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Light-years, orbits, the life cycle of stars, galaxies and dark matter, black holes, red-shift, Hubble's law and the evidence for the Big Bang. Each section follows one lesson: what you need to know, key terms, the equations with units, a worked example, common mistakes and an exam tip.
1 Gravity Across the Universe
What you need to know
Light-Years
- A light-year is a unit of distance, not of time: the distance light travels through space in one year, about 9.5 × 1015 m.
- Light travels at 3.0 × 108 m/s, so distance = speed of light × time. Light-years suit stars and galaxies; metres give unwieldy numbers.
- Light takes time to arrive, so you see distant objects as they were when the light left them: looking further away is looking further back in time.
Orbit Speed
- Gravity holds every orbit: a planet round a star, a moon round a planet, a star round the centre of a galaxy.
- The orbital speed is the distance once round, 2πr, divided by the orbital period T: v = 2πr ÷ T, with T in seconds.
- Planets round other stars are found from the regular dips in the star's brightness as the planet crosses in front of it; the time between dips is the period.
Gravity's Reach
- Gravitational field strength g is the force on each kilogram, in N/kg. Weight anywhere is W = mg, using the g at that place.
- A star's or planet's field strength falls as you move further from its centre: twice as far, a quarter of the g. It never reaches zero, so its pull reaches out until a stronger one takes over.
Key terms
- Light-year
- the distance light travels through space in one year, about 9.5 × 1015 m
- Orbital period
- the time for one complete orbit, in s
- Orbital speed
- the speed of an object in orbit, 2πr ÷ T for a circular orbit
- Gravitational field strength
- the gravitational force on each kilogram of mass, in N/kg
Equations
| Equation | What it says, symbols and units |
|---|---|
1 light-year = the distance light travels through space in one year | A unit of distance, not of time, used for the distances between stars and galaxies. |
1 light-year ≈ 9.5 × 1015 m | The distance light travels through space in one year. |
d = ct | Distance travelled by light in a time t.
|
v = 2πrT | Average orbital speed is the distance round the orbit divided by the time for one orbit.
|
W = mg | Weight is the gravitational force on a mass; on Earth g is about 9.8 N/kg.
|
g = GMr2 | Field strength at distance r from the centre of a mass M: twice as far, a quarter of the g.
AP Physics 1 uses this equation. IGCSE and GCSE need only that g falls with distance. |
Worked example
The Earth orbits the Sun at a radius of 1.5 × 1011 m once every 365 days. (a) How long does sunlight take to reach the Earth? (b) Find the Earth's orbital speed.
- (a) t = d ÷ c = 1.5 × 1011 ÷ 3.0 × 108 = 500 s, which is 500 ÷ 60 = 8.3 minutes.
- (b) Period in seconds: T = 365 × 86 400 = 3.15 × 107 s.
- v = 2πr ÷ T = 2π × 1.5 × 1011 ÷ 3.15 × 107 = 3.0 × 104 m/s, about 30 km/s.
Answer: (a) 500 s, about 8.3 minutes (b) 3.0 × 104 m/s
Common mistakes
- Calling a light-year a unit of time. It is a distance.
- Leaving the period in days or years in v = 2πr ÷ T when the speed is wanted in m/s.
- Using the diameter, or the distance from the surface, instead of the radius measured from the centre.
Exam tip
Before any orbit calculation, convert the period to seconds and write it down. Most lost marks in orbital-speed questions come from a period left in days.
AP Physics and NGSS: AP Physics 1 finds orbital speed from gravity itself, v = √(GM ÷ r), and uses g = GM ÷ r². NGSS HS-ESS1-4 asks for orbits to be modelled mathematically in the same way.
2 How We Read the Sky
What you need to know
The Doppler Effect
- The Doppler effect: when a wave source moves relative to an observer, the observed frequency and wavelength change.
- Source moving towards you: the crests bunch up, so a shorter wavelength and a higher frequency. Moving away: longer wavelength, lower frequency. The wave speed does not change; only the spacing does.
- Light does the same: light from a source moving away is shifted to longer wavelengths, towards the red end. This is red-shift. A source coming towards us is blue-shifted.
Eyes Above the Air
- The atmosphere absorbs X-rays, gamma rays, most ultraviolet and much infrared, so telescopes for those bands must be above it, in orbit.
- Visible light reaches the ground, but moving air blurs it; a telescope in orbit gives much sharper pictures. Radio waves pass through the air and cloud, so radio dishes stay on the ground.
- A high, dry mountain top helps infrared telescopes, because most of the water vapour that absorbs infrared lies below it.
- Astronomy grew from the naked eye to telescopes (Galileo, 1609), then photography, then telescopes for every band of the electromagnetic spectrum.
Key terms
- Doppler effect
- the change in observed frequency and wavelength when a source and observer move relative to each other
- Red-shift
- the increase in the wavelength of light from a source moving away
- Blue-shift
- the decrease in the wavelength of light from a source moving towards us
- Atmospheric absorption
- the air stopping some bands of radiation before they reach the ground
Equations
| Equation | What it says, symbols and units |
|---|---|
v = fλ | Wave speed is frequency times wavelength, for every kind of wave.
The wave speed stays the same whatever the source does; the Doppler effect changes f and λ together. |
Diagram to know
A moving source with circular wavefronts drawn closer together ahead of it and further apart behind it. Label the shorter wavelength (higher frequency) ahead and the longer wavelength (lower frequency) behind.
Worked example
A train's horn sounds at 500 Hz. Sound travels at 340 m/s. The train comes towards Jo at 40 m/s. What frequency does Jo hear?
- At rest, the gap between crests is λ = v ÷ f = 340 ÷ 500 = 0.68 m.
- Between two crests (1/500 s) the train moves 40 ÷ 500 = 0.08 m, so ahead of it the crests are 0.68 − 0.08 = 0.60 m apart.
- Jo hears f = v ÷ λ = 340 ÷ 0.60 = 567 Hz: a higher note, as an approaching source should give.
Answer: 567 Hz
Common mistakes
- Saying the sound or light travels faster ahead of a moving source. Only the spacing of the crests changes.
- Confusing the Doppler effect with loudness. Loudness depends on the amplitude, not on the spacing of the waves.
- Saying telescopes go into space to be closer to the stars. The reason is to get above the air, which absorbs and blurs.
Exam tip
For the Doppler effect, examiners want three linked points: the source moves, so the wavelength in front gets shorter (or behind gets longer), so the frequency observed is higher (or lower). Say what happens to the wavelength before the frequency.
AP Physics and NGSS: This lesson is mapped to GCSE (Edexcel and OCR physics); AP Physics 1 and NGSS do not list it. The calculation in the example shows why the pitch changes; exams usually ask you to describe it.
3 The Lives of Stars
What you need to know
Starlight barcodes
- Each element absorbs and gives out its own set of wavelengths, like a barcode. The dark lines in a star's spectrum are made where cooler outer gas absorbs those wavelengths, so they show which elements are there.
- The Sun is a medium-sized star made mostly of hydrogen (about 73% of its mass) and helium (about 25%). Helium was found in the Sun's spectrum in 1868, before it was found on Earth.
- The Sun gives out most of its energy as infrared, visible light and ultraviolet.
Fusion and balance
- In a star's core, hydrogen nuclei fuse into helium and release energy: nuclear fusion. It needs a core temperature of at least about 10 million °C; the Sun's core is about 15 million °C.
- A star is stable when the inward pull of gravity is balanced by the outward force from the hot gas in its core. Less fusion and it shrinks; more and it swells.
- The Sun fuses about 6.2 × 1011 kg of hydrogen every second and has been stable for about 4.6 billion years.
Star colours
- A star gives out a spread of wavelengths with a peak. The hotter the star, the shorter its peak wavelength.
- So a star's colour gives its surface temperature: red stars are the coolest, blue-white stars the hottest. Cool stars give out mostly infrared; very hot stars mostly ultraviolet.
Star lifetimes
- More massive stars are hotter and bluer and use up their fuel far faster, so they have much shorter lives: about 10 billion years for the Sun, about 30 million for a star of 10 Suns.
- The stars in a cluster are born together, so the heaviest stars still shining give the cluster's age. A cluster with hot blue stars left is young.
Key terms
- Spectrum
- the spread of wavelengths in light; a star's has dark absorption lines
- Nuclear fusion
- light nuclei joining to make a heavier nucleus, releasing energy
- Stable star
- a star whose inward gravity is balanced by the outward force from its hot core
- Peak wavelength
- the wavelength at which a star gives out the most radiation
Equations
| Equation | What it says, symbols and units |
|---|---|
t = mrate | How long a store of fuel lasts when it is used at a steady rate.
|
λmaxT = 2.9 × 10−3 m K | Wien's law: the peak wavelength is inversely proportional to the surface temperature.
Beyond IGCSE and GCSE (AP Physics 2). IGCSE and GCSE need only: hotter means a shorter peak wavelength. |
Worked example
The Sun fuses 6.2 × 1011 kg of hydrogen every second. Only its core, about 2.0 × 1029 kg, is hot enough to fuse. (a) How much hydrogen does it fuse in one year (3.15 × 107 s)? (b) Roughly how many years can it shine?
- (a) Mass = rate × time = 6.2 × 1011 × 3.15 × 107 = 1.95 × 1019 kg each year.
- (b) Time = mass of fuel ÷ mass used per year = 2.0 × 1029 ÷ 1.95 × 1019 = 1.0 × 1010 years: about ten billion years.
- Check: the Sun is 4.6 billion years old, so it is about halfway through its life.
Answer: (a) 1.95 × 1019 kg (b) about 1.0 × 1010 years
Common mistakes
- Saying the Sun burns hydrogen like a fire. It is nuclear fusion, not chemical burning.
- Saying red stars are the hottest because red looks hot. Blue-white stars are the hottest.
- Saying a bigger star lives longer because it has more fuel. It uses its fuel so much faster that its life is shorter.
Exam tip
For "why is a star stable?", name both forces and their directions: gravity pulling inwards, and the outward force (pressure) from the hot gas, kept hot by fusion in the core. One force alone gets one mark at most.
AP Physics and NGSS: NGSS HS-ESS1-1 asks you to model how the Sun's fusion releases energy that reaches Earth as radiation. Spectra, star colour and Wien's law are AP Physics 2 content, not AP Physics 1.
4 Dark Matter
What you need to know
The Milky Way
- The Milky Way is our galaxy: a flat disc of 100 to 400 billion stars, about 100 000 light-years across. The Sun lies in the disc, about 26 000 light-years from the centre.
- The Milky Way is one of billions of galaxies in the Universe.
Rotation curves
- A rotation curve plots the orbital speed of stars and gas against distance from a galaxy's centre.
- The visible mass predicts that the outer stars orbit more slowly, like the outer planets. Measured speeds stay about the same far out: a flat rotation curve.
- The extra gravity must come from dark matter (AQA calls it dark mass): matter that gives out no light. At the same distance, a faster orbit needs more mass inside it.
Galaxy clusters
- In galaxy clusters the galaxies move too fast for the stars and hot gas alone to hold them together, so most of a cluster's mass must be dark.
- About 85% of all the matter in the Universe is dark matter. Nobody yet knows what it is made of.
Key terms
- Galaxy
- a huge collection of stars, gas and dust held together by gravity
- Milky Way
- the galaxy that contains the Sun
- Rotation curve
- a graph of orbital speed against distance from a galaxy's centre
- Dark matter
- matter that gives out no light but has a gravitational effect (dark mass in AQA)
Equations
| Equation | What it says, symbols and units |
|---|---|
1 light-year ≈ 9.5 × 1015 m | The distance light travels through space in one year. |
M = v2rG | The mass inside an orbit of radius r needed for an orbital speed v: twice the speed, four times the mass.
Beyond IGCSE and GCSE; it comes from v = √(GM ÷ r) in AP Physics 1. |
Diagram to know
A rotation curve: orbital speed on the vertical axis, distance from the galaxy's centre on the horizontal. Draw the measured line rising and then staying flat, and a dashed line for the visible mass alone that falls away at large distances.
Worked example
(a) The Large Magellanic Cloud is 1.6 × 1021 m away. How far is that in light-years? (b) A gas cloud in a galaxy orbits at 150 km/s, but the visible mass alone predicts 84 km/s at that distance. What percentage of the mass inside its orbit is dark? (Mass needed is proportional to v².)
- (a) Distance = 1.6 × 1021 ÷ 9.5 × 1015 = 1.7 × 105 light-years, so it lies outside the Milky Way's disc.
- (b) Same radius, so the mass needed goes as v²: speed ratio 150 ÷ 84 = 1.79, mass ratio 1.79² = 3.2.
- Visible share = 1 ÷ 3.2, which is 31%, so 69% of the mass is dark.
Answer: (a) 1.7 × 105 light-years (b) 69% dark
Common mistakes
- Saying dark matter is dark because it is far away or hidden by dust. It gives out no light at all.
- Saying the outer stars in a galaxy orbit more slowly. Measured speeds stay about the same; that is the evidence for dark matter.
- Putting the Sun at the centre of the Milky Way. It is about halfway out.
Exam tip
When asked for the evidence for dark matter, describe the observation (outer stars orbit as fast as inner ones), then the conclusion (there must be more mass than we can see). Naming dark matter without the observation is not enough.
AP Physics and NGSS: IGCSE 0625 does not list dark matter; AQA GCSE Physics (not Combined) does, as dark mass. AP Physics 1 can link the orbital speed to the mass with v = √(GM ÷ r); NGSS HS-ESS1-2 uses dark matter only as part of the wider evidence about the Universe.
5 Black Holes
What you need to know
Star Birth
- Stars form from nebulae: clouds of gas (mostly hydrogen) and dust. Gravity pulls a clump together; it heats up and becomes a protostar.
- When the core reaches about 10 million °C, hydrogen fusion starts and a star is born. A clump smaller than about 0.08 Suns never gets that hot and becomes a brown dwarf.
- Leftover gas forms a spinning disc in which dust clumps into planets; the Solar System formed this way about 4.6 billion years ago.
The Sun's End
- A star spends most of its life on the main sequence, fusing hydrogen in a steady core.
- When a Sun-like star runs out of hydrogen in its core, the core shrinks and heats while the outer layers swell and cool: a red giant.
- It then puffs off its outer layers as a planetary nebula, leaving a hot core, a white dwarf, about the size of the Earth, which slowly cools.
Supernovae
- A star much more massive than the Sun swells into a red supergiant and fuses heavier and heavier elements, up to iron. Fusing iron takes energy in, so the core collapses and the star explodes as a supernova.
- It leaves a neutron star, or a black hole if the remaining core is above about 3 Suns.
- The supernova's debris carries heavy elements into space. New nebulae form from it, and from them new stars with planets; the iron in your blood came from such stars.
Key terms
- Nebula
- a cloud of gas and dust in which stars form
- Protostar
- a clump of gas heating up under gravity, before fusion starts
- Main sequence
- the long, stable stage in which a star fuses hydrogen in its core
- Supernova
- the explosion of a massive star at the end of its life
Diagram to know
The life-cycle flow chart. One start: nebula → protostar → main-sequence star. Then two branches: a star about the Sun's mass → red giant → planetary nebula → white dwarf; a much more massive star → red supergiant → supernova → neutron star or black hole, with an arrow from the supernova back to a new nebula.
Worked example
Today the Sun's radius is 7.0 × 105 km. As a red giant it will swell to about 200 times that. How far out will its surface reach, in astronomical units? (1 AU = 1.5 × 108 km, the Earth–Sun distance.)
- Red-giant radius = 7.0 × 105 × 200 = 1.4 × 108 km.
- In AU: 1.4 × 108 ÷ 1.5 × 108 = 0.93 AU.
- Check: just short of the Earth's orbit at 1 AU, so the Earth is in danger.
Answer: About 0.93 AU
Common mistakes
- Saying a protostar shines because fusion has started. It heats up because gravity squeezes it; fusion starts later.
- Saying every star ends as a supernova or a black hole. A star like the Sun ends as a white dwarf.
- Saying a planetary nebula has something to do with planets. It is the outer layers of a dying star.
Exam tip
Life-cycle questions are often a sequence to complete. Learn the two branches in order, and say what decides the branch: the star's mass.
AP Physics and NGSS: NGSS HS-ESS1-3 asks how elements up to iron are made by fusion in stars and heavier ones in supernovae. AP Physics 1 does not cover the life cycle of stars.
6 Schwarzschild Radius
What you need to know
Escape Speed
- The escape speed is the launch speed needed to leave a planet or star for good, with no further push: v = √(2GM ÷ r).
- For stars of the same density, escape speed grows in step with the radius. A big enough star would have an escape speed above the speed of light: John Michell's "dark star" (1783).
- The Schwarzschild radius rs = 2GM ÷ c² is the radius at which the escape speed equals the speed of light. A mass squeezed inside it is a black hole; nothing inside gets out.
Horizon Size
- rs is directly proportional to the mass: about 2.96 km of radius for every Sun of mass. Twice the mass, twice the radius.
- rs is a radius, so the event horizon is 2rs across.
Black-Hole Density
- The volume inside the horizon grows as rs³, so as M³, and the average density falls as 1 ÷ M². A black hole of about 140 million Suns is on average about as dense as water.
- Far away, a black hole pulls like any equal mass: g = GM ÷ r². It does not suck things in more strongly than a star of the same mass would.
Key terms
- Escape speed
- the minimum launch speed needed to escape a body's gravity for good
- Schwarzschild radius
- the radius at which the escape speed equals the speed of light
- Event horizon
- the boundary of a black hole, 2rs across; nothing inside escapes
- Black hole
- a mass squeezed inside its Schwarzschild radius
Equations
| Equation | What it says, symbols and units |
|---|---|
vesc = √(2GMr) | Escape speed from the surface of a mass M of radius r.
AP Physics 1 (Unit 6) derives it from energy: ½mv² = GMm ÷ r. |
rs = 2GMc2 | The Schwarzschild radius: set the escape speed equal to c and solve for r.
Beyond IGCSE, GCSE and the AP Physics 1 equation sheet. |
Worked example
Find the Schwarzschild radius of a black hole of 10 Suns. One Sun is 2.0 × 1030 kg.
- M = 10 × 2.0 × 1030 = 2.0 × 1031 kg.
- Square c first: c² = (3.0 × 108)² = 9.0 × 1016 m²/s².
- rs = 2GM ÷ c² = 2 × 6.67 × 10−11 × 2.0 × 1031 ÷ 9.0 × 1016 = 3.0 × 104 m, about 30 km.
- Check: about 3 km per Sun, and 10 Suns gives about 30 km.
Answer: 3.0 × 104 m (about 30 km); the horizon is about 60 km across
Common mistakes
- Forgetting to square c, or squaring only the 3.0 and not the power of ten: (3.0 × 108)² = 9.0 × 1016.
- Giving the horizon's width as rs. The width is 2rs.
- Saying a black hole pulls harder than a star of the same mass at the same distance. Far away, both give the same g.
Exam tip
In any calculation with G and c, convert the mass to kilograms first and write c² as its own line. Then the powers of ten are easy to check.
AP Physics and NGSS: This whole lesson goes beyond IGCSE and GCSE. AP Physics 1 covers escape speed through gravitational potential energy (Unit 6) and g = GM ÷ r²; NGSS HS-PS2-4 uses Newton's law of gravitation in the same way.
7 The Universe
What you need to know
Red-shift
- Light from almost every distant galaxy is red-shifted: its spectral lines arrive at longer wavelengths than in a laboratory. So the galaxies are moving away from us.
- Every line moves by the same fraction of its wavelength, and that fraction gives the galaxy's speed: Δλ ÷ λ0 = v ÷ c, for speeds far below the speed of light.
Hubble's Law
- Hubble's law: the further away a galaxy, the faster it moves away. A graph of speed against distance is a straight line through the origin, and its gradient is the Hubble constant H0 = v ÷ d.
- The current estimate is H0 ≈ 2.2 × 10−18 per second, the value IGCSE 0625 uses (about 68 km/s per megaparsec).
- Run backwards, every galaxy was in the same place at the same time, about 1 ÷ H0 ago, roughly 14 billion years: the Big Bang. Space itself is expanding, so there is no centre.
The Oldest Light
- The cosmic microwave background radiation (CMBR) reaches us from every direction. It was given out by hot gas soon after the Big Bang (about 380 000 years after it).
- The expansion of the Universe has stretched its wavelengths about 1100 times, from near-infrared into the microwave region.
- Red-shift, Hubble's law and the CMBR together are the evidence for the Big Bang.
Key terms
- Red-shift
- the increase in wavelength of light from a galaxy moving away from us
- Hubble constant
- the ratio of a galaxy's speed away from us to its distance, H0 = v ÷ d
- Big Bang
- the theory that the Universe expanded from a tiny, hot, dense state about 14 billion years ago
- CMBR
- cosmic microwave background radiation: microwaves from every direction, left over from the early Universe
Equations
| Equation | What it says, symbols and units |
|---|---|
Δλλ0 = vc | The fractional change in wavelength equals the galaxy's speed as a fraction of the speed of light.
IGCSE and AQA ask only that the speed can be found from the red-shift; the equation is used in the lesson and in AP Physics 2. |
H0 = vd | Further galaxies move away faster; current estimate H₀ ≈ 2.2 × 10⁻¹⁸ per second.
|
dv = 1H0 | An estimate of the age of the Universe: run the expansion backwards to a single point. |
Diagram to know
Two spectra one above the other: a laboratory spectrum with dark lines, and a galaxy's spectrum with the same pattern of lines moved towards the red (long-wavelength) end. Label the shift Δλ.
Worked example
A galaxy's calcium line, given out at 393.4 nm, arrives at 401.3 nm. Using c = 3.0 × 105 km/s and H0 = 2.2 × 10−18 per second, find (a) its speed away from us and (b) its distance in light-years.
- (a) Δλ = 401.3 − 393.4 = 7.9 nm, to a longer wavelength, so it is moving away. Δλ ÷ λ0 = 7.9 ÷ 393.4 = 0.020.
- v = 0.020 × 3.0 × 105 = 6.0 × 103 km/s = 6.0 × 106 m/s.
- (b) d = v ÷ H0 = 6.0 × 106 ÷ 2.2 × 10−18 = 2.73 × 1024 m.
- In light-years: 2.73 × 1024 ÷ 9.5 × 1015 = 2.9 × 108 light-years, about 290 million.
Answer: (a) 6.0 × 103 km/s (b) 2.9 × 108 light-years
Common mistakes
- Saying red-shift means the galaxy looks red. It means its lines are shifted towards longer wavelengths.
- Saying the Big Bang was an explosion at one place in space. Space itself is expanding, and there is no centre.
- Mixing km/s and m/s in H0 = v ÷ d. With H0 in per second, v must be in m/s and d in m.
Exam tip
For "give evidence for the Big Bang", the two strongest answers are red-shift increasing with distance (Hubble's law) and the CMBR. Say what each observation is, then what it shows.
AP Physics and NGSS: NGSS HS-ESS1-2 asks you to explain the Big Bang from the same three pieces of evidence. AP Physics 1 does not cover cosmology; the red-shift equation is AP Physics 2.
8 Big Bang or Steady State?
What you need to know
Two Universes
- Big Bang model: the Universe began in a tiny, hot, dense state and has expanded ever since; its density keeps falling.
- Steady State model: the Universe has always existed; it expands, but new matter appears so that its density never changes.
- Both models predict red-shift and Hubble's law, so red-shift alone cannot choose between them.
The Evidence Decides
- Three pieces of evidence fit only the Big Bang: the CMBR (the cooled glow of a hot early Universe, the same from every direction); distant galaxies, seen as they were long ago, look different (younger, more crowded, with many quasars); and about a quarter of the mass of the oldest gas is helium, made in the hot first minutes.
- Because more evidence supports it, the Big Bang is the accepted model. A scientific model stays only while the evidence fits it.
Faster and Faster
- Supernovae of one kind all reach the same peak brightness, so how bright one looks gives its distance: brightness falls as 1 ÷ d².
- In 1998 distant supernovae were found to be fainter, so further away, than a universe slowed by gravity allows. The expansion of the Universe is speeding up.
- The unknown cause is called dark energy. Dark energy and dark matter make up about 95% of the Universe, so the Big Bang model is incomplete.
Key terms
- Steady State model
- an eternal, expanding Universe in which new matter keeps the density constant
- Big Bang model
- a Universe that expanded from a tiny, hot, dense state and has a beginning
- Standard candle
- an object of known brightness, such as one kind of supernova, used to measure distance
- Dark energy
- the name for the unknown cause of the speeding-up expansion of the Universe
Equations
| Equation | What it says, symbols and units |
|---|---|
d = d1 √(B1B) | Distance from peak brightness, comparing two identical supernovae: brightness falls as 1 ÷ d².
IGCSE 0625 (Supplement) asks only that supernova brightness gives distance. |
dv = 1H0 | An estimate of the age of the Universe: run the expansion backwards to a single point. |
Worked example
(a) A supernova peaks at 1/25 of the brightness of an identical one 0.60 billion light-years away. How far away is it? (b) A distant gas cloud has 12 hydrogen atoms for every helium atom, and a helium atom has 4 times the mass. What percentage of its mass is helium?
- (a) Both give out the same light, and brightness falls as 1 ÷ d². 25 times fainter means √25 = 5.0 times further away.
- d = 0.60 × 5.0 = 3.0 billion light-years.
- (b) Count mass, not atoms: hydrogen 12 × 1 = 12 units, helium 1 × 4 = 4 units, total 16 units.
- Helium share = 4 ÷ 16 = 0.25, which is 25% of the mass, as the Big Bang predicts.
Answer: (a) 3.0 billion light-years (b) 25%
Common mistakes
- Saying red-shift proves the Big Bang. The Steady State model predicts red-shift too; the CMBR is what decided it.
- Saying the Big Bang model is proved. It is accepted because the evidence fits it, and it is still changing (dark energy).
- Saying a supernova that looks fainter is smaller or cooler. For standard candles, fainter means further away.
Exam tip
For "why was the Steady State rejected?", name an observation it cannot explain (the CMBR is the safest) and say why: a Universe that was never hotter or denser than today gives no reason for an even microwave glow from every direction.
AP Physics and NGSS: NGSS HS-ESS1-2 asks for the evidence for the Big Bang: the light spectra of distant galaxies, the motion of galaxies and the composition of matter (the helium share). AP Physics 1 does not cover cosmology.
Written in Physiworld's own words. The course tags come from the same mapping as the syllabus maps; equations are on the IGCSE, GCSE, AP Physics 1 and NGSS formula sheets. Values use g = 9.8 N/kg.
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