State that: (a) galaxies are each made up of many billions of stars (b) the Sun is a star in the galaxy known as the Milky Way (c) other stars that make up the Milky Way are much further away from the Earth than the Sun is from the Earth (d) astronom

6 Space Physics – Cambridge IGCSE 0625

Learning Objectives

• Core (mandatory)

  • Explain how the Earth’s rotation and axial tilt produce day/night and the seasons.
  • Describe the Earth‑Sun and Moon‑Earth orbital motions and calculate their average orbital speeds.
  • Identify the eight planets, the recognised dwarf planets and the major moons, and give their relative sizes and distances from the Sun.
  • Use astronomical units (AU), light‑years (ly) and parsecs (pc) to compare distances within the Solar System and in the wider Universe.

• Supplement (optional – 6.2 Stars)

  • State that each galaxy contains many billions (up to trillions) of stars.
  • Identify the Sun as a star in the Milky Way galaxy.
  • Explain why other stars in the Milky Way are far farther from Earth than the Sun.
  • Understand the concept of a light‑year and how it is used to measure astronomical distances.

1. The Earth – Rotation, Tilt and Gravity

1.1 Rotation and the Day‑Night Cycle

• The Earth rotates once about its axis every 24 h (≈ 86 400 s).
• Because of this rotation the Sun and the stars appear to move across the sky each day – this apparent motion creates day on the side facing the Sun and night on the opposite side.
• Angular speed

  \[

  \omega=\frac{2\pi}{T}=\frac{2\pi}{86\,400\ \text{s}}\approx7.27\times10^{-5}\ \text{rad s}^{-1}

  \]

1.2 Axial Tilt and the Seasons

• The Earth’s rotation axis is inclined by 23.5° to the plane of its orbit (the ecliptic).
• Because of this tilt, different hemispheres receive more direct sunlight at different times of the year, producing the four seasons.
• When the Northern Hemisphere is tilted toward the Sun it experiences summer, while the Southern Hemisphere experiences winter, and vice‑versa.

1.3 Surface Gravity

Acceleration due to gravity at the Earth’s surface is g = 9.81 m s⁻². This value is used in many exam calculations (e.g., weight, orbital speed).

2. The Solar System – Planets, Dwarf Planets, Moons and Distances

2.1 Order, Relative Sizes and Distances

Major moons (selected)

• Moon (Earth) – 0.27 R⊕, orbital radius ≈ 384 000 km
• Ganymede (Jupiter) – 0.41 R⊕, largest moon in the Solar System
• Titan (Saturn) – 0.40 R⊕, thick nitrogen atmosphere
• Callisto, Io, Europa (Jupiter) and Triton (Neptune) – also frequently examined.

2.2 Orbital Motion and Average Speed

For a roughly circular orbit the average orbital speed is

\[

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

\]

where \(r\) is the orbital radius and \(T\) the orbital period.

• Earth:

  \(r = 1\ \text{AU}=1.5\times10^{11}\ \text{m}\)

  \(T = 365\ \text{d}=3.156\times10^{7}\ \text{s}\)

  \(\displaystyle v_{\oplus}\approx2.98\times10^{4}\ \text{m s}^{-1}\) (≈ 30 km s⁻¹)

• Moon:

  \(r \approx 3.84\times10^{8}\ \text{m}\) (384 000 km)

  \(T = 27.3\ \text{d}=2.36\times10^{6}\ \text{s}\)

  \(\displaystyle v_{\text{Moon}}\approx1.02\times10^{3}\ \text{m s}^{-1}\) (≈ 1.0 km s⁻¹)

2.3 Astronomical Units, Light‑Years and Parsecs

Scale comparison: The most distant planet, Neptune, is only ~30 AU from the Sun – less than 0.0005 ly. Even the nearest star (Alpha Centauri, 4.37 ly) is over 270 000 times farther away than the Sun.

2.4 The Moon – Phases and Eclipses (optional enrichment)

• Orbital period: 27.3 days (sidereal) → 29.5 days between successive new moons (synodic).
• Phases arise from the changing Sun‑Moon‑Earth angle.
• Solar eclipse: Moon between Sun and Earth.
  

  Lunar eclipse: Earth between Sun and Moon.

3. Stars – Galaxies, the Sun and Inter‑stellar Distances

3.1 Galaxies – Collections of Stars

• A galaxy is a gravitationally bound system of stars, gas, dust and dark matter.
• Typical galaxies contain billions to trillions of stars.

  The Milky Way (a barred‑spiral) is estimated to have ≈ \(10^{11}\) (100 billion) stars.

3.2 The Sun – Our Local Star

• Spectral type: G2 V (G‑type main‑sequence).
• Location: Orion‑Cygnus (Orion) “spur” of the Milky Way, about 8 kpc from the Galactic centre.
• Distance to Earth: 1 AU (≈ 150 million km).

3.3 Why Other Stars Appear Farther Away

• The nearest star system after the Sun is Alpha Centauri at 4.37 ly (≈ 276 000 AU).
• Most visible stars lie tens to thousands of light‑years away, making them vastly more distant than the Sun.
• Distances are measured by stellar parallax:

  \[

  d(\text{pc})=\frac{1}{p(\text{arcsec})}

  \]

  where \(p\) is the apparent shift of the star as Earth orbits the Sun.

3.4 The Light‑Year – A Convenient Distance Unit

Light travels at \(c = 3.00\times10^{8}\ \text{m s}^{-1}\). In one Julian year (365.25 days) it covers

\[

1\ \text{ly}=c\times(1\ \text{yr})\approx9.46\times10^{15}\ \text{m}=9.46\times10^{12}\ \text{km}.

\]

3.5 Worked Example – Converting AU to Light‑Years

Find the distance to Sirius, 8.6 ly, expressed in AU.

• 1 ly = 63 240 AU
• \(8.6\ \text{ly}\times63\,240\ \text{AU / ly}=5.44\times10^{5}\ \text{AU}\).

3.6 Quick Practice Questions

1. How many kilometres are in 2 light‑years? (Use \(1\ \text{ly}=9.46\times10^{12}\ \text{km}\).)
2. The nearest star, Proxima Centauri, is 4.24 ly away. Express this distance in AU.
3. If a galaxy contains \(5\times10^{11}\) stars, how many times more stars does it have than the Solar System (which has one star)?

Summary Checklist

1. Earth’s rotation (24 h) produces day/night; axial tilt (23.5°) produces the seasons.
2. Earth orbits the Sun at ≈ 30 km s⁻¹; the Moon orbits Earth at ≈ 1 km s⁻¹.
3. Eight planets, four recognised dwarf planets and the major moons are ordered by distance from the Sun; relative sizes are given in Earth radii.
4. 1 AU = 1.5 × 10⁸ km; 1 ly = 63 240 AU; 1 pc = 3.26 ly – showing that inter‑stellar distances dwarf Solar‑System scales.
5. Galaxies contain billions‑to‑trillions of stars; the Milky Way holds ≈ \(10^{11}\) stars.
6. The Sun is a G‑type main‑sequence star located in the Milky Way, 1 AU from Earth.
7. Other stars are vastly farther away – the nearest, Alpha Centauri, is 4.37 ly (≈ 276 000 AU) distant.
8. A light‑year is the distance light travels in one year (≈ 9.46 × 10¹⁵ m).