Know that the Earth orbits the Sun once in approximately 365 days and use this to explain the periodic nature of the seasons

6.1.1 The Earth

Learning Objective

Know that the Earth orbits the Sun once in approximately 365 days and rotates on its axis once in approximately 24 h. Use these motions together with the axial tilt (23.5°) to explain the periodic nature of the seasons, the day‑night cycle and the lunar phases.

Key Terminology (first appearance in bold)

Orbit

The curved path followed by a body (e.g., the Earth) around another body (the Sun) because of gravity.

Revolution

One complete orbit; for the Earth this takes ≈ 365.25 days.

Rotation

The spin of a body about its own axis; the Earth rotates once in approximately 24 h (sidereal day ≈ 23 h 56 min, solar day ≈ 24 h).

Axis

An imaginary line through the centre of a rotating body. The Earth’s axis is tilted 23.5° to the line ⊥ to the ecliptic (the plane of Earth’s orbit).

Ecliptic

The plane of the Earth’s orbit around the Sun.

Solstice

Points in the year when the Sun’s apparent declination reaches its extreme north (+23.5°) or south (‑23.5°) values – the longest and shortest days.

Equinox

Points in the year when the Sun’s apparent declination is 0°, giving (approximately) equal day and night lengths.

Lunar phase

The visible portion of the Moon illuminated by the Sun as seen from Earth.

1. Earth’s Orbital Motion

• The Earth follows an almost circular elliptical orbit (eccentricity ≈ 0.0167) around the Sun.
• Orbital period (revolution): ≈ 365.25 days (one year).
• Mean orbital radius = 1 AU = 1.496 × 10¹¹ m.
• Average orbital speed ≈ 29.8 km s⁻¹.

2. Earth’s Rotation and the Day‑Night Cycle

• The Earth rotates eastward about its axis once in approximately 24 h.
• Because Earth rotates eastward, the Sun appears to rise in the east and set in the west, producing the regular alternation of daylight and darkness – the day‑night cycle.

3. Axial Tilt and the Seasons

• The Earth’s axis is inclined 23.5° to the line ⊥ to the ecliptic.
• During a year, each hemisphere is alternately tilted toward or away from the Sun.
• When the Sun’s rays strike a region at a high angle (more direct), the same solar energy is concentrated on a smaller surface area → higher temperature (summer).
• When the Sun’s rays are oblique, the energy is spread over a larger area → lower temperature (winter).

Four Key Positions in the Year

Mathematical description of solar declination

The solar declination δ (the latitude where the Sun is directly overhead at noon) varies with the day number n (where n = 0 at the March equinox) as

\[

\delta \approx 23.5^{\circ}\,\sin\!\left(\frac{2\pi}{365}\,n\right)

\]

This sinusoidal variation gives the regular, repeating pattern of the seasons.

4. The Moon’s Orbit and Phases (Core requirement)

• The Moon orbits the Earth in an almost circular path with a mean distance of 3.84 × 10⁸ m.
• Orbital period (sidereal month): ≈ 27.3 days; synodic month (full cycle of phases): ≈ 29.5 days.
• Lunar phases arise from the changing angle between the Sun, Moon and Earth – the illuminated portion we see varies as the Moon moves around the Earth.
• Key phases: New Moon, First Quarter, Full Moon, Last Quarter.

5. Classroom Activities

• Sun‑shadow experiment: Over a week, record the length of a vertical stick’s shadow at solar noon each day. Plot shadow length versus date – the resulting sinusoidal curve demonstrates the effect of axial tilt.
• Model Earth‑Sun system: Use a lamp (Sun) and a tilted globe (Earth). Rotate the globe once per day and move it around the lamp on a circular track to simulate a year. Observe how the illuminated area changes at the four key positions.
• Lunar‑phase diary: Sketch the Moon each clear night for one month and label the phase. Compare the observations with the predicted 29.5‑day synodic period.

Summary

• The Earth completes one revolution around the Sun in about 365 days and one rotation about its axis in approximately 24 h.
• The 23.5° axial tilt to the line ⊥ to the ecliptic causes the Sun’s rays to strike different latitudes at varying angles during the year, producing the regular cycle of seasons (solstices and equinoxes).
• Rotation produces the daily alternation of daylight and darkness, with the Sun appearing to move east‑to‑west across the sky.
• The Moon’s ≈ 29.5‑day orbit generates the familiar sequence of lunar phases.