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S6 Physics: Astronomy and Space Science – Error Correction Practice (10 Questions)
S6 Physics: Astronomy and Space Science – Error Correction Practice (10 Questions)
The last paper of the set narrows in on the most common lost marks: treating a light year as a time, using parallax directly as a distance, forgetting to square in the inverse square law, swapping numerator and denominator in the redshift formula, and misaligning units in the Hubble law. Every item starts from a typical wrong answer, gives the correct working, then names the mistaken step.
Quick answer 8 ly is 7.57 times 10 to the 16 m; a parallax of 0.2 arcsecond gives 5 pc, or 16.3 ly; three times the distance leaves one ninth, about 11.1 percent; 5800 K peaks at 500 nm; 100 pc with absolute magnitude 2.0 gives apparent magnitude 7.0, 100 times fainter; a redshift of 0.040 gives 1.2 times 10 to the 4 km/s; H zero of 70 gives 171 Mpc; 9 AU gives 27 years; twice the radius and three times the temperature gives 324 times; a transit depth of 1 percent is 10 000 ppm with a planet radius of 4.87 times 10 to the 7 m.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 25 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)
- FoundationA star is 8 light years from Earth. How many years ago was the light we see tonight emitted, and how many metres is 8 light years? Use 1 ly = 9.46 times 10 to the 15 m.
- FoundationA star has a parallax of 0.2 arcsecond. Find its distance in parsecs and in light years.
- FoundationA star is moved to three times its original distance. What fraction of its apparent brightness remains, and what percentage is that?
- FoundationA star has a surface temperature of 5800 K. Use Wien law to find its peak wavelength in nm.
- IntermediateA star is 100 pc away with absolute magnitude 2.0. Find its apparent magnitude and how many times fainter it is than at 10 pc.
- IntermediateThe H alpha line of a galaxy, 656.3 nm in the laboratory, is observed at 682.55 nm. Find the redshift and the recession speed using v = c z.
- IntermediateWith a Hubble constant of 70 km/s per Mpc, find the distance in Mpc of a galaxy receding at 12 000 km/s.
- ChallengeA planet orbits with semi-major axis 9 AU. Use Kepler third law, P squared equals a cubed, to find its period in years.
- ChallengeA star has twice the Sun radius and three times the Sun surface temperature. How many times the Sun luminosity does it emit?
- Error redoDuring a transit the planet radius is 0.1 of the star radius. By what percentage does the starlight drop? If the star radius is 0.7 solar radius, or 6.96 times 10 to the 8 m, find the planet radius in metres, and explain why answering 10 percent is wrong.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | The light left the star 8 years ago, and 8 times 9.46 times 10 to the 15 is 7.57 times 10 to the 16 m | A light year is a unit of length, not of time; a star 8 light years away is seen as it was 8 years ago. |
| 2 | Distance is 1 divided by 0.2, which is 5 pc, and 5 times 3.26 is 16.3 light years | The distance in parsecs is the reciprocal of the parallax in arcseconds, so a larger parallax means a nearer star. |
| 3 | One divided by three squared is one ninth, about 0.111, which is about 11.1 percent | Brightness falls as the inverse square of distance, so three times the distance leaves one ninth. |
| 4 | The peak wavelength is 2.90 times 10 to the minus 3 divided by 5800, which is 5.00 times 10 to the minus 7 m, or 500 nm | Peak wavelength is inversely proportional to temperature; 5800 K peaks in the green-yellow part of the visible band. |
| 5 | The distance modulus is 5 log of 10, which is 5.0, so the apparent magnitude is 2.0 plus 5.0, namely 7.0; ten times the distance means 100 times fainter | A distance modulus of 5 magnitudes corresponds to a factor of 100 in brightness, and a more distant star has a larger apparent magnitude. |
| 6 | The redshift is 26.25 divided by 656.3, which is 0.040, and the speed is 0.040 times 3.00 times 10 to the 5, which is 1.2 times 10 to the 4 km/s | Redshift is the wavelength change divided by the rest wavelength and has no unit; v equals c z is valid only when z is much smaller than one. |
| 7 | The distance is 12 000 divided by 70, which is about 171 Mpc | The Hubble law, speed equals H zero times distance, means more distant galaxies recede faster, the direct evidence of cosmic expansion. |
| 8 | P squared is 9 cubed, which is 729, so P is 27 years | With AU and years as the units, P squared equals a cubed can be used directly without converting to SI. |
| 9 | Luminosity goes as radius squared times temperature to the fourth, so 4 times 81 gives 324 times | Luminosity depends on the square of the radius and the fourth power of temperature, and temperature dominates. |
| 10 | The depth is 0.1 squared, which is 0.01, or 1 percent, that is 10 000 parts per million; the planet radius is 0.1 times 0.7 times 6.96 times 10 to the 8, which is 4.87 times 10 to the 7 m. The error is using a ratio of radii for a ratio of areas: 10 percent is the radius ratio, not the drop in light. | Transit depth is the square of the radius ratio, so an Earth-sized planet produces only a very shallow dip. |
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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