6 – The Universe (IGCSE Physics 0625)
6.1 The Earth
Rotation
- Period: ≈ 24 h (one day).
- Produces the daily cycle of daylight and darkness.
- Linear speed at the equator:
\(v = \dfrac{2\pi r}{T}\) with \(r \approx 6.37\times10^{6}\,\text{m}\), \(T = 86\,400\ \text{s}\)
→ \(v \approx 4.65\times10^{2}\ \text{m s}^{-1}\) (≈ 465 m s⁻¹).
Tilt of the Axis
- Angle of tilt ≈ 23.5° to the orbital (ecliptic) plane.
- Causes the seasons – different hemispheres receive varying amounts of solar energy as Earth orbits the Sun.
Lunar Motion and Phases
- Sidereal period (orbit relative to the stars): ≈ 27 days.
- Synodic period (time between identical phases): ≈ 29.5 days.
- Changing Sun‑Earth‑Moon geometry produces the familiar phases (new, first quarter, full, last quarter).
- Eclipses occur when the three bodies line up:
- Solar eclipse – Moon between Sun and Earth.
- Lunar eclipse – Earth between Sun and Moon.
6.2 The Solar System
Planets – Overview
| Planet |
Mean distance from Sun (AU) |
Orbital period (yr) |
Key feature |
| Mercury | 0.39 | 0.24 | Smallest, no atmosphere |
| Venus | 0.72 | 0.62 | Thick CO₂ atmosphere, hottest planet |
| Earth | 1.00 | 1.00 | Only planet with liquid water |
| Mars | 1.52 | 1.88 | Red surface, thin CO₂ atmosphere |
| Jupiter | 5.20 | 11.86 | Largest planet, strong magnetic field |
| Saturn | 9.58 | 29.46 | Prominent ring system |
| Uranus | 19.2 | 84.01 | Rotates on its side |
| Neptune | 30.1 | 164.8 | Strong winds, deep blue colour |
Dwarf Planets
- Definition: orbit the Sun, are massive enough for self‑gravity to give a roughly spherical shape, but have not cleared their orbital neighbourhood.
- Examples: Pluto, Eris, Haumea, Makemake, Ceres (the latter lies in the asteroid belt).
Moons, Asteroids & Comets
- Moons – natural satellites; Earth has 1, Jupiter > 70.
- Asteroids – rocky bodies, mainly between Mars and Jupiter (the asteroid belt).
- Comets – icy bodies from the Kuiper Belt or Oort Cloud; develop a coma and tail when near the Sun.
Orbital Motion (AO1 & AO2)
The distance travelled in one complete orbit is the circumference of a circle of radius \(r\). The average orbital speed is therefore
\[
v = \frac{2\pi r}{T}
\]
where
r is the orbital radius (≈ average Sun‑planet distance) and
T the orbital period.
Example – Earth
\[
r \approx 1.5\times10^{11}\ \text{m},\qquad
T = 3.16\times10^{7}\ \text{s}
\]
\[
v = \frac{2\pi(1.5\times10^{11})}{3.16\times10^{7}}
\approx 3.0\times10^{4}\ \text{m s}^{-1}
\;(30\ \text{km s}^{-1})
\]
6.3 The Universe (Enrichment)
Qualitative idea of an expanding Universe
- Observations show that distant galaxies are receding from us.
- The farther a galaxy is, the faster it appears to move away – this is the **Hubble‑Law**.
- The law tells us that space itself is expanding.
Hubble Constant – current best estimate
- ≈ 68 km s⁻¹ Mpc⁻¹ (derived from recent observations such as Planck 2018 and supernova surveys).
- In SI units: 2.2 × 10⁻¹⁸ s⁻¹.
- Relation: \(v = H_{0}\,d\) (recession speed = Hubble constant × distance).
Unit conversion (quick reference)
1 km s⁻¹ Mpc⁻¹ = 3.24 × 10⁻²⁰ s⁻¹
\[
68\ \text{km s}^{-1}\text{Mpc}^{-1}
= 68 \times 3.24\times10^{-20}\ \text{s}^{-1}
\approx 2.2\times10^{-18}\ \text{s}^{-1}
\]
Worked example
If a galaxy is observed to recede at 10 200 km s⁻¹, its distance is
\[
d = \frac{v}{H_{0}}
= \frac{10\,200\ \text{km s}^{-1}}{68\ \text{km s}^{-1}\text{Mpc}^{-1}}
\approx 150\ \text{Mpc}
\]
Why it matters (AO3)
- Allows astronomers to estimate the size of the observable Universe.
- Provides a simple way to obtain an order‑of‑magnitude age of the Universe:
\[
\text{Age} \approx \frac{1}{H_{0}}
\approx \frac{1}{2.2\times10^{-18}\ \text{s}^{-1}}
\approx 4.5\times10^{17}\ \text{s}
\approx 14\ \text{billion years}.
\]
Key Points to Remember
- Earth rotates once every 24 h; its axis is tilted by 23.5°, giving day/night cycles and seasons.
- The Moon orbits Earth in about 27 days, producing phases (synodic period ≈ 29.5 days) and eclipses.
- The Solar System contains eight planets (ordered by distance), several dwarf planets, many moons, and smaller bodies such as asteroids and comets.
- Average orbital speed can be estimated with \(v = 2\pi r / T\).
- The Universe is expanding; distant galaxies recede faster, described by the Hubble constant
\(H_{0} \approx 68\ \text{km s}^{-1}\text{Mpc}^{-1}\) (≈ 2.2 × 10⁻¹⁸ s⁻¹).
- From \(H_{0}\) we obtain a rough age of the Universe of ≈ 14 billion years.
Suggested Diagrams
- Earth diagram showing rotation, axis tilt, and the resulting illumination pattern (day/night & seasons).
- Moon’s orbit with labelled phases and eclipse geometry.
- Scale diagram of the Solar System (relative distances and sizes of the eight planets, plus dwarf planets).
- Hubble‑Law plot: recession velocity (y‑axis) versus distance (x‑axis) for a few galaxies, illustrating the straight‑line slope equal to \(H_{0}\).