Ancient cosmologies
Cosmology means ideas about the whole sky and universe. Every old culture watched the Sun, Moon and stars and made calendars from them.
Earth-centred models
The Greek thinker Ptolemy (about 150 CE) put Earth still in the middle. Planets moved in small circles on bigger circles. It matched the sky well enough for 1,400 years.
Other old ideas
- The Indian astronomer Aryabhata (about 499 CE) said Earth spins once a day, so stars only seem to move.
- Chinese astronomers such as Zhang Heng (about 120 CE) built a sky globe that showed the stars and kept careful records of eclipses and comets.
- In 1543 Copernicus put the Sun in the middle. Kepler later showed planets move in ovals (ellipses).
Why a loop? Mars seems to go backward for a few weeks. If Earth overtakes Mars while both circle the Sun, that is just a view effect. The old models needed extra circles to explain it.
Galileo's method
Around 1609 Galileo of Italy built a telescope and turned it to the sky. He saw things nobody had seen.
- Jupiter has four moons that circle it. So some bodies clearly go round something other than Earth.
- Venus shows phases like our Moon, which fits Venus going round the Sun.
- The Moon has mountains and craters, so it is a rocky world, not a perfect smooth ball.
The ramp experiment
Falling is too fast to time. Galileo slowed it down with a ramp. He found that the distance grows with the square of time: s ∝ t². In equal gaps of time the distances are in the ratio 1 : 3 : 5 : 7.
The method
- Observe carefully.
- Guess an idea.
- Test it with an experiment and numbers.
- Keep the idea only if the numbers agree.
Using maths to describe nature is why Galileo is called the father of modern physics.
Relativity and quanta
By 1900, two surprises shook physics.
Relativity (Einstein, 1905)
- Light always travels at the same speed, c = 3 × 10⁸ m/s, for every observer.
- So a fast-moving clock ticks slower: t = γ t₀ where γ = 1 / √(1 − v²/c²). This is time dilation.
- Mass and energy are linked: E = mc². A tiny mass holds a huge energy. This explains the Sun and nuclear power.
- Later (1915) Einstein showed gravity is bent space and time. GPS must correct for this.
At everyday speeds γ is almost exactly 1, so we never notice it.
Quanta (Planck, 1900)
- Light and other radiation come in small packets of energy called quanta (photons).
- E = hf, with h = 6.63 × 10⁻³⁴ J s. Higher frequency means more energy per packet.
- This explains why a metal gives out electrons only for light of enough frequency (the photoelectric effect), and why atoms have fixed energy levels.
Physicists from around the world
Physics is a team effort across countries and centuries.
- Zhang Heng (China, 2nd century): sky globe and an early earthquake detector.
- Aryabhata (India, 5th century): spinning Earth, and the cause of eclipses.
- C. V. Raman (India): scattering of light, Nobel Prize 1930. S. N. Bose (India): counting of photons, which led to "bosons".
- Chien-Shiung Wu (China/USA): in 1956 her experiment showed that nature can tell left from right in weak decay. Chen-Ning Yang and Tsung-Dao Lee won the 1957 Nobel Prize for the idea.
- Qian Sanqiang and others built China's nuclear science. Pan Jianwei led the 2016 Micius satellite, which sent quantum-secure light signals from space.
Notice the pattern: each person tested and checked, just like Galileo.
Key formulas and definitions
- Time dilation: t = γ t₀, γ = 1 / √(1 − v²/c²)
- Mass–energy: E = mc²
- Photon energy: E = hf (h = 6.63 × 10⁻³⁴ J s)
- Ramp from rest: s = ½ a t², distances in equal times 1 : 3 : 5 : 7
- Light speed: c = 3 × 10⁸ m/s
Worked examples
1. A ball on a ramp rolls 2 cm in the first second. How far in 3 s?
Distance ∝ t². So s = 2 × 3² = 18 cm. (Check: gaps 2, 6, 10 add to 18.)
2. Light from the Sun takes how long to reach Earth? (distance 1.5 × 10¹¹ m)
t = d / c = 1.5 × 10¹¹ / 3 × 10⁸ = 500 s, about 8 min 20 s.
3. A rocket clock runs at 0.6c. Find γ.
γ = 1 / √(1 − 0.36) = 1 / 0.8 = 1.25.
4. The rocket clock shows 4 s pass. How long passes on Earth?
t = γ t₀ = 1.25 × 4 = 5 s.
5. Green light has f = 5 × 10¹⁴ Hz. Find the energy of one photon.
E = hf = 6.63 × 10⁻³⁴ × 5 × 10¹⁴ = 3.3 × 10⁻¹⁹ J.
6. How much energy is stored in 1 g (0.001 kg) of mass?
E = mc² = 0.001 × (3 × 10⁸)² = 9 × 10¹³ J.
Common mistakes
- Thinking the old Earth-centred people were foolish. Their models matched what they could see; better tools changed the answer.
- Thinking Galileo invented the telescope. He improved it and was among the first to use it for astronomy.
- Thinking relativity means "everything is relative". Light speed is the same for all; only time and length change.
- Thinking a quantum is a tiny particle of matter. It is a packet of energy.