Know that one light-year is equal to 9.5 × 10^15 m

Topic 6 – Space Physics (Cambridge IGCSE Physics 0625)

Learning Outcomes (AO1–AO3)

• AO1 – Knowledge: Recall key facts about the Earth, the Solar System, stars and the Universe.
• AO2 – Application: Perform conversions, interpret data and solve quantitative problems involving astronomical distances and energies.
• AO3 – Analysis: Explain how astronomical distances are measured (parallax, standard candles, red‑shift) and evaluate the strengths and limitations of each method.

6.1 The Earth and the Solar System

6.1.1 The Earth

• Rotation – 1 sidereal day = 23 h 56 min. Causes the daily cycle of light and darkness.
• Axial tilt – 23.5° to the orbital plane. Result: different hemispheres receive varying solar angles during the year → the seasons.
• Orbit – Nearly circular, mean radius = 1 AU = 1.496 × 10¹¹ m. Orbital period = 1 yr = 3.15576 × 10⁷ s.
• Moon – Orbital period = 27.3 days. Phases arise from the changing Sun–Earth–Moon geometry.

Suggested diagram: A simple Earth‑Sun schematic showing the rotation axis tilted 23.5° and the direction of sunlight at different points in the orbit to illustrate the cause of seasons.

6.1.2 The Solar System

Minor bodies

• Dwarf planets: Pluto, Eris, Haumea, Makemake, Ceres.
• Asteroids: Rocky remnants mainly in the asteroid belt (≈ 2–3 AU).
• Comets: Icy nuclei from the Kuiper Belt or Oort Cloud; develop comae and tails when near the Sun.

6.2 Stars

6.2.1 Properties of Stars

• Colour–temperature relationship – Blue ≈ 30 000 K (hot) → Red ≈ 3 000 K (cool).
• Spectral classification (O → M) – O, B, A, F, G, K, M (decreasing temperature).
• Luminosity – Power output. For a spherical star

  \$L = 4\pi R^{2}\sigma T^{4}\$

  where R = radius, T = surface temperature, σ = 5.67 × 10^‑8 W m^‑2 K^‑4.

• Hertzsprung–Russell (H‑R) diagram – Plots luminosity (or absolute magnitude) against surface temperature (or colour). Main‑sequence stars fuse hydrogen in their cores.

Suggested diagram: Sketch of an H‑R diagram showing the main sequence, red‑giant branch, and white‑dwarf region.

6.2.2 Distances in Space

Key distance units

• Astronomical Unit (AU) – Mean Earth–Sun distance

  \$1\ \text{AU}=1.496\times10^{11}\ \text{m}\$

• Light‑year (ly) – Distance light travels in one Julian year.

  • Speed of light: \$c = 3.00\times10^{8}\ \text{m s}^{‑1}\$
  • 1 yr = \$3.15576\times10^{7}\ \text{s}\$
  • \$1\ \text{ly}=c\times1\ \text{yr}= (3.00\times10^{8})(3.15576\times10^{7})\approx9.5\times10^{15}\ \text{m}\$

• Parsec (pc) – Distance at which 1 AU subtends an angle of 1 arcsecond.

  \$1\ \text{pc}= \frac{1\ \text{AU}}{\tan 1''}\approx3.26\ \text{ly}=3.09\times10^{16}\ \text{m}\$

Conversion table

Measuring stellar distances (AO3)

1. Parallax method – Direct geometric technique.

   • Observe the apparent shift of a nearby star against distant background stars as Earth moves from one side of its orbit to the opposite side (baseline = 2 AU).
   • Parallax angle \$p\$ is measured in arcseconds.
   • Distance (in parsecs) is \$d_{\text{pc}}=\frac{1}{p\ (\text{arcsec})}\$
   • Strength: model‑independent, works up to ≈ 300 pc with ground‑based telescopes.
   • Limitation: requires extremely precise angular measurements; becomes impractical for very distant stars.

2. Standard candles – Objects with known intrinsic brightness.

   • Examples: Cepheid variables (period–luminosity relation), Type Ia supernovae (uniform peak luminosity).
   • Use the distance‑modulus formula

     \$m - M = 5\log_{10}\!\left(\frac{d}{10\ \text{pc}}\right)\$

     where \$m\$ = apparent magnitude, \$M\$ = absolute magnitude, \$d\$ = distance in parsecs.

   • Strength: extends distance scale to millions of parsecs.
   • Limitation: relies on the assumption that the candle’s intrinsic luminosity is truly standard; interstellar extinction can affect \$m\$.

3. Other methods (brief)

   • Spectroscopic parallax – Uses the star’s spectral type to infer absolute magnitude.
   • Red‑shift (Hubble’s law) – For galaxies: \$v = H_{0}d\$.
   • Tully‑Fisher relation – Links spiral‑galaxy rotation speed to luminosity.

Worked example – Parallax

Question: A star shows a parallax of \$0.25''\$. Find its distance in (a) parsecs, (b) light‑years, and (c) metres.

Solution:

1. \$d_{\text{pc}} = \dfrac{1}{p}= \dfrac{1}{0.25}=4.0\ \text{pc}\$
2. \$d_{\text{ly}} = 4.0\ \text{pc}\times3.26\ \dfrac{\text{ly}}{\text{pc}} = 13.0\ \text{ly}\$
3. \$d_{\text{m}} = 4.0\ \text{pc}\times3.09\times10^{16}\ \dfrac{\text{m}}{\text{pc}} = 1.24\times10^{17}\ \text{m}\$

Typical astronomical distances

6.2.3 Energy Generation in Stars

• Nuclear fusion – In main‑sequence stars, hydrogen nuclei fuse to form helium, releasing energy via \$E=\Delta m\,c^{2}\$.
• Energy released per kilogram of hydrogen

  \$\$\Delta m \approx 0.007\ \text{kg per kg H} \;\Rightarrow\; E \approx 0.007c^{2}

  \approx 6.3\times10^{14}\ \text{J kg}^{‑1}\$\$

• Sun’s luminosity – \$L_{\odot}=3.85\times10^{26}\ \text{W}\$ (J s⁻¹).

  Mass converted each second:

  \$\dot m = \frac{L_{\odot}}{c^{2}} \approx 4.3\times10^{9}\ \text{kg s}^{‑1}\$

• Life‑cycle overview (AO1)

  1. Protostar → Main‑sequence (H‑fusion).
  2. Red giant (He‑fusion; for massive stars, CNO cycle and later heavier‑element fusion).
  3. End‑states: white dwarf (≤ 8 M☉), neutron star or black hole (> 8 M☉) after a supernova.

Worked example – Solar mass loss

Question: Using \$E=mc^{2}\$, calculate the mass loss of the Sun per second that accounts for its luminosity \$3.85\times10^{26}\ \text{W}\$.

Solution:

\$\$m = \frac{E}{c^{2}} = \frac{3.85\times10^{26}\ \text{J s}^{‑1}}{(3.00\times10^{8}\ \text{m s}^{‑1})^{2}}

\approx 4.3\times10^{9}\ \text{kg s}^{‑1}\$\$

6.3 The Expanding Universe (optional – if covered in the syllabus)

• Hubble’s law – \$v = H{0}d\$, with \$H{0}\approx70\ \text{km s}^{‑1}\text{Mpc}^{‑1}\$.
• Red‑shift (\$z\$) – \$1+z = \lambda{\text{obs}}/\lambda{\text{emit}}\$; indicates recession velocity.
• Evidence for the Big Bang – Cosmic microwave background, primordial element abundances, universal expansion.

Key Points to Remember

• A light‑year is a unit of distance: 1 ly = 9.5 × 10¹⁵ m.
• 1 pc = 3.26 ly = 3.09 × 10¹⁶ m; 1 AU = 1.496 × 10¹¹ m.
• Parallax gives the most direct distance measurement up to a few hundred parsecs; its accuracy is limited by angular resolution.
• Standard candles extend the distance scale to millions of parsecs but rely on assumptions about intrinsic brightness.
• Stars shine because of nuclear fusion; the Sun loses about 4 × 10⁹ kg of mass each second.
• When converting units, keep track of powers of ten and always express the final answer in scientific notation.
• For AO2 questions: write the relevant formula, substitute with correct units, show each algebraic step, and state the final answer with the appropriate number of significant figures.