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Physics · 6 Space physics

6.2.2 Stars

Before you start

  • Using distance = speed × time, and rearranging it to find the time (1.2).
  • Light, like every electromagnetic wave, travels at 3.0×108 m/s in a vacuum (3.3).
  • Writing and calculating with numbers in standard form, such as 9.5×1015.
  • Stable stars are powered by the nuclear fusion of hydrogen into helium, which releases energy (6.2.1).
  • Gravitational attraction pulls masses towards each other (6.1.2).
  • Balanced forces are equal in size and opposite in direction, so there is no resultant force (1.5.1).
Syllabus objectives covered (3)
  • State that: (a) galaxies are each made up of many billions of stars (b) the Sun is a star in the galaxy known as the Milky Way (c) other stars that make up the Milky Way are much further away from the Earth than the Sun is from the Earth (d) astronomical distances can be measured in light-years, where one light-year is the distance travelled in (the vacuum of) space by light in one year
  • Know that one light-year is equal to 9.5 × 1015 m
  • Describe the life cycle of a star: (a) a star is formed from interstellar clouds of gas and dust that contain hydrogen (b) a protostar is an interstellar cloud collapsing and increasing in temperature as a result of its internal gravitational attraction (c) a protostar becomes a stable star when the inward force of gravitational attraction is balanced by an outward force due to the high temperature in the centre of the star (d) all stars eventually run out of hydrogen as fuel for the nuclear reaction (e) most stars expand to form red giants and more massive stars expand to form red supergiants when most of the hydrogen in the centre of the star has been converted to helium (f) a red giant from a less massive star forms a planetary nebula with a white dwarf star at its centre (g) a red supergiant explodes as a supernova, forming a nebula containing hydrogen and new heavier elements, leaving behind a neutron star or a black hole at its centre (h) the nebula from a supernova may form new stars with orbiting planets

Part 1 of 7

Stars, galaxies and the Milky Way

  1. A star is a huge ball of hot gas in space that gives out its own light. The Sun is a star. It is the nearest star to the Earth.
  2. Stars are not spread evenly through space. They are grouped into enormous collections called galaxies. Each galaxy is made up of many billions of stars.
  3. The Sun is one of the stars in a galaxy called the Milky Way.
  4. Get the order of size right before you go on. The Earth is one planet orbiting one star, the Sun. The Sun is one of many billions of stars in one galaxy, the Milky Way.
  5. The other stars that make up the Milky Way are much further away from the Earth than the Sun is. Light from the Sun reaches the Earth in about 8 minutes. Light from the next nearest star takes more than 4 years.
  6. This is why the Sun looks so much bigger and brighter than every other star. It is only a medium-sized star (6.2.1). It looks special because it is so close to us, not because it is a different kind of object.
  7. When you state these facts, keep the scale words from the objective: many billions of stars, and much further away. 'Galaxies are made of stars' and 'other stars are further away' leave out the part that makes each statement worth learning.

Part 2 of 7

The light-year: a distance, not a time

  1. Distances to the stars are so large that metres and kilometres give clumsy numbers. Astronomers measure them in a much bigger unit, the light-year.
  2. One light-year is the distance travelled in (the vacuum of) space by light in one year. Learn this sentence as it stands.
  3. The trap is the word 'year'. It makes the light-year sound like a time, but it is a distance. It tells you how far, never how long. A time is used only to fix the distance, in the same way that 'an hour's drive' describes how far away a town is.
  4. Why does the definition say 'in space'? In a vacuum, light always travels at the same speed, 3.0×108 m/s. So the distance it covers in one year is always the same, and the unit is fixed.
  5. This gives a useful link. Light travels one light-year in one year. So if a star is 10 light-years away, its light has taken 10 years to reach you. The light you see tonight left that star 10 years ago.
  6. Use the link in both directions. A distance of n light-years means the light took n years. Light that took n years to arrive came from n light-years away.

Part 3 of 7

One light-year in metres

  1. You need to know that one light-year is 9.5×1015 m. Paper 4 has no data sheet, so learn this value. If a question gives you a value, use the one in the question.
  2. In the syllabus list the value may be printed as '9.5 × 1015 m'. The 15 is a power of ten. The value is 9.5×1015 m, nine and a half thousand million million metres.
  3. You do not have to take the number on trust. A light-year is the distance light travels in one year, so it comes from distance = speed × time.
    d=v×t
  4. The speed of light is in metres per second, so the time must be in seconds. Convert one year: days, then hours, then minutes, then seconds.
    t=365×24×60×60=31536000 s≈3.15×107 s
  5. Multiply by the speed of light, 3.0×108 m/s.
    d=3.0×108×31536000=9.46×1015 m≈9.5×1015 m
  6. Now the two conversions. Light-years to metres: multiply by 9.5×1015. Metres to light-years: divide by 9.5×1015.
  7. Check the direction with size. One light-year is a huge number of metres, so the same distance is always a much bigger number in metres than in light-years. If your number of light-years comes out bigger than your number of metres, you used the wrong operation: going to light-years you must divide, going to metres you must multiply.
  8. A calculator trap when you divide. Typing 5.7×1016÷9.5×1015 straight in divides by 9.5 and then multiplies by 1015, which is wrong. Put brackets round 9.5×1015, or enter it with the EXP or ×10x key.

Part 4 of 7

How a star forms: from cloud to protostar

  1. A star starts as an interstellar cloud of gas and dust: a huge, thin, cold cloud in the space between stars. The gas in it contains hydrogen. That hydrogen will later be the star's fuel.
  2. Every particle in the cloud attracts every other particle by gravity. This is the cloud's own internal gravitational attraction. The cloud pulls itself together.
  3. So the cloud collapses. It gets smaller and denser, with more and more matter crowded towards its centre.
  4. As the particles fall inwards they speed up. Faster particles mean a higher temperature, so the collapsing cloud increases in temperature.
  5. A collapsing interstellar cloud that is heating up in this way is a protostar. The definition has two parts, collapsing and increasing in temperature, and one cause for both: the cloud's internal gravitational attraction.
  6. Name the cause when you explain a protostar. It heats up because it collapses under its own gravity. 'It gets hot' without the collapse and the gravity gives no reason at all.

Part 5 of 7

A stable star: two forces in balance

  1. As the protostar keeps collapsing, its centre gets hotter and hotter. Once the centre is hot enough, hydrogen nuclei fuse to form helium and release energy (6.2.1). That energy keeps the centre of the star very hot.
  2. Two forces now act on the material of the star. Inward: the gravitational attraction of the star's own mass, which still pulls everything towards the centre.
  3. Outward: a force due to the high temperature in the centre of the star. The gas there is so hot that its particles move very fast, and the gas pushes outwards strongly.
  4. When the inward force of gravitational attraction is balanced by the outward force due to the high temperature, the star stops collapsing. It is now a stable star, and it stays the same size.
    forces diagram — not drawn yet

    A large circle labelled 'star' with a small shaded circle at its centre labelled 'very hot centre'; at four points on the edge of the large circle (top, bottom, left, right) a pair of arrows of equal length starts at the same point: one points inwards towards the centre, labelled 'inward force: gravitational attraction', and one points outwards away from the centre, labelled 'outward force: due to high temperature in the centre'.

    At each point the inward and outward arrows are the same length. The forces are balanced, so the star neither collapses nor expands.
  5. Balanced means equal in size and opposite in direction, as for any object with no resultant force (1.5.1). It does not mean that no forces act. Two large forces act all the time, and they cancel.
  6. A star spends most of its life as a stable star, fusing hydrogen into helium in its centre. The Sun is a stable star now.
  7. When you explain why a stable star stays the same size, name both forces and say they are balanced. 'Gravity is balanced' on its own does not say what it is balanced by.

Part 6 of 7

Running out of hydrogen: red giants and red supergiants

  1. Fusion uses up hydrogen. All stars eventually run out of hydrogen as fuel for the nuclear reaction.
  2. The change comes when most of the hydrogen in the centre of the star has been converted to helium. The star then stops being a stable star and expands.
  3. Its outer layers become much larger and cooler, so the star glows red. What it becomes depends on its mass.
  4. Most stars, including the Sun, expand to form a red giant.
  5. More massive stars expand to form a red supergiant, which is even larger than a red giant.
  6. Keep the trigger exact. The star expands when most of the hydrogen in its centre has been converted to helium. 'When the star gets old' says when, but not why.
  7. From here the life cycle has two paths. The mass of the star decides which one it takes, so always check whether a question is about a star like the Sun or a much more massive star.

Part 7 of 7

How stars end, and how new ones begin

  1. Both paths start the same way.
    cloud of gas and dust→protostar→stable star
  2. The less massive path. A red giant from a less massive star forms a planetary nebula with a white dwarf star at its centre. This is how the Sun will end.
    red giant→planetary nebula+white dwarf
  3. The planetary nebula is the outer layers of the red giant, drifting away into space as a glowing shell of gas. The name comes from how these clouds looked through early telescopes. They have nothing to do with planets.
  4. The white dwarf is the hot core that is left behind. It is small and very dense, it no longer fuses hydrogen, and it slowly cools.
  5. The more massive path. A red supergiant explodes as a supernova.
    red supergiant→supernova→nebula+neutron star or black hole
  6. The explosion throws the star's outer material into space. It forms a nebula containing hydrogen and new heavier elements. The heavier elements were made by nuclear reactions in the star and in the explosion.
  7. At the centre of the nebula a neutron star or a black hole is left behind. A neutron star is extremely dense. A black hole has gravity so strong that not even light can escape from it. Which one is left depends on the mass of the core that remains; you only need to know that it is one or the other.
  8. The cycle starts again. The nebula from a supernova is a cloud of gas and dust that contains hydrogen. Like the first cloud, it can collapse under its own gravity, so it may form new stars with orbiting planets.
  9. This links to how the Solar System formed (6.1.2): the cloud it came from contained many elements, not only hydrogen. Elements such as carbon and oxygen in the Earth were made in earlier stars.
  10. Keep the pairs together, because each ending belongs to one path only. Red giant goes with planetary nebula and white dwarf. Red supergiant goes with supernova, then neutron star or black hole. A white dwarf after a supernova, or a black hole for the Sun, is wrong physics.

Worked examples

Example 1. Light travels through space at 3.0×108 m/s. Calculate the distance, in metres, that light travels through space in one year. Take one year to be 365 days. Compare your answer with the value of one light-year that you need to know.

Show the working
  1. A light-year is a distance, so use distance = speed × time. The speed is in metres per second, so you need the time in seconds.
    d=v×t
  2. Convert one year to seconds. Multiply the days by 24 hours, then by 60 minutes, then by 60 seconds.
    t=365×24×60×60=31536000 s
  3. Multiply the speed by the time. Keep the full time in your calculator, so that you round only once, at the end.
    d=3.0×108×31536000=9.46×1015 m
  4. Round to two significant figures, the same as the speed you were given: 9.5×1015 m. That is the value of one light-year. A year of 365.25 days gives 9.47×1015 m, which is also 9.5×1015 m to two significant figures.

Answer: 9.46×1015 m, which is 9.5×1015 m to two significant figures: the same as one light-year.

Example 2. Star A is 12 light-years from the Earth. Star B is 2.66×1017 m from the Earth. (a) Calculate the distance from the Earth to star A in metres. (b) Calculate the distance from the Earth to star B in light-years. (c) Deduce which star is further away, and how long light from star B has taken to reach the Earth.

Show the working
  1. (a) Light-years to metres. Each light-year is 9.5×1015 m, so multiply.
    12×9.5×1015=1.14×1017 m
  2. Check the size: the number of metres is far bigger than the number of light-years, as it must be. To two significant figures this is 1.1×1017 m.
  3. (b) Metres to light-years. Divide by the number of metres in one light-year. Put brackets round 9.5×1015 on your calculator, or use the EXP key, so you divide by the whole number.
    2.66×10179.5×1015=28 light-years
  4. (c) Compare the two distances in the same unit. Star A is 12 light-years away and star B is 28 light-years away, so star B is further away.
  5. Light travels one light-year in one year. So light from star B, 28 light-years away, has taken 28 years to reach the Earth.

Answer: (a) 1.1×1017 m (1.14×1017 m). (b) 28 light-years. (c) Star B is further away; its light has taken 28 years to reach the Earth.

Example 3. The Sun is 1.5×1011 m from the Earth. The nearest star to the Earth after the Sun is about 4.2 light-years away. Light travels at 3.0×108 m/s. (a) Calculate the time light takes to travel from the Sun to the Earth. (b) Calculate the distance from the Earth to the nearest star in metres. (c) Calculate how many times further from the Earth the nearest star is than the Sun is.

Show the working
  1. (a) Rearrange distance = speed × time to make time the subject: divide the distance by the speed.
    t=dv=1.5×10113.0×108=500 s
  2. 500 s is 500÷60=8.3 minutes. Light from the Sun reaches the Earth in about 8 minutes.
  3. (b) Light-years to metres: multiply by 9.5×1015.
    4.2×9.5×1015=3.99×1016 m≈4.0×1016 m
  4. (c) 'How many times further' means divide the larger distance by the smaller one. Both are in metres, so the units cancel and the answer is just a number.
    3.99×10161.5×1011=2.66×105≈2.7×105
  5. So even the nearest of the other stars is more than a quarter of a million times further away than the Sun. Its light takes about 4.2 years to reach us; the Sun's takes about 8 minutes. That is what 'much further away' means.

Answer: (a) 500 s (about 8.3 minutes). (b) 4.0×1016 m. (c) About 2.7×105 times (no unit).

Example 4. A star forms that has a much greater mass than the Sun. Describe the life cycle of this star, from the cloud it forms from to what is left at the end.

Show the working
  1. Work through the stages in order. Give each stage its own sentence, and give the cause wherever the objective names one.
  2. Formation: the star forms from an interstellar cloud of gas and dust that contains hydrogen.
  3. Protostar: the cloud collapses because of its own internal gravitational attraction, and its temperature increases. This collapsing, heating cloud is a protostar.
  4. Stable star: the protostar becomes a stable star when the inward force of gravitational attraction is balanced by the outward force due to the high temperature in its centre.
  5. Running out: the star uses hydrogen as fuel for the nuclear reaction. When most of the hydrogen in its centre has been converted to helium, it expands. This star is massive, so it forms a red supergiant, not a red giant.
  6. End: the red supergiant explodes as a supernova. This forms a nebula containing hydrogen and new heavier elements, and leaves a neutron star or a black hole at its centre.
  7. What comes next: the nebula from the supernova may form new stars with orbiting planets.

Answer: Interstellar cloud of gas and dust containing hydrogen → collapses and heats up because of its own gravitational attraction (protostar) → stable star when the inward gravitational force is balanced by the outward force due to the high temperature in the centre → most of the hydrogen in the centre is converted to helium → expands to form a red supergiant → explodes as a supernova → nebula of hydrogen and new heavier elements, with a neutron star or a black hole at its centre → the nebula may form new stars with orbiting planets.

Where people go wrong

Mistake: Writing that a light-year is a unit of time, or 'the time light takes to travel for a year'.

Instead: A light-year is a distance: the distance travelled in (the vacuum of) space by light in one year.

The year is there only to fix how far the light goes. The quantity is how far, so its value is in metres: 9.5×1015 m.

Mistake: Converting metres to light-years by multiplying by 9.5×1015.

Instead: Divide metres by 9.5×1015 to get light-years. Multiply light-years by 9.5×1015 to get metres.

Each light-year is 9.5×1015 metres, so any distance is a far smaller number in light-years than in metres. If the light-years come out bigger, the conversion went the wrong way.

Mistake: Explaining that a protostar heats up 'because of nuclear fusion'.

Instead: A protostar increases in temperature because it is collapsing under its own internal gravitational attraction.

The objective gives gravity as the cause. The hydrogen fusion that powers a stable star begins once the centre has become hot enough.

Mistake: Saying the Sun will explode as a supernova or end as a black hole.

Instead: The Sun will expand to form a red giant, which then forms a planetary nebula with a white dwarf at its centre.

Only more massive stars form red supergiants and explode as supernovas. The Sun is a medium-sized star, so it follows the red giant path.

Mistake: Thinking that a planetary nebula contains planets or is made from planets.

Instead: A planetary nebula is the outer layers of a red giant, spread out as a shell of gas around a white dwarf.

The name comes from how these clouds looked through early telescopes. In this objective, it is the nebula from a supernova that may form new stars with orbiting planets.

Check yourself

  1. State what a galaxy is made up of, and name the galaxy that contains the Sun.
    AnswerA galaxy is made up of many billions of stars. The Sun is in the Milky Way.
  2. The Sun is a medium-sized star, but it looks far bigger and brighter than any other star. Explain why.
    AnswerThe other stars of the Milky Way are much further away from the Earth than the Sun is. The Sun is so much closer that it looks much bigger and brighter.
  3. A student writes: 'A light-year is the time it takes light to travel a very long way.' Identify what is wrong, and give the correct definition.
    AnswerA light-year is a distance, not a time. It is the distance travelled in (the vacuum of) space by light in one year.
  4. A star is 8.0 light-years from the Earth. Calculate its distance from the Earth in metres.
    Answer8.0×9.5×1015=7.6×1016 m.
  5. A star is 5.7×1016 m from the Earth. Calculate its distance in light-years, and deduce how long its light takes to reach the Earth.
    Answer(5.7×1016)÷(9.5×1015)=6.0 light-years, so its light takes 6.0 years to reach the Earth.
  6. Explain why a protostar increases in temperature.
    AnswerIt is an interstellar cloud collapsing because of its own internal gravitational attraction. As it collapses, its particles speed up, so its temperature increases.
  7. State the two forces that are balanced in a stable star, and give the direction of each.
    AnswerThe force of gravitational attraction, acting inwards, and the force due to the high temperature in the centre of the star, acting outwards.
  8. Describe what happens after a red supergiant explodes as a supernova.
    AnswerA nebula forms that contains hydrogen and new heavier elements, with a neutron star or a black hole left at its centre. The nebula may later form new stars with orbiting planets.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. The Sun is a star. The distance from the Earth to the Sun is 1.5×1011 m. Star Q is in the same galaxy as the Sun. Star Q is 3.8×1017 m from the Earth.

(a) State the name of the galaxy that the Sun is in. 1 mark No calculator

Mark scheme
  • B1 the Milky Way

(b) Define the light-year. 1 mark No calculator

Mark scheme
  • B1 the distance travelled by light in (the vacuum of) space in one year; must be a distance: 'the time light takes to …' scores 0

(c) Calculate the distance from the Earth to star Q in light-years. 2 marks

Mark scheme
  • C1 (3.8 × 10¹⁷) ÷ (9.5 × 10¹⁵) seen, or time = (3.8 × 10¹⁷) ÷ (3.0 × 10⁸) = 1.27 × 10⁹ s then ÷ (3.15 × 10⁷ s in a year), or any correct equivalent method
  • A1 40 light-years; accept 40.1 or 40.2 light-years from a calculated value of the light-year; unit required

(d) Calculate how many times further from the Earth star Q is than the Sun is. 2 marks

Mark scheme
  • C1 (3.8 × 10¹⁷) ÷ (1.5 × 10¹¹) seen
  • A1 2.5 × 10⁶ (2.53 × 10⁶); no unit

(e) Deduce how long the light from star Q has taken to reach the Earth. 1 mark No calculator

Mark scheme
  • B1 40 years; ecf from (c), the same number of years as light-years

Question 2. A star forms from an interstellar cloud of gas and dust. The star that forms has a much greater mass than the Sun.

(a) State the element that the cloud must contain for a star to form from it. 1 mark No calculator

Mark scheme
  • B1 hydrogen

(b) The cloud collapses to form a protostar. Explain why the cloud collapses and why its temperature increases. 2 marks No calculator

Mark scheme
  • B1 the (internal) gravitational attraction of the cloud / between its particles pulls it inwards
  • B1 temperature increases because the cloud is collapsing / because its particles speed up as they fall inwards, owtte; 'the temperature increases' with no cause is insufficient

(c) The protostar becomes a stable star. Explain why a stable star does not change in size. 2 marks No calculator

Mark scheme
  • B1 inward force of gravitational attraction (gravity)
  • B1 is balanced by / equal and opposite to an outward force due to the high temperature in the centre of the star

(d) Describe what happens to this star after most of the hydrogen in its centre has been converted to helium. 4 marks No calculator

Mark scheme
  • B1 expands to form a red supergiant; 'red giant' alone is insufficient
  • B1 explodes as a supernova
  • B1 forming a nebula containing hydrogen and (new) heavier elements
  • B1 leaving a neutron star or a black hole at its centre; accept either one named alone; white dwarf or planetary nebula as the end of this star is CON

Question 3. The Sun is a stable star of medium size.

(a) Predict what will happen to the Sun when most of the hydrogen in its centre has been converted to helium. 1 mark No calculator

Mark scheme
  • B1 it expands to form a red giant; 'red supergiant' or 'supernova' scores 0

(b) Describe what the red giant formed from the Sun will eventually form. 2 marks No calculator

Mark scheme
  • B1 a planetary nebula
  • B1 with a white dwarf (star) at its centre

(c) A different star, much more massive than the Sun, explodes as a supernova. State what may form from the nebula left by the supernova. 1 mark No calculator

Mark scheme
  • B1 new stars (with orbiting planets), owtte

How this is examined

  • The life cycle of a massive star once its hydrogen runs out, stage by stage: a Describe worth three or four marks, or a flow diagram of the life cycle with stages to fill in One point per stage, in order: 'expands to form a red supergiant'; 'explodes as a supernova'; 'forms a nebula containing hydrogen and new heavier elements'; 'leaves a neutron star or a black hole at its centre'. A white dwarf or a planetary nebula as the end of this star contradicts the supergiant path.
  • Why a stable star stays the same size: a two-mark Explain Both forces named, and the word balanced: 'the inward force of gravitational attraction' is 'balanced by the outward force due to the high temperature in the centre'. Naming gravity alone, or saying 'the forces are balanced' without naming them, gives only half of the explanation.
  • How a cloud of gas and dust becomes a hot protostar: a two-mark Explain or Describe about the start of a star's life 'The cloud collapses because of its own (internal) gravitational attraction' and 'its temperature increases as it collapses'. For where stars come from: 'interstellar clouds of gas and dust that contain hydrogen'.
  • Converting a star's distance between light-years and metres: a two-mark Calculate, which can be followed by a one-mark Deduce about how long the light has taken Multiply light-years by 9.5×1015 to get metres, or divide metres by 9.5×1015 to get light-years. The working seen can earn the C mark if the final answer is wrong. The final answer needs its unit, m or light-years. A distance of n light-years means the light took n years.
  • How a star like the Sun ends: a one- or two-mark Predict or Describe about the Sun's future 'It expands to form a red giant', then 'a planetary nebula with a white dwarf at its centre'. A supernova, a red supergiant or a black hole for the Sun is wrong physics.
  • What a light-year is, and where the Sun is: one-mark Define and State items 'The distance travelled by light in (the vacuum of) space in one year', with the word distance. 'Galaxies are made up of many billions of stars'; 'the Sun is a star in the Milky Way'; 'the other stars in the Milky Way are much further from the Earth than the Sun is'.

Words to know

Star
A huge ball of hot gas in space that gives out its own light. The Sun is a star.
Galaxy
A huge group of many billions of stars.
Milky Way
The galaxy that contains the Sun.
Light-year
The distance travelled in (the vacuum of) space by light in one year, equal to 9.5×1015 m. It is a distance, not a time.
Interstellar cloud
A cloud of gas and dust in the space between stars, containing hydrogen. Stars form from these clouds.
Protostar
An interstellar cloud that is collapsing and increasing in temperature as a result of its own internal gravitational attraction.
Stable star
A star in which the inward force of gravitational attraction is balanced by the outward force due to the high temperature in its centre, so it stays the same size.
Red giant
The large star, with cooler red outer layers, that most stars (including the Sun) expand into when most of the hydrogen in the centre has been converted to helium.
Red supergiant
The even larger star that more massive stars expand into when most of the hydrogen in the centre has been converted to helium.
Planetary nebula
The shell of gas from the outer layers of a red giant, with a white dwarf at its centre. It has nothing to do with planets.
White dwarf
The small, hot, very dense star left at the centre of a planetary nebula.
Supernova
A huge explosion of a star. A red supergiant ends its life as a supernova.
Nebula
A cloud of gas and dust in space.
Neutron star
An extremely dense object that can be left at the centre of the nebula after a supernova.
Black hole
An object that can be left at the centre of the nebula after a supernova, with gravity so strong that not even light can escape from it.