Know that planets, minor planets and comets have elliptical orbits, and recall that the Sun is not at the centre of the elliptical orbit, except when the orbit is approximately circular

6.1.2 The Solar System

Learning Objective

Students must be able to:

• State that planets, minor planets and comets move in elliptical orbits with the Sun at one focus.
• Explain why the Sun is not at the geometric centre of an ellipse, except when the orbit is almost circular (very low eccentricity).
• Describe the motions of the Earth–Moon–Sun system that give rise to day‑night cycles, seasons, and lunar phases – all required for Cambridge IGCSE Physics (0625).

1 Geometry of Orbits

1.1 Kepler’s First Law – Elliptical Paths

• Every body that orbits the Sun follows an ellipse with the Sun at one of the two foci.
• Standard equation of an ellipse centred at the origin:

  \$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\$

  where a = semi‑major axis, b = semi‑minor axis.

• Distance from the centre to each focus:

  \$c=\sqrt{a^{2}-b^{2}}\$

  Eccentricity: e = c / a.

• If a = b (i.e. e = 0) the ellipse becomes a circle and the Sun lies at the geometric centre.

1.2 Sun’s Position in an Ellipse

• In a genuine ellipse the Sun occupies one focus, not the centre.
• When the eccentricity is very small (e ≲ 0.02) the Sun is effectively at the centre for most calculations, so a circular‑orbit approximation is acceptable.

1.3 Orbital Speed (circular approximation)

For a (nearly) circular orbit the average orbital speed is

\$v=\frac{2\pi r}{T}\$

• v – orbital speed (m s⁻¹)
• r – radius of the orbit (≈ semi‑major axis for low‑e orbits) (m)
• T – orbital period (s)

Example – Earth: r ≈ 1.496 × 10⁸ km, T = 365.25 d → v ≈ 29.8 km s⁻¹.

1.4 Typical Orbital Eccentricities

1.5 Why the Sun Is Not at the Geometric Centre

• Both the Sun and the orbiting body attract each other; they actually orbit their common centre of mass (barycentre).
• For Sun–planet systems the barycentre lies inside the Sun, but it is offset from the Sun’s geometric centre – this offset is the focus of the ellipse.

2 The Earth–Moon–Sun System

2.1 Earth’s Rotation

• Earth rotates eastwards on its axis once every ≈ 24 h (sidereal day ≈ 23 h 56 min).
• This rotation produces the daily day‑night cycle.
• Axial tilt ≈ 23.5° relative to the ecliptic (the plane of Earth’s orbit).

2.2 Earth’s Orbit & Seasons

• Earth follows an elliptical orbit (e = 0.0167) with a period of 1 year.
• The 23.5° tilt, not the slight change in Sun‑Earth distance, is the primary cause of the seasons.
• Because of the tilt, the Sun’s apparent height above the horizon changes throughout the year, giving summer in the hemisphere tilted toward the Sun and winter in the opposite hemisphere.
• Perihelion (closest approach) occurs around 3 January; aphelion (farthest) around 4 July. The resulting temperature change is small compared with the effect of the tilt.

2.3 Moon’s Orbit & Phases

• Moon orbits Earth in ≈ 27.3 days (sidereal month) on a slightly elliptical path (e ≈ 0.055).
• The synodic month – time between identical phases – is ≈ 29.5 days because Earth moves in its orbit while the Moon orbits.
• Phases arise from the changing Sun‑Moon‑Earth geometry:

  • Full Moon – Earth is between Sun and Moon.
  • New Moon – Moon is between Sun and Earth.

• During each lunar month the Moon rises about 50 minutes later each night.

3 The Solar System at a Glance

3.1 Order of the Eight Planets

• Mercury → Venus → Earth → Mars → Jupiter → Saturn → Uranus → Neptune

3.2 Key Facts (relative to Earth)

3.3 Minor Planets, Dwarf Planets, Asteroids & Comets

• Minor planets – objects that orbit the Sun but have not cleared their neighbourhood (e.g., Ceres, Vesta).
• Dwarf planets – a subset of minor planets that are massive enough to be roughly spherical (e.g., Pluto, Eris, Haumea, Makemake, Ceres).
• Asteroids – small, rocky bodies, mostly confined to the main belt between Mars and Jupiter.
• Comets – icy bodies with highly eccentric orbits; they develop a coma and tail when near perihelion.

4 Implications for Observation

• Orbital distance varies: at perihelion a planet appears slightly larger and brighter.
• Orbital speed is not constant – faster at perihelion, slower at aphelion (Kepler’s Second Law).
• Highly eccentric comets move rapidly across the sky near perihelion and then fade for many months.
• Earth’s axial tilt explains the seasonal change in the Sun’s noon altitude.
• The 24‑hour rotation and the ≈ 50‑minute daily lunar rise delay are readily observable with simple backyard equipment.

5 Summary

All major Solar‑System bodies travel in elliptical orbits with the Sun at one focus. The Sun is effectively at the centre only for orbits of very low eccentricity. Earth’s eastward rotation, 23.5° axial tilt, and slightly elliptical orbit together produce the day‑night cycle, the seasons, and modest variations in solar distance. The Moon’s 27‑day orbit generates the familiar phases and a 50‑minute nightly rise‑time shift. Knowing the order of the eight planets, their key comparative facts, and the categories of minor planets, dwarf planets, asteroids and comets provides the factual framework required for the Cambridge IGCSE Physics (0625) syllabus.