Know that the current estimate for H_0 is 2.2 × 10^-18 per second

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

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 \(H_{0}\).