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S6 Physics: Astronomy and Space Science – Practice Paper 2 (Intermediate, 10 Questions)
S6 Physics: Astronomy and Space Science – Practice Paper 2 (Intermediate, 10 Questions)
Paper two works from stellar properties: how luminosity depends on radius and temperature, Kepler third law for orbital periods, transit depth as a planet sizer, then redshift and the Hubble law to link galaxies with cosmic expansion. It closes with the peak wavelength of the cosmic microwave background, the distance modulus, and the directional error of reading redshift as approach.
Quick answer Twice the radius gives four times the luminosity and twice the temperature sixteen times; a semi-major axis of 4 AU gives a period of 8 years; a radius ratio of 0.1 gives a transit depth of 1 percent; the redshift is 0.050 and v equals c z gives 15 000 km/s; the distance is 214 Mpc, about 699 million light years; 2.7 K peaks at 1.1 mm; a distance modulus of 5 at 100 pc gives magnitude 6.0; redshift means recession.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 28 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 has twice the Sun radius and the same surface temperature. How many times the Sun luminosity does it emit?
- FoundationA star has the Sun radius but twice its surface temperature. How many times the Sun luminosity does it emit?
- FoundationA planet orbits with semi-major axis 4 AU. Using Kepler third law in the form P squared equals a cubed, find its period in years.
- FoundationDuring a transit the planet radius is 0.1 of the star radius. By what percentage does the starlight drop?
- IntermediateThe H alpha line of a galaxy, 656.3 nm in the laboratory, is observed at 689.1 nm. Find the redshift z.
- IntermediateUsing the previous redshift of 0.050 and v = c z, estimate the recession speed of the galaxy.
- IntermediateWith a Hubble constant of 70 km/s per Mpc, find the distance in Mpc of a galaxy receding at 15 000 km/s, and in million light years.
- ChallengeThe cosmic microwave background has a temperature of about 2.7 K. Find its peak wavelength.
- ChallengeA star is 100 pc away with absolute magnitude 1.0. Find its apparent magnitude using the distance modulus.
- Error redoA student says a redshifted galaxy spectrum means the galaxy is approaching us. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Luminosity goes as radius squared times temperature to the fourth, so twice the radius gives four times the luminosity | Luminosity depends on both radius and temperature; doubling the radius at the same temperature gives four times. |
| 2 | Luminosity goes as temperature to the fourth, so twice the temperature gives sixteen times the luminosity | Temperature enters luminosity to the fourth power, so it dominates the luminosity of a star. |
| 3 | P squared is 4 cubed, which is 64, so P is 8 years | With AU and years as units, P squared equals a cubed can be used directly without SI conversion. |
| 4 | The drop is the square of 0.1, which is 1 percent, or 10 000 parts per million | Transit depth gives the radius ratio directly, which is the main way to size an exoplanet. |
| 5 | z is the change in wavelength divided by the rest wavelength, 32.8 over 656.3, which is 0.050 | Redshift is the wavelength change divided by the rest wavelength and has no unit. |
| 6 | v is 0.050 times 3.00 times 10 to the 5, which is 1.5 times 10 to the 4 km/s | The approximation v equals c z is valid only when z is much smaller than one. |
| 7 | d is 15 000 divided by 70, about 214 Mpc, and 214 times 3.26 is about 699 million light years | The Hubble law, speed equals H zero times distance, is the most direct evidence of cosmic expansion. |
| 8 | The peak wavelength is 2.90 times 10 to the minus 3 divided by 2.7, about 1.07 times 10 to the minus 3 m, or 1.1 mm, in the microwave band | The cosmic microwave background is blackbody radiation left from the cooling early universe, now redshifted into microwaves. |
| 9 | The distance modulus is 5 log of 10, which is 5.0, so the apparent magnitude is 1.0 plus 5.0, which is 6.0 | The distance modulus links apparent and absolute magnitude and is a basic distance formula. |
| 10 | Redshift means a longer wavelength and a lower frequency, so the galaxy is moving away; an approaching galaxy shows a blueshift | The rule is simple: stretched wavelengths mean recession, squeezed wavelengths mean approach. |
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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