cycles in the Sky: Crash Course Astronomy #3", CrashCourse, embedded from YouTube.

1Why the sun rises at six in Kigali all year

2What makes the Earth special

3Effects of rotation

4Effects of revolution with a tilted axis

Why the sun rises at six in Kigali all year

What makes the Earth special

Effects of rotation

Effects of revolution with a tilted axis