The Earth Revision Notes

The Earth is a spherical planet that rotates about an imaginary line called its axis. This axis is tilted at an angle of approximately 23.5° relative to the plane of its orbit around the Sun.

One complete rotation of the Earth takes about 24 hours (more precisely, 23 hours 56 minutes 4 seconds, known as a sidereal day). This rotation is from west to east when viewed from above the North Pole.

Because of this rotation, different parts of the Earth's surface move into and out of sunlight, causing the cycle of day and night.

• Earth's axis tilt: approximately 23.5°
• Rotation period: about 24 hours
• Rotation direction: west to east

As the Earth rotates, the side facing the Sun experiences daylight, while the opposite side is in darkness, experiencing night.

This continuous rotation means that any given location on Earth experiences a period of daylight followed by a period of darkness every 24 hours.

The boundary between day and night is called the terminator or twilight zone, which moves westward as the Earth rotates eastward.

• Day occurs when a location faces the Sun
• Night occurs when a location faces away from the Sun
• Terminator separates day and night regions

From the perspective of an observer on Earth, the Sun appears to rise in the east, move across the sky, and set in the west each day.

This apparent motion is caused by the Earth's rotation towards the east, making celestial objects appear to move westward across the sky.

The Sun's path and the length of daylight vary with latitude and the Earth's axial tilt, but the daily east-to-west motion is consistent everywhere on Earth.

• Sun appears to rise in the east and set in the west
• Apparent motion caused by Earth's eastward rotation
• Sun's path varies with latitude and season

To draw a diagram illustrating Earth's rotation and the day-night cycle:

1. Draw a circle to represent the Earth, tilted so that its axis is inclined at about 23.5° from vertical.

2. Mark the axis with a line through the centre, labelled 'Earth's axis'. Indicate the tilt angle approximately 23.5° from the vertical line representing the orbital plane (ecliptic). 3. Shade half the Earth to represent the night side and leave the other half unshaded to represent the day side, with the boundary between them as the terminator line, a great circle perpendicular to the axis. 4. Draw an arrow around the Earth indicating the direction of rotation (west to east). 5. Label the Sun on the side illuminating the day half, showing that sunlight comes from one direction. 6. Optionally, add cardinal points (N, S, E, W) on the Earth's surface to show the Sun rising in the east and setting in the west.

• Axis tilted at 23.5°
• Half Earth illuminated (day), half dark (night)
• Rotation arrow west to east
• Sunlight direction indicated

The Earth rotates once approximately every 24 hours on its tilted axis.

This rotation causes the cycle of day and night as different parts of Earth face towards or away from the Sun.

The Sun appears to move across the sky from east to west due to Earth's rotation towards the east.

• Rotation period ≈ 24 hours
• Tilted axis causes day/night cycle
• Apparent Sun movement east to west

The Earth revolves around the Sun in an almost circular orbit, completing one full revolution in approximately 365.25 days, which defines one year. This orbital period is the time taken for the Earth to return to the same position relative to the Sun.

The average distance from the Earth to the Sun is about 1.5 × 10^11 metres (150 million kilometres), known as one astronomical unit (AU). The Earth's orbital speed is roughly 30 km/s.

The orbit lies in a plane called the ecliptic plane. The Earth's path is slightly elliptical but close enough to be considered nearly circular for basic explanations of seasons.

• Orbital period ≈ 365.25 days (1 year)
• Average orbital radius ≈ 1.5 × 10^11 m (1 AU)
• Orbital speed ≈ 30 km/s
• Orbit nearly circular in the ecliptic plane

The Earth's axis is tilted at an angle of approximately 23.5° to the perpendicular of its orbital plane. This tilt remains pointed in the same direction in space as the Earth orbits the Sun.

Because of this tilt, during different parts of the orbit, either the Northern Hemisphere or the Southern Hemisphere is tilted towards the Sun, affecting the angle and duration of sunlight received.

This axial tilt is the primary reason for the variation in solar intensity and day length throughout the year, which causes the seasons.

• Axial tilt ≈ 23.5°
• Tilt direction fixed relative to stars during orbit
• Causes variation in sunlight angle and day length
• Key factor in seasonal changes

As the Earth moves around the Sun, the hemisphere tilted towards the Sun experiences summer, receiving more direct sunlight and longer daylight hours.

Conversely, the hemisphere tilted away from the Sun experiences winter, with less direct sunlight and shorter days.

Spring and autumn (equinoxes) occur when the Earth's axis is neither tilted towards nor away from the Sun, resulting in roughly equal day and night lengths worldwide.

• Summer: hemisphere tilted towards Sun, more direct sunlight, longer days
• Winter: hemisphere tilted away from Sun, less direct sunlight, shorter days
• Equinoxes: axis perpendicular to Sun-Earth line, equal day and night

To draw a diagram showing Earth's orbit and seasons:

1. Draw a large circle to represent Earth's orbit around the Sun, placing the Sun at the centre.

2. Mark four positions on the orbit corresponding to the solstices and equinoxes: Northern Hemisphere summer solstice, autumn equinox, winter solstice, and spring equinox, spaced approximately 90° apart along the orbit path, labelled accordingly with months (e.g., June, September, December, March). 3. At each position, draw the Earth as a small circle with its axis tilted at 23.5°, always pointing in the same direction (e.g., towards the top of the page). 4. Indicate sunlight direction as parallel rays from the Sun to Earth. 5. Show the hemisphere tilted towards the Sun receiving more direct sunlight and longer daylight, and the opposite hemisphere receiving less.

• Orbit circle with Sun at centre
• Four key positions labelled with months and seasons
• Earth's axis tilted 23.5° consistently
• Sunlight rays shown parallel
• Highlight hemisphere receiving more sunlight

The cyclical nature of seasons results from Earth's orbital motion combined with its axial tilt. The tilt causes the Sun's rays to strike different parts of Earth at varying angles and durations throughout the year.

This leads to changes in temperature and daylight length, producing the familiar pattern of spring, summer, autumn, and winter.

The entire cycle repeats approximately every 365 days, defining the calendar year.

• Seasons caused by axial tilt and orbit
• Sunlight angle and day length vary with Earth's position
• Temperature changes correspond to sunlight variations
• Cycle repeats every 365 days

The Moon orbits the Earth in an elliptical path, completing one full orbit approximately every 29.5 days. This period is known as the lunar month or synodic month. The Moon's orbit lies roughly in the same plane as the Earth's orbit around the Sun, but is slightly tilted by about 5 degrees.

Because the Moon is tidally locked to the Earth, the same side of the Moon always faces Earth. However, the amount of the illuminated portion visible from Earth changes as the Moon moves around the Earth.

• Orbital period of the Moon ≈ 29.5 days (synodic month).
• Orbit is elliptical and slightly tilted relative to Earth's orbit.
• Same side of the Moon always faces Earth due to tidal locking.

The phases of the Moon are the different shapes of the illuminated portion of the Moon visible from Earth. These phases occur in a regular cycle as the Moon orbits Earth.

The main phases are: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, and waning crescent.

Each phase corresponds to the relative positions of the Sun, Earth, and Moon, which determine how much of the Moon's sunlit side is visible from Earth.

• New Moon: Moon is between Earth and Sun; illuminated side faces away from Earth.
• First Quarter: Half of the Moon's sunlit side is visible; right half illuminated.
• Full Moon: Earth is between Sun and Moon; entire sunlit side visible.
• Last Quarter: Opposite half illuminated compared to first quarter.
• Waxing phases: illumination increasing; waning phases: illumination decreasing.

The phases result from the changing angle between the Sun, Moon, and Earth as the Moon orbits Earth.

The Sun always illuminates half of the Moon, but the portion visible from Earth changes.

At new moon, the Moon is between Earth and Sun, so the illuminated side faces away from Earth, making the Moon appear dark. At full moon, Earth is between the Sun and Moon, so the entire illuminated side faces Earth, making the Moon appear fully bright.

• Sun illuminates half the Moon at all times.
• Visible illuminated portion depends on Moon's position in orbit.
• Phases cycle repeats every 29.5 days.

Because the Moon takes about 29.5 days to orbit Earth, the phases repeat in this period.

This period is slightly longer than the Moon's orbital period relative to the stars (sidereal month, about 27.3 days) due to Earth's simultaneous orbit around the Sun.

The synodic month (29.5 days) is the time between successive new moons or full moons, explaining the monthly recurrence of the phases.

• Synodic month ≈ 29.5 days: time between identical phases.
• Phases cycle is predictable and periodic.
• Difference between synodic and sidereal month due to Earth's orbit around Sun.

To draw a diagram showing Moon phases: start with Earth at the centre.

Draw the Sun to the right of Earth, indicating the direction of sunlight with arrows pointing from the Sun towards Earth and Moon.

Draw the Moon at several positions around Earth representing key phases: new moon (between Earth and Sun), first quarter (90° from new moon), full moon (opposite side of Earth from Sun), and last quarter (270° from new moon). At each position, shade the Moon's dark side and leave the illuminated side bright, showing how the visible portion changes from Earth's perspective.

• Earth at centre, Sun to the right.
• Arrows show sunlight direction.
• Moon positions marked for new, first quarter, full, last quarter phases.
• Illumination shown by shading half the Moon at each position.

Objects such as planets, moons, and satellites often move in approximately circular orbits around a central body due to gravitational forces. The orbital speed is the speed at which the object travels along its circular path.

Orbital speed is a scalar quantity representing how fast the object moves along the orbit, regardless of direction. It is different from orbital velocity, which is a vector including direction.

The average orbital speed is the total distance travelled in one complete orbit divided by the time taken for one orbit, called the orbital period (T).

• Orbit: The path an object follows around another due to gravity, often circular or elliptical.
• Orbital period (T): The time taken for one complete orbit, measured in seconds (s).
• Orbital radius (r): The radius of the circular orbit, measured in metres (m).

For an object moving in a circular orbit of radius r, the distance travelled in one complete orbit is the circumference of the circle, given by 2πr.

The average orbital speed (v) is therefore the circumference divided by the orbital period (T):

v = distance/time = 2πr / T. This formula gives the average speed over one full orbit.

• v = average orbital speed (m/s)
• r = orbital radius (m)
• T = orbital period (s)
• π ≈ 3.1416 (constant)

Calculate the average orbital speed of the Moon around the Earth, given:

Orbital radius, r = 3.84 × 10⁸ m (average Earth-Moon distance)

Orbital period, T = 27.3 days = 27.3 × 24 × 3600 s = 2.36 × 10⁶ s

• Step 1: Write down the formula: v = 2πr / T
• Step 2: Substitute values: v = 2 × 3.1416 × 3.84 × 10⁸ m / 2.36 × 10⁶ s
• Step 3: Calculate numerator: 2 × 3.1416 × 3.84 × 10⁸ ≈ 2.415 × 10⁹ m
• Step 4: Divide by T: 2.415 × 10⁹ m / 2.36 × 10⁶ s ≈ 1023 m/s
• Answer: The average orbital speed of the Moon is approximately 1.0 × 10³ m/s.

A frequent mistake is mixing units, especially for the orbital period T. Always convert time to seconds before substituting into the formula.

Another error is confusing orbital radius with diameter. The radius is the distance from the centre of the orbit to the orbiting object, not the full diameter.

Remember that the formula assumes a circular orbit; for elliptical orbits, this gives an average speed approximation.

• Convert all units to SI units before calculation.
• Use radius (r), not diameter, in the formula.
• Ensure T is in seconds (s).
• Use π ≈ 3.1416 for calculations.

To draw a diagram illustrating average orbital speed:

Draw a circle representing the orbit with centre labelled O.

Mark the orbiting object at a point on the circumference labelled P, and the radius r as the line OP from the centre to P, labelled with length r (in metres).

• Draw a circle with centre O.
• Draw radius OP from O to circumference point P.
• Label radius as r (m).
• Indicate direction of motion with an arrow along the circumference.
• Label orbital period T (s) as the time for one full revolution.