1True or false
A blue-white star has a hotter surface than a red star.
Show answer
Answer: True
Wien's law: a shorter peak wavelength (blue) means a higher temperature.
!Common mistakeEveryday experience (red-hot) misleads many learners; blue-white stars, above 10 000 K, are the hottest.
2True or false · ★ Challenge
Two stars that look equally bright in the sky must be the same distance from the Earth.
Show answer
Answer: False
Brightness depends on luminosity and distance; a more luminous star farther away can look as bright as a dimmer, closer one.
!Common mistakeThis is the mistake of treating apparent brightness as if it showed distance alone.
3True or false
Dark matter is called "dark" because it is made of black holes that swallow light.
Show answer
Answer: False
Dark matter neither emits nor absorbs light; it is detected only by its gravity. Black holes are far too few to explain it.
!Common mistakeLearners link "dark" with black holes; dark matter is simply matter that does not interact with light.
4True or false · ★ Challenge
A star with ten times the mass of the Sun lives about ten times longer, because it has ten times more fuel.
Show answer
Answer: False
Its luminosity is thousands of times greater, so it uses its fuel much faster and lives only a few tens of millions of years, not 10 billion.
!Common mistakeLearners reason "more fuel lasts longer", forgetting that the rate of burning rises much faster than the amount of fuel.
5True or false
X-ray telescopes must be placed in space, because the atmosphere absorbs X-rays from space.
Show answer
Answer: True
Only visible light, some infrared and radio waves pass well through the atmosphere ("windows"); X-rays and most ultraviolet are absorbed.
!Common mistakeSome learners think telescopes go to space only to get "closer to the stars"; the gain in distance is tiny, the real reason is the atmosphere.
6True or false · ★ Challenge
If a galaxy 3 billion light-years away had been destroyed 1 billion years ago, we would still see it in our telescopes today.
Show answer
Answer: True
The light we receive now left it 3 billion years ago; light from the time of its destruction will not arrive for another 2 billion years.
!Common mistakeLearners often think what we see is happening "now"; we see distant objects as they were when the light left them.
7True or false
The Milky Way and the Andromeda galaxy are the two largest members of the Local Group of galaxies.
Show answer
Answer: True
The Local Group has a few dozen galaxies; most are small dwarf galaxies around these two large spirals.
!Common mistakeSome learners confuse the Local Group with the Solar System or with a constellation; it is a group of galaxies bound by gravity.
8Multiple choice · ★ Challenge
The spectral lines of a star in a binary system shift to longer wavelengths, then to shorter ones, and back again every few days. What does this show?
- AIt moves away from us and towards us in turn as it orbits
- BIt is expanding and shrinking in size every few days
- CIts surface heats up and cools down every few days
- DIts light is being bent by dust between it and the Earth
Show answer
Answer: A. It moves away from us and towards us in turn as it orbits
Redshift means moving away, blueshift means moving towards us; a regular change between them shows orbital motion.
!Common mistakeChoosing heating and cooling confuses a Doppler shift with a change in colour from temperature; temperature changes the whole spectrum, not the positions of the lines.
9True or false
The parallax angle p of a star is half of the total angular shift seen when it is observed six months apart.
Show answer
Answer: True
Six months apart the Earth is at opposite ends of a 2 AU baseline; p is defined using a 1 AU baseline, so it is half the total shift.
!Common mistakeUsing the whole shift as p halves the calculated distance.
10Multiple choice · ★ Challenge
About 90 % of the stars we can study lie on the main sequence of the HR diagram. What is the best explanation?
- AMost stars are born with exactly the mass of the Sun
- BStars move up and down the main sequence as they age
- CGiants and white dwarfs are too faint to detect at all
- DStars spend most of their lives fusing hydrogen in the core
Show answer
Answer: D. Stars spend most of their lives fusing hydrogen in the core
The main sequence is the long, stable hydrogen-burning stage; the giant and white-dwarf stages are shorter or harder to see, so a random sample finds most stars there.
!Common mistakeChoosing "stars move along the main sequence" is a common error: a star stays at nearly the same point until its core hydrogen runs out.
11Multiple choice
Where is the Sun found in the Milky Way?
- AAt the centre, next to the central black hole
- BIn the halo, far above the flat galactic disc
- CIn a spiral arm, about halfway out from the centre
- DAt the outer edge, beyond all the spiral arms
Show answer
Answer: C. In a spiral arm, about halfway out from the centre
The Sun lies in the disc, in a minor spiral arm about 26 000 light-years from the centre of a galaxy 100 000 light-years across.
!Common mistakeChoosing the centre repeats the old idea that we are at the middle of everything; the Sun is in an ordinary place in the disc.
12Multiple choice · ★ Challenge
In 1929 Hubble found H₀ ≈ 500 km/s/Mpc, about seven times today's value. What was the main reason?
- AHe measured redshifts that were seven times too small
- BHe underestimated the distances to the galaxies
- CThe universe was expanding faster in 1929 than now
- DHe used the wrong speed of light in v = zc
Show answer
Answer: B. He underestimated the distances to the galaxies
H₀ = v/d. His speeds were fine but his distances (from Cepheids that were wrongly calibrated) were too small, which made v/d too large.
!Common mistakeChoosing "the universe expanded faster in 1929" is wrong: 100 years is nothing on the cosmic time-scale; the error was in measurement.
13Fill in the blank
One parsec is the distance at which a length of 1 AU subtends an angle of one ______.
Show answer
Answer: arcsecond (1/3600 of a degree)
The name comes from "parallax of one arcsecond".
!Common mistakeSome learners write "degree"; an angle of 1° would put the star only about 57 AU away, far closer than any star.
14Multiple choice · ★ Challenge
About a quarter of the ordinary matter in the universe, by mass, is helium. Why does this support the Big Bang theory?
- AHelium is the lightest element, so it formed first of all
- BStars cannot make so much; it formed in the first minutes
- CHelium is made when hydrogen nuclei undergo fission
- DSupernovae turn most of their matter into helium
Show answer
Answer: B. Stars cannot make so much; it formed in the first minutes
Fusion in stars over the whole history of the universe can account for only a few per cent of helium; the hot, dense early universe predicts about 25 %.
!Common mistakeChoosing "helium is the lightest element" is a factual slip: hydrogen is lighter, and the argument is about the AMOUNT of helium, not its mass.
15Multiple choice
On a Hertzsprung–Russell diagram, where are white dwarfs found?
- ABottom left: hot but faint
- BTop right: cool but very bright
- CTop left: hot and very bright
- DBottom right: cool and faint
Show answer
Answer: A. Bottom left: hot but faint
White dwarfs are hot (left side) but tiny, so their luminosity is low (bottom).
!Common mistakeChoosing bottom right puts them with the red dwarfs; "white" tells us they are hot, so they are on the left.
16Multiple choice · ★ Challenge
Two stars have the same surface temperature, but star B has three times the radius of star A. What is the ratio of their luminosities LB/LA?
- A3
- B9
- C27
- D81
Show answer
Answer: B. 9
L = 4πR²σT⁴; with T the same, L ∝ R², so LB/LA = 3² = 9.
!Common mistakeChoosing 81 raises the radius ratio to the fourth power; it is the TEMPERATURE that is raised to the fourth power in Stefan's law.
17Multiple choice
According to current measurements, the energy content of the universe is roughly:
- A68 % ordinary matter, 27 % dark matter, 5 % dark energy
- B27 % ordinary matter, 68 % dark matter, 5 % dark energy
- C5 % ordinary matter, 68 % dark matter, 27 % dark energy
- D5 % ordinary matter, 27 % dark matter, 68 % dark energy
Show answer
Answer: D. 5 % ordinary matter, 27 % dark matter, 68 % dark energy
Everything made of atoms (stars, planets, gas, people) is only about 5 %; dark matter about 27 % and dark energy about 68 %.
!Common mistakeChoosing a large share of ordinary matter is natural, as it is all we can see, but most of the universe does not give out light.
18Short answer · ★ Challenge
Describe the path of the Sun on the Hertzsprung–Russell diagram from today until the end of its life.
Show answer
Model answer: Today it is on the main sequence (middle). When its core hydrogen runs out it moves up and to the right to become a red giant: brighter but cooler. After losing its outer layers as a planetary nebula, the exposed core moves down and to the left to become a white dwarf: hot but faint, which then slowly cools.
!Common mistakeLearners often move the Sun to the "supernova" or "black hole" region; the Sun is not massive enough and ends as a white dwarf.
19Fill in the blank
The lines in the spectrum of the Andromeda galaxy appear at slightly shorter wavelengths than in the laboratory. This ______ shows that Andromeda is approaching the Milky Way.
Show answer
Answer: blueshift
A source moving towards us has its waves squashed to shorter wavelengths, towards the blue end of the spectrum.
!Common mistakeWriting "redshift" is the usual slip: redshift is a shift to LONGER wavelengths and means moving away.
20Multiple choice
What stops a main-sequence star such as the Sun from collapsing under its own gravity?
- AThe star's rotation flings its gas outwards
- BIts magnetic field pushes the layers apart
- COutward pressure of hot gas balances gravity
- DIts iron core is too hard to be squashed
Show answer
Answer: C. Outward pressure of hot gas balances gravity
Energy from fusion in the core keeps the gas hot, and the gas (and radiation) pressure pushes outwards as strongly as gravity pulls inwards.
!Common mistakeChoosing "an iron core" is wrong: iron collects only at the end of a massive star's life, and an iron core actually leads to collapse.
21Short answer · ★ Challenge
Suggest two reasons why large optical telescopes are built on high, dry mountain tops far from cities.
Show answer
Model answer: There is less atmosphere above them, so less absorption and less blurring from moving air (better seeing). Dry air has little water vapour, which absorbs infrared, and there are fewer clouds. Far from cities there is less light pollution, so faint objects stand out against a dark sky.
!Common mistakeA common error is to say mountains are chosen because they are "closer to the stars"; a few kilometres makes no difference to the distance of a star.
22Fill in the blank
A cloud of gas contracting under gravity heats up; when its core reaches about 10 million K, ______ begins and a star is born.
Show answer
Answer: nuclear fusion (of hydrogen)
At these temperatures hydrogen nuclei move fast enough to overcome their electric repulsion and fuse into helium.
!Common mistakeWriting "burning" suggests chemical combustion; stars shine by nuclear fusion, which releases millions of times more energy per kilogram.
23Short answer · ★ Challenge
Explain why images of the most distant galaxies taken by the James Webb Space Telescope tell astronomers about the early universe.
Show answer
Model answer: Light from these galaxies has travelled for more than 13 billion years, so we see them as they were when the light left, only a few hundred million years after the Big Bang. Looking farther away therefore means looking further back in time, so these images show young galaxies forming in the early universe.
!Common mistakeA common mistake is to think the telescope sees the galaxies as they are today; the farther the galaxy, the older the picture.
24True or false
In SI units, H₀ = 70 km/s/Mpc is about 2.3 × 10⁻¹⁸ s⁻¹.
Show answer
Answer: True
1 Mpc = 3.09 × 10¹⁹ km, so H₀ = 70 ÷ 3.09 × 10¹⁹ = 2.3 × 10⁻¹⁸ s⁻¹ (km cancels).
!Common mistakeLeaving Mpc unconverted gives nonsense values for 1/H₀; km/s per Mpc reduces to a unit of 1/time.
25Short answer · ★ Challenge
On a dark night away from the lights of Kigali, the Milky Way is seen as a pale band across the sky rather than as stars spread evenly everywhere. Explain why.
Show answer
Model answer: The Milky Way is a flat disc of stars and we are inside the disc. Looking along the plane of the disc we see through huge numbers of distant stars, which merge into a band of light; looking above or below the disc we see far fewer stars.
!Common mistakeA common error is to think the band is a cloud in our atmosphere or a separate galaxy; it is our own galaxy seen edge-on from inside.
26Multiple choice
Estimating the age of the universe as 1/H₀ assumes that:
- AThe universe has not expanded at all since the start
- BAll galaxies are the same distance from the Earth
- CLight from distant galaxies arrives at once
- DThe expansion rate has always been the same
Show answer
Answer: D. The expansion rate has always been the same
If each galaxy has always moved at its present speed v = H₀d, the time to reach distance d is d/v = 1/H₀.
!Common mistakeSome learners think 1/H₀ needs all galaxies at one distance; it gives the same time for every galaxy because v is proportional to d.
27Short answer · ★ Challenge
A red giant and a white dwarf happen to have the same luminosity. Use L = 4πR²σT⁴ to explain which one is hotter and why.
Show answer
Model answer: With equal L, R²T⁴ must be equal. The red giant has a huge radius, so its T must be low (red, cool); the white dwarf is tiny, so to give out the same power its surface must be very hot. The white dwarf is hotter.
!Common mistakeA common error is to think the bigger star must be hotter because it is "giant"; for the same power, a larger surface needs a LOWER temperature.
28Multiple choice
Why are radio telescopes built much larger than optical telescopes?
- ARadio waves are long, so a big dish is needed to see detail
- BRadio waves are weaker, so they need more metal to stop them
- CRadio waves travel slower than light, so they need more time
- DRadio sources are all much closer than the visible stars are
Show answer
Answer: A. Radio waves are long, so a big dish is needed to see detail
The detail a telescope can resolve depends on λ/D; radio wavelengths are about a million times longer than light, so D must be much larger.
!Common mistakeChoosing "radio waves travel slower" is wrong: all electromagnetic waves travel at c in a vacuum.
29Multiple choice · ★ Challenge
A gas cloud orbits the centre of a galaxy at 200 km/s, at a radius of 3.1 × 10²⁰ m. Using v² = GM/r, what mass lies inside its orbit? (G = 6.67 × 10⁻¹¹ N m² kg⁻²)
- A1.9 × 10³⁵ kg
- B9.3 × 10³⁵ kg
- C1.9 × 10⁴¹ kg
- D9.3 × 10³⁸ kg
Show answer
Answer: C. 1.9 × 10⁴¹ kg
M = v²r/G = (2.0 × 10⁵)² × 3.1 × 10²⁰ ÷ 6.67 × 10⁻¹¹ = 1.9 × 10⁴¹ kg.
!Common mistakeChoosing 1.9 × 10³⁵ kg comes from using v = 200 m/s instead of 2.0 × 10⁵ m/s; change km/s into m/s before squaring.
30Multiple choice
A lamp is viewed from 3 times its original distance. Its apparent brightness becomes:
- A1/3 of the original
- B3 times the original
- C1/9 of the original
- D1/27 of the original
Show answer
Answer: C. 1/9 of the original
b = L/(4πd²), so b ∝ 1/d²: (1/3)² = 1/9.
!Common mistakeChoosing 1/3 forgets that the light spreads over an area that grows as the SQUARE of the distance.
31Short answer · ★ Challenge
As a loaf of raisin bread rises in the oven, every raisin moves away from every other raisin. Use this model to explain why more distant galaxies recede faster, and give one way in which the model is not like the real universe.
Show answer
Model answer: If the dough doubles in size in a given time, a raisin 1 cm away becomes 2 cm away (moving 1 cm) while one 3 cm away becomes 6 cm away (moving 3 cm) in the same time, so speed is proportional to distance, as in v = H₀d. Every raisin sees the same thing, so there is no special centre. Limitation: the loaf has an edge and a centre and expands into the oven, while the universe has no edge and is not expanding into anything; also raisins are not held together by gravity like galaxies in clusters.
!Common mistakeLearners often say the raisins near the edge move faster because they are "pushed"; it is the stretching of the dough between them that causes the faster recession.
32True or false
On a Hertzsprung–Russell diagram, surface temperature is usually plotted increasing from left to right.
Show answer
Answer: False
By tradition temperature DECREASES from left (hot, blue) to right (cool, red).
!Common mistakeLearners used to ordinary graphs read the axis the usual way and so put hot stars in the wrong place.
33Short answer · ★ Challenge
Explain how astronomers use a Cepheid variable star to find the distance to a galaxy.
Show answer
Model answer: A Cepheid's brightness rises and falls with a regular period, and its period is linked to its luminosity (period–luminosity relation, calibrated using nearby Cepheids of known distance). Measure the period to find the luminosity L, measure the apparent brightness b, then use b = L/(4πd²) to calculate d.
!Common mistakeLearners often think the period gives the distance directly; the period gives the luminosity, and the distance comes from comparing it with the observed brightness.
34Multiple choice
The cosmic microwave background was released as visible and infrared light. Why is it detected as microwaves today?
- ADust in the galaxy has absorbed its short waves
- BThe Earth's atmosphere changes it into microwaves
- CIt has slowed down while crossing the universe
- DExpansion of space has stretched its wavelength
Show answer
Answer: D. Expansion of space has stretched its wavelength
Since the radiation was released the universe has expanded about 1000 times, stretching every wavelength by the same factor into the microwave region.
!Common mistakeChoosing "it has slowed down" is wrong: all electromagnetic waves travel at c in a vacuum; it is the wavelength that changes.
35Multiple choice · ★ Challenge
A school telescope has a mirror 0.20 m across; the pupil of the eye at night is about 5 mm across. How many times more light does the telescope collect?
- A40
- B200
- C1600
- D4.0 × 10⁴
Show answer
Answer: C. 1600
Light collected ∝ area ∝ D²: (0.20 ÷ 0.005)² = 40² = 1600.
!Common mistakeChoosing 40 compares diameters only; the collecting AREA depends on the diameter squared.
36Multiple choice
Which list puts these distances in order of increasing size?
- ALight-year, AU, parsec, megaparsec
- BAU, light-year, parsec, megaparsec
- CAU, parsec, light-year, megaparsec
- DParsec, light-year, AU, megaparsec
Show answer
Answer: B. AU, light-year, parsec, megaparsec
1 AU = 1.5 × 10¹¹ m, 1 ly = 9.46 × 10¹⁵ m, 1 pc = 3.26 ly = 3.09 × 10¹⁶ m, 1 Mpc = 10⁶ pc.
!Common mistakeChoosing parsec before light-year is a common slip: 1 pc is 3.26 light-years, so the parsec is the larger unit.
37Fill in the blank
Taking H₀ = 70 km/s/Mpc, a galaxy receding at 35 000 km/s is about ______ Mpc away.
Show answer
Answer: 500
d = v/H₀ = 35 000 ÷ 70 = 500 Mpc.
!Common mistakeMultiplying (35 000 × 70) instead of dividing gives 2.45 × 10⁶, a distance far larger than the observable universe.
38Multiple choice · ★ Challenge
A type Ia supernova in a distant galaxy appears 100 times fainter than an identical supernova in a galaxy 20 Mpc away. How far away is the distant galaxy?
- A2000 Mpc
- B200 Mpc
- C40 Mpc
- D0.20 Mpc
Show answer
Answer: B. 200 Mpc
Same luminosity, so d ∝ 1/√b: d = 20 × √100 = 20 × 10 = 200 Mpc.
!Common mistakeChoosing 2000 Mpc treats brightness as inversely proportional to distance; it falls as 1/d², so take the square root of 100.
39Short answer · ★ Challenge
The oldest stars known are about 13 billion years old. Explain why finding stars clearly older than the age given by 1/H₀ would be a serious problem for cosmology.
Show answer
Model answer: Stars form inside the universe, so they cannot be older than the universe itself. If the oldest stars were older than 1/H₀, either the measured H₀ (or the assumption of steady expansion) or the models of how stars age would be wrong. At present 1/H₀ ≈ 14 billion years is just greater than 13 billion years, so the two methods agree.
!Common mistakeA common mistake is to treat 1/H₀ and stellar ages as unrelated numbers; they are independent checks on each other.
40Fill in the blank
Observations of distant type Ia supernovae show that the expansion of the universe is ______, an effect blamed on dark energy.
Show answer
Answer: accelerating (speeding up)
The distant supernovae were fainter (farther) than expected for a slowing expansion.
!Common mistakeMany expected gravity to slow the expansion; the surprise of 1998 was that it is speeding up.
41Short answer · ★ Challenge
Describe two possible futures of the universe and state what decides which one happens.
Show answer
Model answer: Big Freeze: the universe keeps expanding for ever, galaxies move apart, stars burn out and everything cools towards absolute zero. Big Crunch: gravity stops the expansion and the universe collapses back to a hot, dense state. Which happens depends on the total density of matter compared with the critical density, and on dark energy; present measurements of accelerating expansion favour the Big Freeze.
!Common mistakeLearners often think the universe must eventually stop because "everything slows down"; with dark energy the expansion is speeding up.
42Fill in the blank
An object of known luminosity, used to find distances by comparing it with its observed brightness, is called a standard ______.
Show answer
Answer: candle
Cepheid variable stars and type Ia supernovae are standard candles.
!Common mistakeSome learners think any bright star is a standard candle; its luminosity must be known independently of its distance.
43Short answer · ★ Challenge
How many astronomical units are there in one light-year? (1 AU = 1.5 × 10¹¹ m, 1 ly = 9.46 × 10¹⁵ m) Use your answer to explain why the AU is used inside the Solar System but not for stars.
Show answer
Model answer: 9.46 × 10¹⁵ ÷ 1.5 × 10¹¹ ≈ 6.3 × 10⁴ AU in one light-year. Planets are a few AU to about 30 AU from the Sun, so the AU gives convenient numbers there; the nearest star is about 2.7 × 10⁵ AU away, so light-years or parsecs give smaller, easier numbers for stars.
!Common mistakeDividing the wrong way (1.5 × 10¹¹ ÷ 9.46 × 10¹⁵) gives 1.6 × 10⁻⁵, which would mean the light-year is the smaller unit.
44Multiple choice
The spectrum of star X peaks at 400 nm and that of star Y at 800 nm. What is the ratio of their surface temperatures TX/TY?
- A2
- B0.5
- C4
- D16
Show answer
Answer: A. 2
Wien: λmax T = constant, so TX/TY = λY/λX = 800 ÷ 400 = 2.
!Common mistakeChoosing 0.5 assumes T is proportional to λmax; a shorter peak wavelength means a HOTTER star.
45Short answer · ★ Challenge
The Steady State model said the universe has always looked the same, with new matter created as it expands. Compare it with the Big Bang model and state which observation decided between them.
Show answer
Model answer: Both models describe an expanding universe that agrees with redshift. The Big Bang says the universe was hotter and denser in the past and changes with time; the Steady State says it never changes. The discovery of the cosmic microwave background in 1965 decided it: this cooled radiation from a hot early universe is predicted by the Big Bang but has no natural explanation in the Steady State model.
!Common mistakeLearners often think redshift alone proves the Big Bang; both models predicted redshift, so it could not decide between them.
46Multiple choice
A spectral line with a laboratory wavelength of 500.0 nm is seen at 502.5 nm in the light of a star cluster. What is the cluster's motion? (c = 3.0 × 10⁵ km/s)
- ATowards us at 1500 km/s
- BAway from us at 15 000 km/s
- CAway from us at 1500 km/s
- DAway from us at 1.5 km/s
Show answer
Answer: C. Away from us at 1500 km/s
Δλ = 2.5 nm; z = 2.5 ÷ 500.0 = 0.0050; v = zc = 0.0050 × 3.0 × 10⁵ = 1500 km/s, and the longer wavelength means it is receding.
!Common mistakeChoosing "towards us" mixes up the shifts: a longer observed wavelength is a redshift, so the source is moving away.
47Multiple choice
The Moon is 3.84 × 10⁸ m from the Earth. How long does moonlight take to reach us? (c = 3.0 × 10⁸ m/s)
- A0.78 s
- B2.6 s
- C1.3 × 10⁻³ s
- D1.3 s
Show answer
Answer: D. 1.3 s
t = d/c = 3.84 × 10⁸ ÷ 3.0 × 10⁸ = 1.28 s ≈ 1.3 s.
!Common mistakeChoosing 2.6 s is the time for a radar or laser signal to go to the Moon AND back; moonlight makes only the one-way trip.
48Short answer · ★ Challenge
Rigel, the bright star in Orion, has a surface temperature of about 12 000 K. Calculate the wavelength at which its radiation is most intense (Wien constant = 2.9 × 10⁻³ m K) and use your answer to explain its colour.
Show answer
Model answer: λmax = 2.9 × 10⁻³ ÷ 12 000 = 2.4 × 10⁻⁷ m = 240 nm, in the ultraviolet. Within the visible range it gives out more blue light than red, so Rigel looks blue-white.
!Common mistakeLearners often say "it peaks in UV so we cannot see it"; the star still emits strongly across the visible range, with blue strongest.
49Short answer · ★ Challenge
The Gaia space telescope can measure parallax angles as small as about 1 × 10⁻⁴ arcsecond. Find the greatest distance it can measure in parsecs and in light-years, and compare it with the diameter of the Milky Way (about 100 000 light-years).
Show answer
Model answer: d = 1/p = 1 ÷ 1 × 10⁻⁴ = 10 000 pc = 10 000 × 3.26 ≈ 3.3 × 10⁴ ly. This is about one third of the diameter of the Milky Way, so Gaia can measure stars across a large part of our galaxy, but not other galaxies.
!Common mistakeLearners sometimes multiply instead of dividing (d = p); a smaller angle must give a LARGER distance.
50Multiple choice
Star A has a parallax angle of 0.25 arcsecond and star B of 0.05 arcsecond. How do their distances compare?
- AB is 5 times as far away as A
- BB is 5 times nearer than A is
- CB is 25 times as far away as A
- DB is √5 times as far away as A
Show answer
Answer: A. B is 5 times as far away as A
d = 1/p: dA = 4 pc and dB = 20 pc, so dB/dA = 5. A smaller parallax means a greater distance.
!Common mistakeChoosing "5 times nearer" assumes a bigger angle means a bigger distance; distance is inversely proportional to the parallax angle.