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.

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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

Planet	Mean distance from Sun (AU)	Mean diameter (km)	Key feature
Mercury	0.39	4 880	No atmosphere
Venus	0.72	12 104	Thick CO₂ atmosphere, greenhouse effect
Earth	1.00	12 742	Life‑supporting, liquid water
Mars	1.52	6 779	Thin CO₂ atmosphere, polar ice caps
Jupiter	5.20	139 822	Gas giant, strongest magnetic field
Saturn	9.58	116 464	Prominent ring system
Uranus	19.2	50 724	Axial tilt ≈ 98°, “sideways” rotation
Neptune	30.1	49 244	Fastest winds in 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.

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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

From → To	Conversion factor
1 ly → m	9.5 × 1015 m
1 m → ly	1.05 × 10‑16 ly
1 pc → ly	3.26 ly
1 pc → m	3.09 × 1016 m
1 AU → m	1.496 × 1011 m

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

Object	Distance (ly)	Distance (×1015 m)
Sun–Mercury	6 × 10⁻⁶	5.8
Sun–Pluto	6 × 10⁻⁴	5.8 × 10²
Sun–Proxima Centauri	4.2	4.0 × 10¹⁶
Milky Way diameter	1.0 × 10⁵	9.5 × 10²⁰
Andromeda Galaxy	2.5 × 10⁶	2.4 × 10²²
Observable Universe	≈ 1.4 × 10¹⁰	≈ 1.3 × 10²⁶

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:

$$m = \frac{E}{c^{2}} = \frac{3.85\times10^{26}\ \text{J s}^{‑1}}{(3.00\times10^{8}\ \text{m s}^{‑1})^{2}} \approx 4.3\times10^{9}\ \text{kg s}^{‑1}$$

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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.

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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.