The Universe by size: galaxies, stars, planets, moons, asteroids and meteors, and how parallax measures the distance to a star
By the end of this lesson you will be able to
- Describe galaxies, stars, planets, dwarf planets, moons, asteroids, comets and meteoroids, and state the differences between a star, a planet and a moon.
- Compare the relative sizes of the Moon, the Earth, Jupiter, the Sun, a giant star and the Milky Way, using standard form.
- Distinguish between a meteoroid, a meteor and a meteorite.
- Convert between metres, astronomical units, light-years and parsecs, and calculate light-travel times.
- Explain stellar parallax and use d = 1 ÷ p to find the distance to a star.
- Evaluate why parallax works only for relatively nearby stars.
You met this before
- The Solar System: the Sun and eight planets in order — Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune — held in orbit by the Sun’s gravity (Year 2).
- The inner four planets are small and rocky; the outer four are giants made mostly of gas and ice (Year 3).
- Light travels at 3.00 × 10⁸ m/s in a vacuum, so distance = speed × time can turn a light-travel time into a distance.
- Standard form: 150 000 000 000 m is written 1.5 × 10¹¹ m; multiplying adds the powers of ten, dividing subtracts them.
- Stars produce their own light; planets and moons shine only by reflecting sunlight (Year 2).
Sunlight takes 500 s to reach the Earth. Calculate the Earth–Sun distance in metres, in standard form.
Reveal
distance = speed × time
distance = 3.00 × 10⁸ m/s × 500 s
distance = 1.50 × 10¹¹ m
This distance is so useful that it has its own name: one astronomical unit (AU).
Revise it in full: Year 2 · Unit 6 · Lesson 4 — The Solar System and gravity: eight planets, one rule · Year 3 · Physics · Unit 9 · Lesson 4 — The Solar System by the numbers · Year 2 · Unit 6 · Lesson 5 — Exploring space: rockets, satellites, telescopes
The puzzle
On a clear night in the Kalahari, look south and find the Southern Cross. Beside it are two bright “pointer” stars. The brighter one, Alpha Centauri, is 4.37 light-years away — 4.1 × 10¹⁶ m.
Nobody has ever been there. No probe has come close. Radar echoes are useless at that distance. So how can anyone know the number to three significant figures?
The answer is a long, thin triangle whose short side is the Earth–Sun distance and whose tip angle at the star is 0.747 arcseconds — the angle a 2 cm coin makes when you look at it from 5.5 km away. Measuring that angle is one of the great achievements of physics, and by the end of this lesson you will be able to do the calculation yourself.
Hold a finger at arm’s length and look at it with your left eye, then your right eye. It jumps against the background. Predict what happens to the size of the jump if you bring the finger halfway towards your face. Then predict what would happen to Alpha Centauri’s tiny shift if it were twice as far away.
Compare your answer
Closer finger, bigger jump; the jump roughly doubles when the distance halves. The shift is an angle, and the same baseline (the gap between your eyes) makes a larger angle at a nearer object.
A star twice as far away would show half the shift: 0.37 arcseconds instead of 0.747. The angle is inversely proportional to the distance — the rule this lesson turns into d = 1 ÷ p.
The science — structured notes
1.1 The cast: what is out there
Astronomers sort the natural objects in space by what they are made of, how they produce or reflect light, and what they orbit. The examiners ask you to name them and to tell them apart, so the definitions below need to be exact.
| Object | What it is | Example and size (diameter) |
|---|---|---|
| Galaxy | A huge system of billions of stars, gas and dust, held together by gravity | The Milky Way, about 100 000 light-years across (about 9 × 10²⁰ m) |
| Star | A massive, hot ball of gas that produces its own light by nuclear fusion in its core | The Sun, 1.39 × 10⁶ km; Betelgeuse, several hundred times wider |
| Planet | A large body that orbits a star, is massive enough for its own gravity to pull it into a round shape, and has cleared its orbit of other large objects; it reflects light | Jupiter, 1.40 × 10⁵ km; Earth, 1.27 × 10⁴ km |
| Dwarf planet | Orbits a star and is round, but has not cleared its orbit | Pluto, 2 380 km; Ceres, about 940 km |
| Moon (natural satellite) | A natural body that orbits a planet or dwarf planet | The Moon, 3 470 km; Jupiter’s Ganymede, 5 270 km |
| Asteroid | A rocky or metallic body orbiting the Sun, too small to be a planet; most lie between Mars and Jupiter | From metres to hundreds of kilometres |
| Comet | A small body of ice and dust from the outer Solar System; near the Sun it releases gas and dust in tails that point away from the Sun | Nucleus a few km; tails up to millions of km |
| Meteoroid | A small rock or grain travelling through space | Dust grain to about 1 m |
The definition of a planet was agreed by the International Astronomical Union in August 2006, which is why Pluto — round, but sharing its region with thousands of icy bodies — became a dwarf planet.
A student writes: “The Moon is a star because it is the brightest thing in the night sky, and the Sun is a planet because the Earth goes round it.”
Reveal answer
Two errors. The Moon is a natural satellite: it orbits the Earth and only reflects sunlight — brightness depends on distance, not on what an object is. The Sun is a star: it produces its own light by nuclear fusion in its core. Being orbited does not make something a planet; a planet is what does the orbiting.
1.2 Meteoroid, meteor, meteorite — and the asteroid that fell on Botswana
The three words describe one object at three stages. A meteoroid is a small rock travelling through space. When it enters the atmosphere at 11–72 km/s it compresses and heats the air in front of it so strongly that the air and the rock’s surface glow: the streak of light is a meteor (“shooting star”), usually 80–120 km above the ground.
Most meteoroids are grains of dust that vaporise completely. Any piece that survives and lands is a meteorite.
On 2 June 2018 a small asteroid, about two metres across and later named 2018 LA, was discovered by a telescope in Arizona only hours before it struck the atmosphere over Botswana. It became a fireball filmed by cameras in Botswana and South Africa. Weeks later a search team including scientists from Botswana found fragments in the Central Kalahari Game Reserve.
It was only the third asteroid ever spotted before hitting the Earth, and only the second whose fragments were then found on the ground.
“A meteor is a rock that has landed on the Earth’s surface.”
Reveal answer
False. A meteor is the streak of light in the sky — glowing air and vapour around a meteoroid entering the atmosphere. A rock that lands is a meteorite. In space, before it arrives, it is a meteoroid.
1.3 Units for enormous distances
Metres are the SI unit, but astronomical distances in metres need standard form and are hard to picture. Astronomers use three larger units.
| Unit | Definition | In metres | Used for |
|---|---|---|---|
| Astronomical unit (AU) | Mean Earth–Sun distance | 1.50 × 10¹¹ m | Distances inside the Solar System |
| Light-year (ly) | Distance light travels in a vacuum in one year | 9.46 × 10¹⁵ m | Distances to stars and galaxies |
| Parsec (pc) | Distance at which 1 AU makes an angle of one arcsecond (Section 1.5) | 3.09 × 10¹⁶ m = 3.26 ly | Professional astronomy; kpc and Mpc for galaxies |
(1) Calculate the length of one light-year in metres. (2) Proxima Centauri, the nearest star to the Sun, is 4.0 × 10¹⁶ m away. Express this in light-years.
(1) one year in seconds = 365.25 × 24 × 3600 s
one year = 3.156 × 10⁷ s
1 ly = speed of light × time
1 ly = 3.00 × 10⁸ m/s × 3.156 × 10⁷ s
1 ly = 9.47 × 10¹⁵ m (9.46 × 10¹⁵ m with c = 2.998 × 10⁸ m/s)
(2) distance in ly = 4.0 × 10¹⁶ m ÷ 9.46 × 10¹⁵ m
distance = 4.2 ly
Light leaving Proxima Centauri today will arrive in 2030 or 2031. You always see a star as it was, never as it is.
Neptune is 4.5 × 10¹² m from the Sun. Express this in AU and calculate how long sunlight takes to reach Neptune, in hours.
Reveal answer
distance in AU = 4.5 × 10¹² m ÷ 1.50 × 10¹¹ m
distance = 30 AU
time = distance ÷ speed
time = 4.5 × 10¹² m ÷ 3.00 × 10⁸ m/s
time = 1.5 × 10⁴ s
time = 1.5 × 10⁴ s ÷ 3600 s/h
time = 4.2 h
A radio command sent to a probe near Neptune takes over four hours to arrive, which is why deep-space probes must run themselves.
A teacher places a 30 cm ball in the middle of a school field in Gaborone to stand for the Sun. Using the same scale, calculate the size of the Earth, its distance from the “Sun”, and how far away Proxima Centauri would be. The Sun’s diameter is 1.39 × 10⁹ m.
scale factor = model size ÷ real size
scale factor = 0.30 m ÷ 1.39 × 10⁹ m
scale factor = 2.16 × 10⁻¹⁰
Earth: 1.27 × 10⁷ m × 2.16 × 10⁻¹⁰
Earth = 2.7 × 10⁻³ m, a 2.7 mm grain of sand
Earth–Sun: 1.50 × 10¹¹ m × 2.16 × 10⁻¹⁰
Earth–Sun = 32 m, across the field
Proxima: 4.0 × 10¹⁶ m × 2.16 × 10⁻¹⁰
Proxima = 8.6 × 10⁶ m
Proxima = 8 600 km
With the Sun as a football in Gaborone, the nearest star is another football further away than the whole length of Africa from Botswana to the Mediterranean. Space is mostly empty.
Select the list that is in order of increasing size: A Moon, Earth, Jupiter, Sun, Milky Way · B Earth, Moon, Sun, Jupiter, Milky Way · C Moon, Jupiter, Earth, Sun, Milky Way · D Moon, Earth, Sun, Jupiter, Milky Way.
Reveal answer
A. Moon 3 470 km, Earth 12 700 km, Jupiter 140 000 km, Sun 1 390 000 km, Milky Way about 9 × 10¹⁷ km. Each step is roughly a factor of 4 to 11, except the last: the Milky Way is over a hundred billion times wider than the Sun.
1.4 Galaxies: islands of stars
The Sun is one of roughly 100 to 400 billion stars in the Milky Way, a barred spiral galaxy about 100 000 light-years across and only about 1 000 light-years thick in the disc. We live about 26 000 light-years from its centre, where a black hole of about four million solar masses sits.
The whole disc rotates: the Sun takes roughly 230 million years to complete one orbit of the galactic centre. Gravity — the pull of all that matter on every star — keeps the stars from flying apart (Lesson 2).
Beyond the Milky Way are galaxies of every size. The nearest large one, the Andromeda Galaxy, is 2.5 million light-years away. From southern Africa you can see two small companion galaxies with the naked eye: the Large and Small Magellanic Clouds, about 160 000 and 200 000 light-years away. Deep images suggest the observable Universe holds hundreds of billions of galaxies or more.
The Moon looks as big in our sky as the Sun, yet the Sun’s diameter is 400 times larger. Explain how this is possible, and state what it tells you about the Sun’s distance compared with the Moon’s.
Reveal answer
How big something looks depends on the angle it makes at your eye, which is its size divided by its distance. The Sun is about 400 times wider than the Moon and also about 400 times further away (1.50 × 10¹¹ m against 3.84 × 10⁸ m), so the two angles are almost equal — about half a degree. That coincidence is why total solar eclipses are possible.
1.5 Parallax: a triangle to the stars
Parallax is the apparent shift in position of a nearby object against a distant background when it is viewed from two different places. For the stars, the two places are opposite sides of the Earth’s orbit, six months apart.
Photograph a nearby star in January and again in July. Against much more distant stars it appears to have moved by a small angle. The parallax angle p is half of that shift: the angle that the radius of the Earth’s orbit (1 AU) makes at the star.
Because p is tiny, the triangle is extremely long and thin, and tan p ≈ p in radians, so p = 1 AU ÷ d. Astronomers chose a unit that makes this as simple as possible: a star whose parallax angle is one arcsecond is at a distance of one parsec (“parallax second”).
d (in parsecs) = 1 ÷ p (in arcseconds)
d (in parsecs) = 1000 ÷ p (in milliarcseconds, mas)
(1) Show that one parsec is 3.09 × 10¹⁶ m. (2) Sirius, the brightest star in the night sky, has a parallax angle of 0.379 arcseconds. Calculate its distance in parsecs and in light-years.
(1) 1 arcsecond = 1 ÷ 3600 degree
1 arcsecond = 2.778 × 10⁻⁴ °
1 arcsecond = 4.848 × 10⁻⁶ rad
d = 1 AU ÷ tan p
d = 1.496 × 10¹¹ m ÷ 4.848 × 10⁻⁶
d = 3.086 × 10¹⁶ m, which rounds to 3.09 × 10¹⁶ m
(2) d = 1 ÷ p
d = 1 ÷ 0.379
d = 2.64 pc
in light-years: 2.64 × 3.26 ly
d = 8.6 ly
Check the logic: 0.379 is less than one arcsecond, so Sirius must be further than one parsec. Always ask whether the answer is bigger or smaller than 1 pc before you divide.
Barnard’s Star has a parallax angle of 547 mas. Calculate its distance in parsecs and in light-years.
Reveal answer
d = 1000 ÷ p (p in mas)
d = 1000 ÷ 547
d = 1.83 pc
d = 1.83 × 3.26 ly
d = 5.96 ly
It is the second-nearest star system to the Sun, after the three stars of Alpha Centauri.
A telescope in orbit around the Sun at the distance of Mars (1.52 AU) photographs the same star half a Mars year apart. Predict how the parallax angle it measures compares with the one measured from the Earth, and explain why the star’s distance has not changed.
Reveal answer
The half-baseline is 1.52 AU instead of 1 AU, so the angle is 1.52 times larger. The distance is a property of the star; only the triangle’s base changed.
The rule d = 1 ÷ p works only for a half-baseline of exactly 1 AU; with Mars you would use d = 1.52 ÷ p. A longer baseline gives a bigger, easier-to-measure angle — the reason astronomers dream of parallax telescopes far out in the Solar System.
1.6 Why parallax runs out
The further the star, the smaller the angle. A telescope on the ground, looking through the shimmering atmosphere, can measure positions to a few milliarcseconds at best, so its parallaxes become unreliable beyond a few hundred parsecs.
In space there is no atmosphere. The European Space Agency’s Gaia spacecraft (2013–2025) measured the positions of nearly two billion stars, with parallax uncertainties as small as about 0.02 mas for bright stars. Even so, most of the Milky Way — and every other galaxy — is too far for parallax. Lesson 5 shows how astronomers reach further, with “standard candles” and red-shift.
A ground telescope measures parallaxes with an uncertainty of ±5 mas. Explain, with two calculations, why it gives a useful distance for a star at 10 pc but not for a star at 500 pc.
Reveal answer
At 10 pc: p = 1000 ÷ 10
At 10 pc: p = 100 mas
percentage uncertainty = 5 ÷ 100 × 100 %
percentage uncertainty = 5 %
At 500 pc: p = 1000 ÷ 500
At 500 pc: p = 2 mas
percentage uncertainty = 5 ÷ 2 × 100 %
percentage uncertainty = 250 %
An uncertainty bigger than the angle itself means the star could be anywhere from about 140 pc (p = 7 mas) to “too far to tell”. A fixed absolute uncertainty becomes a larger and larger fraction as the angle shrinks.
Gaia measured the parallax of a bright star with an uncertainty of ±0.020 mas. Calculate the greatest distance at which Gaia’s parallax would still give the distance to within ±10 %, and compare it with the Sun’s distance from the galactic centre (8.2 kpc).
Reveal answer
For a ±10 % uncertainty, 0.020 mas must be 10 % of p.
p = 0.020 mas ÷ 0.10
p = 0.20 mas
d = 1000 ÷ p
d = 1000 ÷ 0.20
d = 5 000 pc = 5 kpc
That is about 60 % of the way to the galactic centre: a huge advance on the few hundred parsecs possible from the ground, but still only a corner of our own galaxy. (For fainter stars Gaia’s uncertainty was larger, so the reach was shorter.)
Try it — measuring parallax angles in a simulated sky
In the lab a telescope photographs a nearby star against the distant background twice — six months apart — and measures the apparent shift. You choose stars placed at known distances from 1 to 20 parsecs (the independent variable) and read the parallax angle in milliarcseconds (the dependent variable). The point is to test, with real processing, the geometry astronomers then use in reverse: measure p, work out d.
Common mistakes to avoid
- “A star is bigger than a planet” as the only difference. Give the physics: produces its own light, by nuclear fusion; far more massive and hotter.
- Mixing up meteoroid, meteor and meteorite. In space, the streak of light, on the ground.
- Treating the light-year as a time. It is a distance: 9.46 × 10¹⁵ m.
- Dividing the wrong way. d = 1 ÷ p, so a parallax smaller than 1″ gives a distance greater than 1 pc.
- Using mas in d = 1 ÷ p. Convert to arcseconds (÷ 1000) or use d = 1000 ÷ p.
- Calling p the whole shift. The total apparent shift over six months is 2p.
- Standard-form slips. 4.0 × 10¹⁶ ÷ 9.46 × 10¹⁵ is 4.2, not 0.42 or 42: estimate first (40 ÷ 9.5 ≈ 4).
- “The star moves.” The Earth moves; the star’s shift is apparent.
Study smart: how this is examined
Study routine. Today: write the object table from memory and draw the parallax triangle with p, 1 AU and d labelled. In two days: redo the light-year, Sirius and scale-model EXAMPLES with the notes closed, estimating each answer before calculating. In a week: run the lab as a full investigation, plot p against 1 ÷ d, and take the quiz.
How we found out — three centuries of chasing an angle
If the Earth goes round the Sun, the stars should show parallax. The ancient Greeks knew this, and because they could see no shift, most concluded that the Earth stood still. The alternative — that the stars were unimaginably far away — seemed absurd. Copernicus (1543) took the absurd option.
Measuring the Solar System came first. In 1672 Giovanni Cassini in Paris and Jean Richer in French Guiana observed Mars at the same time from two ends of a baseline across the Atlantic. The small parallax of Mars gave the scale of the Solar System, and an Earth–Sun distance within about 10 % of today’s value.
The stars held out for another 166 years. Telescopes improved; astronomers chased the angle and kept finding nothing reliable. Then, within about two years, three astronomers succeeded. In 1838 Friedrich Bessel in Königsberg published a parallax of about 0.31″ for the star 61 Cygni, a distance of about 10 light-years.
Thomas Henderson, working at the Royal Observatory at the Cape of Good Hope in 1832–33, had measured Alpha Centauri, but did not publish until 1839. Friedrich Struve measured Vega. Suddenly the stars had distances, and they were light-years away, just as Copernicus required.
By 1900 fewer than a hundred stellar parallaxes had been measured reliably. The Hipparcos satellite (1989–1993) measured about 118 000. Gaia, launched in December 2013, measured nearly two billion before it stopped observing in January 2025, turning parallax from a heroic single measurement into a map of our corner of the galaxy.
The Greeks’ failure to see stellar parallax was real evidence. Explain what it actually showed, and why it was reasonable at the time to draw the wrong conclusion from it.
Reveal answer
It showed that, if the Earth moves, the stars must be so far away that their parallax angles are smaller than the naked eye can detect (about one arcminute). Both “the Earth is still” and “the stars are very far away” explained the data.
With no telescopes and no way to test either idea, choosing the one that fitted everyday experience was reasonable. The question was settled only when instruments became precise enough — a reminder that “no effect seen” can mean “effect too small for our instrument”.
Where it is used now
- Planetary defence. Survey telescopes scan the sky every night for near-Earth asteroids; the 2018 LA fireball over Botswana was predicted hours in advance. NASA’s DART spacecraft deliberately struck the small asteroid Dimorphos in September 2022 and shortened its orbit around its companion by about half an hour.
- Meteorite science in southern Africa. Meteorites preserve material from the birth of the Solar System. Botswana’s own 2018 fragments, and the famous Hoba meteorite in Namibia — at about 60 tonnes the largest known single meteorite — are studied for their chemistry.
- Navigation. Star-tracker cameras on satellites recognise star patterns to fix the spacecraft’s orientation, using star catalogues whose positions and distances come from Hipparcos and Gaia.
- Calibrating the Universe. Every distance to a galaxy rests on a “ladder” whose first rung is parallax: nearby stars of known type, measured by parallax, calibrate the brightness of similar stars far away.
- Southern African astronomy. The South African Astronomical Observatory at Sutherland, home of the Southern African Large Telescope (SALT), continues the tradition begun at the Cape, where Henderson measured Alpha Centauri.
Science now — and the scientist you need to be
What is happening in 2026
Astronomy has become a data science. Gaia stopped observing in January 2025, and its team is preparing the next data release, expected around the end of 2026, from more than ten years of measurements. Its catalogue already underpins almost every study of stars in the Milky Way.
In Chile, the Vera C. Rubin Observatory released its first images in 2025 and is starting a ten-year survey of the southern sky. It photographs the whole visible sky every few nights and is expected to discover millions of new asteroids, so software — including machine-learning classifiers — must sort millions of alerts each night.
ESA’s Hera spacecraft, launched in October 2024, is travelling to the asteroid Dimorphos to study the crater and changed orbit left by DART. Careers here range from software engineering and data analysis to instrument design and planetary geology.
The mindshift
What you need to be able to do
Name and define each kind of object, and give the physics that separates a star from a planet. Handle standard form confidently, with a rough estimate before every calculation. Convert between m, AU, ly and pc. Use d = 1 ÷ p, and explain why a fixed measuring uncertainty limits parallax to nearby stars.
See an example
Example values: Sirius 379 mas gives 2.64 pc (8.6 ly); Canopus about 10.6 mas gives about 94 pc (about 310 ly); Achernar about 23 mas gives about 43 pc (about 140 ly).
For Alpha Centauri A, p ≈ 747 mas gives 1.34 pc, or 4.37 ly. If an assistant answers “4.2 light-years”, it has probably given Proxima Centauri instead — a different star of the same system. Checking the calculation catches that.
Key terms
| Galaxy | A huge system of billions of stars, gas and dust held together by gravity; ours is the Milky Way. |
| Star | A massive ball of hot gas that produces its own light by nuclear fusion in its core. |
| Planet | A large, round body orbiting a star that has cleared its orbit; it reflects light. |
| Moon (natural satellite) | A natural body orbiting a planet or dwarf planet. |
| Asteroid | A rocky or metallic body orbiting the Sun, smaller than a planet. |
| Meteoroid · meteor · meteorite | A small rock in space · the streak of light as it enters the atmosphere · the piece that reaches the ground. |
| Astronomical unit (AU) | The mean Earth–Sun distance, 1.50 × 10¹¹ m. |
| Light-year (ly) | The distance light travels in a vacuum in one year, 9.46 × 10¹⁵ m. |
| Parallax | The apparent shift of a nearby object against a distant background when viewed from two positions. |
| Parallax angle (p) | Half the apparent shift of a star over six months; the angle 1 AU subtends at the star. |
| Parsec (pc) | The distance at which p is one arcsecond: 3.09 × 10¹⁶ m, or 3.26 ly; d (pc) = 1 ÷ p (arcseconds). |
Think like a scientist
Criterion A Use your knowledge in an unfamiliar situation. An astronomy club in Maun keeps a log. Entry 1: “A bright streak crossed the sky from west to east in about one second, then faded.” Entry 2: “Through the telescope, a star near the Southern Cross appears in a slightly different place against the fainter background stars in March and in September.”
Entry 3: “A news report says a 3 m object will pass the Earth at 1.2 × 10⁶ km next month.”
(a) Identify what the club saw in Entry 1, and explain why it glowed. [3]
(b) State the name of the 3 m object while it is in space, and what it would be called if a piece landed near Maun. [2]
(c) Calculate the passing distance in Entry 3 as a multiple of the Earth–Moon distance (3.84 × 10⁵ km) and in light-seconds. [3]
(d) The club measures the total shift in Entry 2 as 0.40 arcseconds. Calculate the star’s distance in parsecs and light-years. [3]
(e) Explain why the club’s two observations had to be about six months apart, and why the measured shift is apparent rather than real. [2]
Model answer
(a) A meteor [1]. A meteoroid entered the atmosphere at many kilometres per second [1]; it compressed and heated the air in front of it, so the air and the vaporising surface of the rock glowed, about 80–120 km up [1]. (“It caught fire from friction” alone scores 1.)
(b) In space: a meteoroid — a small asteroid, since it is 3 m across (either accepted) [1]. On the ground: a meteorite [1].
(c)
multiple = 1.2 × 10⁶ km ÷ 3.84 × 10⁵ km
multiple = 3.1 times the Earth–Moon distance [1]
time = distance ÷ speed
time = 1.2 × 10⁹ m ÷ 3.00 × 10⁸ m/s [1]
time = 4.0 light-seconds [1]
(d)
p = total shift ÷ 2
p = 0.40″ ÷ 2
p = 0.20″ [1]
d = 1 ÷ p
d = 1 ÷ 0.20
d = 5.0 pc [1]
d = 5.0 × 3.26 ly
d = 16 ly [1]
(Using 0.40″ directly gives 2.5 pc and scores 1 of the 3, for the method.)
(e) Six months apart, the Earth is on opposite sides of its orbit, giving the largest possible baseline of 2 AU and so the largest shift [1]. The star has not moved; the observer has, so the direction to the star changes relative to much more distant background stars [1].
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
Outline two differences between a star and a planet.
Reveal answer
A star produces its own light, while a planet only reflects light [1]. A star is powered by nuclear fusion in its core; a planet is not — or: a star is far more massive and much hotter [1]. (“The Sun is a star” scores 0.)
State one natural object, other than the Sun and the planets, that forms part of the Solar System, and state one difference between a moon and a planet.
Reveal answer
Any one of: a moon, asteroid, comet or dwarf planet [1] (not a satellite or a rocket — they are human-made). A moon orbits a planet, while a planet orbits a star [1].
Proxima Centauri is 4.0 × 10¹⁶ m away. Calculate this distance in light-years and in parsecs (1 ly = 9.46 × 10¹⁵ m; 1 pc = 3.09 × 10¹⁶ m).
Reveal answer
d = 4.0 × 10¹⁶ m ÷ 9.46 × 10¹⁵ m
d = 4.2 ly [1]
d = 4.0 × 10¹⁶ m ÷ 3.09 × 10¹⁶ m
d = 1.3 pc [1]
Two significant figures, matching the data [1].
Suggest one advantage and one disadvantage of astronomers using the parsec rather than the metre.
Reveal answer
Advantage: distances become small, simple numbers (1.3 pc instead of 4.0 × 10¹⁶ m), with less need for standard form, and d = 1 ÷ p links it directly to the measured angle [1].
Disadvantage: it is not an SI unit, so it must be converted before use in equations with other SI quantities, and people outside astronomy are unfamiliar with it [1].
Describe what happens to a meteoroid from the moment it enters the Earth’s atmosphere, using the words meteor and meteorite correctly.
Reveal answer
It enters the atmosphere at a high speed (tens of km/s) and compresses and heats the air in front of it [1]. The hot, glowing air and vaporised rock form a streak of light, a meteor, usually 80–120 km up [1]. Most meteoroids vaporise completely; any piece that survives and reaches the ground is a meteorite [1].
A star has a parallax angle of 0.10 arcseconds. Calculate its distance in parsecs, light-years and metres.
Reveal answer
d = 1 ÷ p
d = 1 ÷ 0.10
d = 10 pc [1]
d = 10 × 3.26 ly
d = 33 ly [1]
d = 10 × 3.09 × 10¹⁶ m
d = 3.1 × 10¹⁷ m [1]
7. In a scale model the Earth is a 1.0 cm marble. The Earth’s diameter is 1.27 × 10⁴ km. Calculate the model diameter of the Sun (1.39 × 10⁶ km), the model Earth–Sun distance (1.50 × 10⁸ km) and the model distance to Proxima Centauri (4.0 × 10¹³ km). Comment on whether such a model could be built.
Reveal answer
scale = 1.0 cm ÷ 1.27 × 10⁴ km
scale = 7.87 × 10⁻⁵ cm per km [1]
Sun = 1.39 × 10⁶ km × 7.87 × 10⁻⁵ cm/km
Sun = 109 cm, about 1.1 m [1]
Earth–Sun = 1.50 × 10⁸ × 7.87 × 10⁻⁵
Earth–Sun = 1.18 × 10⁴ cm
Earth–Sun = 118 m [1]
Proxima = 4.0 × 10¹³ × 7.87 × 10⁻⁵
Proxima = 3.1 × 10⁹ cm
Proxima = 31 000 km
The Sun and Earth fit on a sports field, but the nearest star would be about 31 000 km away — over three-quarters of the way round the Earth. No single model can show sizes and star distances to one scale [1].
8. A student takes the two photographs of a star only three months apart, when the Earth has moved a quarter of its orbit, then halves the measured shift and uses d = 1 ÷ p. The star is really at 5.0 pc. Calculate the distance the student obtains and the percentage error, and state whether this is a random or a systematic error.
Reveal answer
A quarter of the orbit is a chord of √2 AU = 1.41 AU, so the half-baseline is 0.707 AU instead of 1 AU [1].
p measured = 0.707 ÷ 5.0
p measured = 0.141″
d calculated = 1 ÷ 0.141
d = 7.1 pc [1]
percentage error = (7.1 − 5.0) ÷ 5.0 × 100 %
percentage error = +41 % [1]
Systematic: every star measured this way gives a distance 1.41 times too large, in the same direction; repeating the measurement does not reduce it [1].
Summary
- Galaxy → star → planet → moon: a star makes its own light by nuclear fusion; planets orbit stars and moons orbit planets, both only reflecting light. Asteroids and comets are small bodies orbiting the Sun.
- Meteoroid (in space) → meteor (the streak of light in the atmosphere) → meteorite (the piece that lands).
- Relative sizes: Moon 3 470 km, Earth 12 700 km, Jupiter 140 000 km (11 Earths), Sun 1.39 × 10⁶ km (109 Earths), Milky Way about 100 000 ly.
- 1 AU = 1.50 × 10¹¹ m
- 1 ly = 9.46 × 10¹⁵ m
- 1 pc = 3.09 × 10¹⁶ m = 3.26 ly
- Parallax: a nearby star shifts against distant stars as the Earth orbits; p is half the six-month shift; d (pc) = 1 ÷ p (arcseconds). A fixed measuring uncertainty limits parallax to relatively nearby stars.
Next time → Gravitation: why the same force holds the Moon to the Earth, the planets to the Sun and the stars in the galaxy, Newton law of universal gravitation with its inverse square, and how satellites stay up without engines.