6.2.3 The Universe
Core Syllabus – Space Physics (Cambridge IGCSE 0625)
1. Earth’s rotation and axial tilt
- Rotates once every 24 h → produces day and night.
- Axis is tilted ≈ 23.5° to the plane of its orbit (the ecliptic).
- Result of the tilt:
- Different hemispheres receive varying amounts of solar energy during a year.
- Explains the seasons – when a hemisphere is tilted toward the Sun it experiences summer, when tilted away it experiences winter.
2. Earth’s orbit around the Sun
- Orbit is nearly circular; mean distance (radius) ≈ 1 AU = 1.5 × 10⁸ km.
- Orbital period ≈ 1 year = 365.25 days.
- Average orbital speed (syllabus formula):
\[
v=\frac{2\pi r}{T}
\]
Worked example:
\[
v=\frac{2\pi(1.5\times10^{8}\,\text{km})}{365.25\times24\times3600\ \text{s}}
\approx 30\ \text{km s}^{-1}
\]
3. Moon’s orbit and phases
- Sidereal period (time to complete one orbit relative to the stars) ≈ 27.3 days.
- Synodic period (time between successive identical phases) ≈ 29.5 days.
- Phases are caused by the changing geometry of Sun–Earth–Moon:
- New Moon – Moon between Sun and Earth (illuminated side faces away).
- First quarter – half‑illuminated, Moon 90° east of the Sun.
- Full Moon – Earth between Sun and Moon (fully illuminated side faces Earth).
- Last quarter – half‑illuminated, Moon 90° west of the Sun.
- Eclipses:
- Solar eclipse** – Moon blocks Sun’s light; occurs at new moon when the three bodies are nearly aligned.
- Lunar eclipse** – Earth’s shadow falls on the Moon; occurs at full moon.
4. Overview of the Solar System (IGCSE focus)
| Object | Mean distance from Sun | Orbital period | Key feature (IGCSE emphasis) |
|---|
| Planets |
|---|
| Mercury | 0.39 AU | 88 days | No atmosphere; extreme temperature swings |
| Venus | 0.72 AU | 225 days | Thick CO₂ atmosphere; runaway greenhouse effect |
| Earth | 1.00 AU | 365 days | Supports life; liquid water cycle |
| Mars | 1.52 AU | 687 days | Thin CO₂ atmosphere; polar ice caps |
| Jupiter | 5.20 AU | 12 yr | Largest planet; many moons |
| Saturn | 9.58 AU | 29 yr | Prominent ring system |
| Uranus | 19.2 AU | 84 yr | Axial tilt ≈ 98° (lies on its side) |
| Neptune | 30.1 AU | 165 yr | Strong winds; blue colour from methane |
| Dwarf planets (e.g., Pluto) |
| Pluto | ≈ 39 AU | ≈ 248 yr | Small, icy body beyond Neptune |
5. Simple quantitative relationships (IGCSE level)
Extension / Enrichment – Cosmology and the Cosmic Microwave Background Radiation (CMBR)
Optional material for motivated learners who wish to explore modern astrophysics beyond the core syllabus.
Why the CMBR Exists
- In the first few hundred thousand years after the Big Bang the Universe was a hot, dense plasma of photons, electrons and protons.
- When the temperature fell to about 3000 K (≈ 380 000 yr after the start), electrons combined with protons to form neutral hydrogen – the epoch called recombination.
- Neutral hydrogen no longer scattered photons, so the radiation decoupled from matter and began to travel freely. Those photons are the Cosmic Microwave Background Radiation.
From Visible/Infra‑red Light to Microwaves
As the Universe expands, space itself stretches, and so do the wavelengths of travelling photons. The cosmological red‑shift is expressed as
\[
\lambda{\text{obs}} = (1+z)\,\lambda{\text{emit}}
\]
At recombination the scale factor was roughly \(\displaystyle a_{\text{emit}} \approx \frac{1}{1100}\) of its present value, giving a red‑shift \(z \approx 1100\).
Consequences:
- Photons that peaked in the visible/near‑infrared (\(\lambda{\text{emit}} \sim 1\,\mu\text{m}\)) are now observed with \(\lambda{\text{obs}} \sim 1\,\text{mm}\).
- A wavelength of 1 mm lies in the microwave region of the electromagnetic spectrum.
Key Properties of the CMBR
- Almost perfectly isotropic – the same intensity in every direction.
- Black‑body spectrum with a temperature of 2.73 K.
- Temperature variations of only \(\sim10^{-5}\) (anisotropies) – these tiny fluctuations are the seeds of later galaxy formation.
Timeline of the Early Universe (illustrative)
| Time after the Big Bang | Temperature (K) | Key event |
|---|
| 10⁻⁴³ s | > 10³² | Planck epoch – quantum gravity dominates |
| 10⁻¹² s | 10¹⁵ | Electroweak symmetry breaking |
| 1 s | 10¹⁰ | Neutrino decoupling; nucleosynthesis begins |
| 3 min | 10⁹ | Formation of light nuclei (H, He, Li) |
| 380 000 yr | ≈ 3000 | Recombination – photons decouple → CMBR released |
| 13.8 Gyr (today) | 2.73 | CMBR observed as microwave radiation |
Suggested Classroom Diagram
Figure: Black‑body spectrum of the CMBR, peaking at a wavelength of ~1 mm (frequency ≈ 160 GHz) corresponding to a temperature of 2.73 K.
Why the CMBR Matters
- Provides strong evidence that the Universe began in a hot, dense state (the Big Bang model).
- Offers a “snapshot” of the Universe 380 000 yr after its birth, before stars and galaxies formed.
- Precise measurements of its temperature, spectrum and anisotropies allow astronomers to determine:
- Geometry (flat, open, or closed) of the Universe.
- Relative amounts of ordinary matter, dark matter and dark energy.
- The current expansion rate (the Hubble constant).
Summary (Enrichment)
Shortly after the Big Bang the Universe cooled enough for electrons and protons to combine, releasing a flood of photons. These photons have travelled unhindered for billions of years. As space itself expanded, their wavelengths were stretched, shifting the original visible/infra‑red radiation into the microwave region we detect today as the Cosmic Microwave Background Radiation. The CMBR is a cornerstone of modern cosmology, confirming the hot‑big‑bang model and providing a wealth of information about the early Universe.