Stars

1. Overview

This topic explores the vast scale of the universe and the lifecycle of the stars within it. Understanding stars is fundamental to physics as they are the primary sites for the creation of heavy elements and the central bodies around which planetary systems form.

Key Definitions

• Galaxy: A massive system consisting of billions of stars, gas, and dust, all held together by gravitational attraction.
• Star: A luminous sphere of plasma held together by its own gravity, powered by nuclear fusion in its core.
• Milky Way: The specific spiral galaxy that contains our Solar System.
• Light-year: The distance that light travels in a vacuum in one Earth year.
• Protostar: A collapsing cloud of gas and dust that is heating up but has not yet started nuclear fusion.
• Nebula: A vast cloud of interstellar gas and dust.
• Supernova: A powerful and luminous stellar explosion that occurs at the end of a massive star's life.

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Core Content

Galaxies and the Sun

• The universe contains billions of galaxies.
• Each galaxy is composed of many billions of stars.
• Our Sun is a medium-sized star located in a galaxy called the Milky Way.
• While the Sun is the closest star to Earth (approx. 150 million km), all other stars in the Milky Way are significantly further away.

Astronomical Distances Distances in space are too large to be measured conveniently in kilometers. Instead, we use light-years.

• A light-year is a unit of distance, not time.
• It is defined as the distance light travels in a vacuum over the course of one year.

Worked Example: Question: If a star is 4.2 light-years away, how long does it take for its light to reach Earth? Answer: Since a light-year is the distance light travels in one year, it takes exactly 4.2 years for the light to reach us.

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Extended Content (Extended Curriculum Only)

Calculating the Light-year One light-year is equal to approximately $9.5 \times 10^{15}$ meters.

• This is calculated using $Distance = speed \times time$.
• $Speed \text{ of light} (c) = 3.0 \times 10^8 \text{ m/s}$
• $Time \text{ in one year} = 365.25 \times 24 \times 60 \times 60 \text{ seconds}$

The Life Cycle of a Star

1. Formation: Stars form from interstellar clouds of gas and dust containing hydrogen.
2. Protostar: Internal gravitational attraction causes the cloud to collapse. As it collapses, the particles move faster and the temperature increases.
3. Stable Star (Main Sequence): A protostar becomes stable when the inward force of gravitational attraction is perfectly balanced by an outward force (pressure) caused by the high temperatures in the center. In this stage, hydrogen fuses into helium.
4. Running out of Fuel: All stars eventually run out of hydrogen in their core to fuel nuclear reactions.
5. Expansion:
   • Low-mass stars (like the Sun) expand to become Red Giants.
   • High-mass stars expand to become Red Supergiants.
   • This happens when the hydrogen in the center has been converted to helium.

The End of a Star's Life

• From a Red Giant: The outer layers are shed as a planetary nebula, leaving behind a hot, dense core called a white dwarf.
• From a Red Supergiant: The star explodes in a supernova.
  • This forms a new nebula containing hydrogen and new heavier elements.
  • The remaining core collapses into either a neutron star or, if the mass is great enough, a black hole.
• Recycling: The nebula created by a supernova can eventually collapse to form new stars and orbiting planets.

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Key Equations

• Distance (m) = $speed \text{ of light (m/s)} \times time \text{ (s)}$
• 1 light-year $\approx 9.5 \times 10^{15} \text{ m}$

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Common Mistakes to Avoid

• ❌ Wrong: A planetary nebula is caused by a massive star exploding.
• ✓ Right: Planetary nebulae are formed from the relatively "gentle" death of low-mass stars (Red Giants), leaving a white dwarf. Supernovae only result from the collapse of much more massive stars.
• ❌ Wrong: A star becomes stable immediately after a supernova explosion.
• ✓ Right: A supernova is a terminal event. Stability only occurs during the Main Sequence stage when gravity and pressure are balanced.
• ❌ Wrong: Redshift means a star is moving towards us and the wavelength decreases.
• ✓ Right: If a star moves away (Redshift), the wavelength increases. If it moves towards us (Blueshift), the wavelength decreases.

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Exam Tips

1. Balance of Forces: When asked why a star is "stable," you must mention that the inward gravitational force is balanced by the outward pressure/force due to high temperature.
2. Mass is Key: Always identify the mass of the star in the question. The path a star takes (Red Giant vs. Red Supergiant) depends entirely on its initial mass.
3. Light-year Units: If a calculation asks for distance in meters, ensure you use the value $9.5 \times 10^{15}$ m rather than just saying "one light-year."

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [4 marks]

Question:

(a) State what a galaxy is made up of. [1]

(b) Our solar system is located in the Milky Way galaxy. State two other facts about the Milky Way galaxy. [2]

(c) State the name given to the distance that light travels in one year. [1]

Worked Solution:

(a)

1. A galaxy is made up of many billions of stars. [A galaxy is a large collection of stars]

How to earn full marks:

• State "many billions of stars" or equivalent like "a large number of stars"

(b)

1. The Sun is a star in the Milky Way galaxy. [The Sun is one of the stars in the Milky Way]

2. The stars that make up the Milky Way are much further away from Earth than the Sun is from Earth. [The other stars are very distant]

How to earn full marks:

• One mark for each correct fact.
• Do not accept "it contains planets" as this is not specific to the Milky Way.

(c)

1. Light-year. [The unit for astronomical distances]

How to earn full marks:

• Only "light-year" is acceptable.

Common Pitfall: Students sometimes confuse galaxies with solar systems or constellations. Remember that a galaxy is a vast collection of stars, gas, and dust, while a solar system is a star and the objects that orbit it.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

(a) Describe how a protostar is formed. [3]

(b) Explain why a protostar becomes a stable star. [3]

Worked Solution:

(a)

1. A star is formed from interstellar clouds of gas and dust that contain hydrogen. [Clouds of gas and dust are the starting point]

2. The interstellar cloud collapses. [The cloud is pulled inwards]

3. The temperature increases as a result of its internal gravitational attraction. [Gravity causes the temperature to rise]

How to earn full marks:

• One mark for each stage of the protostar formation.

(b)

1. The inward force of gravitational attraction is balanced by an outward force. [There are two opposing forces]

2. The outward force is due to the high temperature in the centre of the star. [Heat generates the outward force]

3. When the forces are balanced, the star becomes stable. [Equilibrium means stability]

How to earn full marks:

• One mark for each stage of the explanation, including mentioning the balancing of forces.

Common Pitfall: It's important to remember that a protostar heats up due to gravitational collapse. Don't confuse this with nuclear fusion, which only starts when the star becomes stable.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

(a) State what happens to most stars when most of the hydrogen in the centre of the star has been converted to helium. [1]

(b) Describe the next stages in the life cycle of a red giant formed from a less massive star, after it has expanded. [4]

(c) A light-year is equal to $9.5 \times 10^{15} , \text{m}$. A particular star is $4.2$ light-years from Earth. Calculate the distance, in metres, from this star to Earth. Give your answer in standard form. [3]

Worked Solution:

(a)

1. Most stars expand to form red giants. [Red giants are the next stage]

How to earn full marks:

• Must state "red giant" or equivalent.

(b)

1. A red giant forms a planetary nebula. [The red giant sheds its outer layers]

2. The planetary nebula is a shell of gas and dust. [Description of the nebula]

3. A white dwarf star is left at its centre. [The core of the star remains]

4. The white dwarf eventually cools and fades. [The end of the process]

How to earn full marks:

• One mark for each correct stage in the description, in the correct sequence.

(c)

1. Distance = (number of light-years) $\times$ (metres per light-year) [Formula for calculating distance]

2. Distance = $4.2 \times 9.5 \times 10^{15} , \text{m} = 3.99 \times 10^{16} , \text{m}$ [Multiplication of values]

3. Distance = $\boxed{4.0 \times 10^{16} , \text{m}}$ (to 2 s.f.) [Standard form and final answer with units]

How to earn full marks:

• One mark for the correct method.
• One mark for the correct numerical value.
• One mark for the correct standard form and units.
• Accept answers in the range of $3.99 \times 10^{16} , \text{m}$ to $4.0 \times 10^{16} , \text{m}$.

Common Pitfall: When converting light-years to meters, be very careful with the powers of ten. Double-check your calculator input to avoid errors in standard form.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

(a) State what happens to more massive stars when most of the hydrogen in the centre of the star has been converted to helium. [1]

(b) Describe the subsequent stages in the life cycle of a red supergiant, after it has expanded. [5]

(c) Explain how the nebula from a supernova may form new stars with orbiting planets. [3]

Worked Solution:

(a)

1. More massive stars expand to form red supergiants. [Red supergiants are the next stage]

How to earn full marks:

• Must state "red supergiant" or equivalent.

(b)

1. A red supergiant explodes as a supernova. [The star ends its life in a massive explosion]

2. This explosion creates a nebula containing hydrogen and new heavier elements. [Composition of the nebula after the explosion]

3. A neutron star or a black hole is left behind at its centre. [Two possible outcomes of the supernova]

4. A neutron star is extremely dense. [Property of a neutron star]

5. A black hole has such strong gravity that nothing, not even light, can escape. [Property of a black hole]

How to earn full marks:

• One mark for each correct and distinct stage in the description.

(c)

1. The nebula contains gas and dust. [The nebula is the raw material]

2. Gravitational attraction causes the gas and dust to collapse. [Gravity pulls the material together]

3. As the gas and dust collapses, it heats up and eventually forms a new star, and the remaining material can form orbiting planets. [Formation of the star and planets]

How to earn full marks:

• One mark for each stage of the explanation, including the role of gravity.

Common Pitfall: Remember the difference between the life cycles of less massive stars (red giants, white dwarfs) and more massive stars (red supergiants, neutron stars, black holes). Don't mix up the stages!