Explain that the CMBR was produced shortly after the Universe was formed and that this radiation has been expanded into the microwave region of the electromagnetic spectrum as the Universe expanded

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)

ObjectMean distance from SunOrbital periodKey feature (IGCSE emphasis)
Planets
Mercury0.39 AU88 daysNo atmosphere; extreme temperature swings
Venus0.72 AU225 daysThick CO₂ atmosphere; runaway greenhouse effect
Earth1.00 AU365 daysSupports life; liquid water cycle
Mars1.52 AU687 daysThin CO₂ atmosphere; polar ice caps
Jupiter5.20 AU12 yrLargest planet; many moons
Saturn9.58 AU29 yrProminent ring system
Uranus19.2 AU84 yrAxial tilt ≈ 98° (lies on its side)
Neptune30.1 AU165 yrStrong winds; blue colour from methane
Dwarf planets (e.g., Pluto)
Pluto≈ 39 AU≈ 248 yrSmall, icy body beyond Neptune

5. Simple quantitative relationships (IGCSE level)

  • Orbital speed – \(v = \dfrac{2\pi r}{T}\)
  • Linear speed at the equator – \(v = \dfrac{2\pi R}{T_{\text{day}}}\)

    (where \(R\) = Earth’s radius ≈ 6.37 × 10³ km).

  • Kepler’s 3rd law (simplified for circular orbits) – \(\displaystyle \frac{T^{2}}{r^{3}} = \text{constant}\)

    Useful for comparing orbital periods of different planets.


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 BangTemperature (K)Key event
10⁻⁴³ s> 10³²Planck epoch – quantum gravity dominates
10⁻¹² s10¹⁵Electroweak symmetry breaking
1 s10¹⁰Neutrino decoupling; nucleosynthesis begins
3 min10⁹Formation of light nuclei (H, He, Li)
380 000 yr≈ 3000Recombination – photons decouple → CMBR released
13.8 Gyr (today)2.73CMBR 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

  1. Provides strong evidence that the Universe began in a hot, dense state (the Big Bang model).
  2. Offers a “snapshot” of the Universe 380 000 yr after its birth, before stars and galaxies formed.
  3. 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.