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S6 Physics: Astronomy and Space Science – Practice Paper 3 (Challenge, 10 Questions)
S6 Physics: Astronomy and Space Science – Practice Paper 3 (Challenge, 10 Questions)
Paper three pushes the scale to extremes: the Hubble time as an age estimate, distance from a recession speed, the Schwarzschild radius of a black hole, stellar lifetime from the mass luminosity relation, exoplanet density from mass and radius, and angular diameter together with photon energy. It ends with weighing a binary by Kepler law and taking apart the claim that the Milky Way sits at the centre.
Quick answer One over H zero is about 14.0 billion years; 0.1 c gives 429 Mpc; a ten solar mass black hole has a Schwarzschild radius of about 29.5 km; a ten solar mass star lives about 31.6 million years; five Earth masses at 1.5 Earth radii gives 8 170 kg per cubic metre; 100 000 ly at 10 million ly subtends 0.57 degree; a 500 nm photon carries 3.98 times 10 to the minus 19 J, or 2.48 eV; the binary axis is 2 AU; five magnitudes gives a distance ratio of 10; expansion has no centre.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 32 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S6 Physics | Astronomy and Space Science: Light Year, Luminosity, Redshift and Cosmic Expansion |
| Level | S6 |
02 Questions (10 items)
- FoundationWith a Hubble constant of 70 km/s per Mpc, find the Hubble time one over H zero in billions of years.
- FoundationA galaxy recedes at 0.1 of the speed of light. Using the Hubble law, estimate its distance in Mpc.
- FoundationFind the Schwarzschild radius of a 10 solar mass black hole using R s equals 2 G M over c squared.
- FoundationStellar lifetime goes as mass over luminosity, and luminosity goes as mass to the 3.5. Estimate the lifetime of a 10 solar mass star if the Sun lives 10 billion years.
- IntermediateAn exoplanet has five Earth masses and 1.5 Earth radii. Estimate its mean density, given the Earth density of 5 515 kg per cubic metre.
- IntermediateA galaxy 100 000 light years across lies 10 million light years away. Find its angular diameter in degrees.
- IntermediateFind the energy of a 500 nm photon in joules and in electronvolts.
- ChallengeA binary has a total mass of 2 solar masses and a period of 2 years. Find the semi-major axis in AU using P squared equals a cubed over M.
- ChallengeTwo stars have the same absolute magnitude. Star A has apparent magnitude 6 and star B has 11. How many times farther is B?
- Error redoA student says cosmic expansion means galaxies flying apart through existing space, so the Milky Way must sit at the centre. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | H zero is 70 times 1000 divided by 3.086 times 10 to the 22, about 2.27 times 10 to the minus 18 per second, so one over H zero is about 14.0 billion years | The Hubble time is a rough estimate of the age of the universe; the true age needs a model of the expansion history. |
| 2 | The speed is 3.0 times 10 to the 4 km/s, so the distance is 30 000 divided by 70, about 429 Mpc | This is only a linear Hubble law estimate; at large distances a relativistic formula is needed. |
| 3 | R s is 2 times 6.67 times 10 to the minus 11 times 1.99 times 10 to the 31, divided by 9.00 times 10 to the 16, about 2.95 times 10 to the 4 m, or 29.5 km | The Schwarzschild radius is proportional to mass; a one solar mass black hole is only about 3 km across. |
| 4 | Lifetime goes as mass to the minus 2.5, so it is 10 billion times 10 divided by 10 to the 3.5, about 31.6 million years | Massive stars have more fuel but burn it far faster, so their lifetimes are much shorter. |
| 5 | The density ratio is 5 divided by 3.375, about 1.48, so the density is about 1.48 times 5 515, which is 8 170 kg per cubic metre | Density needs both mass and radius; mass alone cannot tell a rocky planet from a gaseous one. |
| 6 | The angle is 10 to the 5 divided by 10 to the 7, which is 0.010 radian, about 0.57 degree | The small angle formula is size over distance, and astronomers often express the result in arcminutes or arcseconds. |
| 7 | E is h c over lambda, about 3.98 times 10 to the minus 19 J, which is about 2.48 eV | Shorter wavelengths carry more energy per photon, which is why ultraviolet light can break chemical bonds. |
| 8 | a cubed is 2 times 4, which is 8, so a is 2 AU | The binary form puts total mass in the denominator, and it is the most direct way to weigh stars. |
| 9 | Five magnitudes means a hundredfold brightness ratio, and brightness goes as one over distance squared, so the distance ratio is the square root of 100, which is 10 | At equal luminosity a more distant object is dimmer, so a brightness ratio gives a distance ratio. |
| 10 | Expansion stretches space itself, so observers in every galaxy see the same recession pattern and there is no centre; redshift grows with distance because the scale factor grows | Uniform expansion has no special centre, which is quite different from debris flying out of an explosion. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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