Stars, cosmology and scientific evidence

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課程筆記

Big idea: stars, cosmology and scientific evidence

Key concept: Change. Stellar fusion releases energy. Galaxy redshifts and the cosmic microwave background support models of an expanding universe with a hot, dense early state.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Astronomical observations test models over distances and times impossible to recreate in a classroom.

The Sun as a Star

The Sun is a medium-sized star at the centre of the Solar System.
It consists mostly of hydrogen and helium.
It radiates most energy in the infrared, visible and ultraviolet regions.
In the core, nuclear fusion converts hydrogen into helium, releasing huge energy.
Main-sequence stars release energy through hydrogen fusion in their cores.

The Sun as a star

Scale of the Universe

The Universe is a large collection of billions of galaxies.
A galaxy is a large collection of billions of stars.
The Milky Way is our galaxy; the Sun is one of its billions of stars.
Other stars in the Milky Way are much further from Earth than the Sun.
A light-year is the distance light travels in one year (≈ 9.5 × 10¹⁵ m).
The Milky Way's diameter is about 100 000 light-years.

Hierarchy of the Universe

Star Formation

Stars form from a nebula (cloud of gas and dust).
Gravity pulls particles together to form a protostar; density and temperature increase.
When the core is hot enough, nuclear fusion begins → stable star.
In a stable star, inward gravitational forces balance outward thermal pressure.

Balanced forces in a stable star

Life Cycle of Low-Mass Stars (≤ 8 solar masses)

After stable phase: red giant → planetary nebula → white dwarf.
Red giant: hydrogen depleted, core shrinks and heats, helium fuses to carbon, outer layers expand.
Planetary nebula: outer layers ejected; core collapses.
White dwarf: hot, dense core that cools and dims over time.

Life Cycle of High-Mass Stars (> 8 solar masses)

After stable phase: red supergiant → supernova → neutron star or black hole.
Red supergiant: fuses heavier elements up to iron; core collapses and expands repeatedly.
Supernova: core collapses rapidly, triggering a huge explosion; heavy elements (heavier than iron) are formed.
Neutron star: dense remnant at the centre; if massive enough, collapses to a black hole.
Nebulae from supernovae may form new stars and planets.

Galactic Redshift

Redshift is the increase in wavelength of light from a source moving away (Doppler effect).
Light from distant galaxies is redshifted compared to hydrogen on Earth → galaxies are moving away.
Greater redshift means the galaxy is further away and moving faster.
This shows the Universe is expanding.

The Big Bang Theory

The Universe began about 14 billion years ago from a hot, dense single point.
Evidence: galactic redshift (galaxies receding → expansion) and cosmic microwave background radiation (CMBR).
The cosmic microwave background is nearly uniform radiation observed across the sky, with small temperature variations, left over from the early Universe.
The radiation last scattered when the Universe became transparent had a much hotter thermal spectrum. Expansion stretched its wavelengths into the microwave region observed today.

Age of the Universe

Hubble's law: recession speed v is proportional to distance d: v = H₀ d.
Hubble constant H₀ = 2.2 × 10⁻¹⁸ per second (current accepted value).
Age of Universe ≈ 1 / H₀ ≈ 13.7 billion years.
Distance to galaxies measured using redshift and brightness of supernovae (standard candles).

Think like a scientist

Use teacher-provided galaxy spectra to compare measured redshift with independently estimated distance.
Comparison: the galaxy distance in the dataset. Outcome: the spectral redshift.
Control: compare shifts of the same identified spectral line. Explain why this makes the comparison fairer.
Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

Astronomical observations test models over distances and times impossible to recreate in a classroom.
A redshift-distance relationship has scatter and measurement limits; individual nearby galaxies need not follow the overall trend.
Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

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練習題

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1.Which of the following is the correct definition of a galaxy?
Easy
- AA large collection of billions of stars
- BA large collection of billions of planets
- CA large collection of billions of galaxies
- DA large collection of billions of moons
2.What is the approximate diameter of the Milky Way galaxy in light-years?
Easy
- A100 000 light-years
- B1 million light-years
- C10 000 light-years
- D1 billion light-years
3.What is the name of the force that pulls the outer layers of a star inwards during its stable phase?
Easy
- AGravitational force
- BThermal pressure
- CNuclear force
- DElectromagnetic force
4.What is the correct order of stages in the life cycle of a star similar in mass to the Sun after the stable star phase?
Easy
- ARed giant, planetary nebula, white dwarf
- BRed supergiant, supernova, neutron star
- CPlanetary nebula, white dwarf, red giant
- DWhite dwarf, red giant, planetary nebula
5.What does the observed redshift in the light from distant galaxies indicate?
Easy
- AGalaxies are moving away from Earth
- BGalaxies are moving towards Earth
- CGalaxies are stationary
- DGalaxies are shrinking
6.The Hubble constant H0 is approximately 2.2 × 10⁻¹⁸ per second. A galaxy is at a distance of 1.0 × 10²³ m. What is its recessional velocity?
Medium
- A2.2 × 10⁵ m/s
- B2.2 × 10⁻⁴¹ m/s
- C4.5 × 10⁴⁰ m/s
- D2.2 × 10⁻⁵ m/s
7.Which of the following is evidence for the Big Bang theory?
Easy
- AGalactic redshift and cosmic microwave background radiation
- BThe Sun's energy from nuclear fusion
- CThe existence of black holes
- DThe formation of planetary nebulae
8.What is the approximate age of the Universe according to the Hubble constant?
Easy
- A13.7 billion years
- B13.7 million years
- C4.5 billion years
- D100 billion years

複習筆記

## Big idea: stars, cosmology and scientific evidence - **Key concept: Change.** Stellar fusion releases energy. Galaxy redshifts and the cosmic microwave background support models of an expanding universe with a hot, dense early state. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Astronomical observations test models over distances and times impossible to recreate in a classroom. ## The Sun as a Star - The Sun is a **medium-sized star** at the centre of the Solar System. - It consists mostly of **hydrogen** and **helium**. - It radiates most energy in the **infrared**, **visible** and **ultraviolet** regions. - In the core, **nuclear fusion** converts hydrogen into helium, releasing huge energy. - Main-sequence stars release energy through hydrogen fusion in their cores. ## Scale of the Universe - The **Universe** is a large collection of billions of **galaxies**. - A **galaxy** is a large collection of billions of **stars**. - The **Milky Way** is our galaxy; the Sun is one of its billions of stars. - Other stars in the Milky Way are much further from Earth than the Sun. - A **light-year** is the distance light travels in one year (≈ 9.5 × 10¹⁵ m). - The Milky Way's diameter is about **100 000 light-years**. ## Star Formation - Stars form from a **nebula** (cloud of gas and dust). - Gravity pulls particles together to form a **protostar**; density and temperature increase. - When the core is hot enough, **nuclear fusion** begins → **stable star**. - In a stable star, inward **gravitational forces** balance outward **thermal pressure**. ## Life Cycle of Low-Mass Stars (≤ 8 solar masses) - After stable phase: **red giant** → **planetary nebula** → **white dwarf**. - Red giant: hydrogen depleted, core shrinks and heats, helium fuses to carbon, outer layers expand. - Planetary nebula: outer layers ejected; core collapses. - White dwarf: hot, dense core that cools and dims over time. ## Life Cycle of High-Mass Stars (> 8 solar masses) - After stable phase: **red supergiant** → **supernova** → **neutron star** or **black hole**. - Red supergiant: fuses heavier elements up to iron; core collapses and expands repeatedly. - Supernova: core collapses rapidly, triggering a huge explosion; heavy elements (heavier than iron) are formed. - Neutron star: dense remnant at the centre; if massive enough, collapses to a **black hole**. - Nebulae from supernovae may form new stars and planets. ## Galactic Redshift - **Redshift** is the increase in wavelength of light from a source moving away (Doppler effect). - Light from distant galaxies is **redshifted** compared to hydrogen on Earth → galaxies are moving away. - Greater redshift means the galaxy is **further away** and **moving faster**. - This shows the **Universe is expanding**. ## The Big Bang Theory - The Universe began about **14 billion years ago** from a hot, dense single point. - Evidence: **galactic redshift** (galaxies receding → expansion) and **cosmic microwave background radiation (CMBR)**. - The cosmic microwave background is nearly uniform radiation observed across the sky, with small temperature variations, left over from the early Universe. - The radiation last scattered when the Universe became transparent had a much hotter thermal spectrum. Expansion stretched its wavelengths into the microwave region observed today. ## Age of the Universe - **Hubble's law**: recession speed v is proportional to distance d: v = H₀ d. - **Hubble constant** H₀ = 2.2 × 10⁻¹⁸ per second (current accepted value). - Age of Universe ≈ 1 / H₀ ≈ **13.7 billion years**. - Distance to galaxies measured using **redshift** and **brightness of supernovae** (standard candles). ## Think like a scientist - Use teacher-provided galaxy spectra to compare measured redshift with independently estimated distance. - **Comparison:** the galaxy distance in the dataset. **Outcome:** the spectral redshift. - **Control:** compare shifts of the same identified spectral line. Explain why this makes the comparison fairer. - **Evidence:** Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause. - **Safety:** Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it. - **Inquiry task:** State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction. ## Evaluate the science - Astronomical observations test models over distances and times impossible to recreate in a classroom. - A redshift-distance relationship has scatter and measurement limits; individual nearby galaxies need not follow the overall trend. - **Evaluation task:** Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Big Bang Evidence: Describe the Big Bang theory and evidence from galactic redshift and cosmic microwave background radiation.
Star Formation and Lifecycle: Describe the stages of star formation from nebula to protostar to stable star, and the subsequent life cycles of low-mass and high-mass stars including red giant, white dwarf, supernova, neutron star, and black hole.
Hubble's Law and Age of Universe: Apply Hubble's law to relate recession speed and distance, and use the Hubble constant to estimate the age of the Universe.
Nuclear Fusion in Stars: Describe nuclear fusion as the process powering stars, including the fusion of hydrogen into helium and the release of energy.
Galactic Redshift: **Redshift** is the increase in wavelength of light from a source moving away (Doppler effect).
Astronomical Distances: Define the light-year and use it to describe astronomical distances, performing calculations involving light-years.
Designing scientific inquiries: Plan a fair comparison: Use teacher-provided galaxy spectra to compare measured redshift with independently estimated distance.
Evaluating evidence and impacts: Astronomical observations test models over distances and times impossible to recreate in a classroom. A redshift-distance relationship has scatter and measurement limits; individual nearby galaxies need not follow the overall trend.
The Sun as a Star: The Sun is a **medium-sized star** at the centre of the Solar System.
Scale of the Universe: The **Universe** is a large collection of billions of **galaxies**.
Star Formation: Stars form from a **nebula** (cloud of gas and dust).
Life Cycle of Low-Mass Stars (≤ 8 solar masses): After stable phase: **red giant** → **planetary nebula** → **white dwarf**.
Life Cycle of High-Mass Stars (> 8 solar masses): After stable phase: **red supergiant** → **supernova** → **neutron star** or **black hole**.
The Big Bang Theory: The Universe began about **14 billion years ago** from a hot, dense single point.
Age of the Universe: **Hubble's law**: recession speed v is proportional to distance d: v = H₀ d.
medium-sized star: The Sun is a **medium-sized star** at the centre of the Solar System.

字卡

Which of the following is the correct definition of a galaxy?

A large collection of billions of stars A galaxy is defined as a large collection of billions of stars. The Universe is a collection of galaxies, and the Solar System is part of a galaxy.

What is the approximate diameter of the Milky Way galaxy in light-years?

100 000 light-years The diameter of the Milky Way galaxy is approximately 100 000 light-years.

What is the name of the force that pulls the outer layers of a star inwards during its stable phase?

Gravitational force In a stable star, gravitational force acts inwards, pulling the outer layers inward, while thermal pressure pushes outward.

What is the correct order of stages in the life cycle of a star similar in mass to the Sun after the stable star phase?

Red giant, planetary nebula, white dwarf A low-mass star like the Sun becomes a red giant, then a planetary nebula, and finally a white dwarf.

What does the observed redshift in the light from distant galaxies indicate?

Galaxies are moving away from Earth Redshift shows that the wavelength of light has increased, meaning the source (galaxy) is moving away from the observer.

The Hubble constant H0 is approximately 2.2 × 10⁻¹⁸ per second. A galaxy is at a distance of 1.0 × 10²³ m. What is its recessional velocity?

2.2 × 10⁵ m/s Using v = H0 × d = (2.2 × 10⁻¹⁸) × (1.0 × 10²³) = 2.2 × 10⁵ m/s.

Which of the following is evidence for the Big Bang theory?

Galactic redshift and cosmic microwave background radiation The two main pieces of evidence are galactic redshift (showing the Universe is expanding) and cosmic microwave background radiation (the afterglow of the Big Bang).

What is the approximate age of the Universe according to the Hubble constant?

13.7 billion years Astronomers estimate the age of the Universe to be about 13.7 billion years using Hubble's law.

What is the name of the galaxy that contains the Sun?

The Milky Way The Sun is a star in the Milky Way galaxy.

What is a protostar?

A hot ball of gas formed from a nebula before nuclear fusion begins A protostar forms from a nebula when gravitational attraction pulls particles together, creating a hot ball of gas. It becomes a stable star once nuclear fusion starts.

What is the ultimate fate of a very massive star (more than 8 solar masses) after a supernova?

Neutron star or black hole For high-mass stars, after a supernova, a neutron star or black hole forms. Only the most massive become black holes.

A galaxy is at a distance of 9.0 × 10⁷ light-years from Earth. The Hubble constant is 2.2 × 10^−18 per second. What is the recessional speed of this galaxy in m/s? (1 light-year = 9.5 × 10¹⁵ m)

1.9 × 10⁶ m/s Distance d = 9.0×10⁷ × 9.5×10¹⁵ = 8.55×10²³ m. v = H0 × d = 2.2×10^−18 × 8.55×10²³ = 1.88×10⁶ m/s ≈ 1.9×10⁶ m/s.

The spectrum of light from a distant galaxy shows a dark line at a wavelength of 656 nm. The same line from a laboratory source on Earth is at 656 nm. What can be concluded about the galaxy?

The galaxy is stationary relative to Earth. Since the observed wavelength equals the rest wavelength, there is no redshift or blueshift, so the galaxy is stationary relative to Earth.

The Sun is a stable star. Which two forces are in equilibrium during this stage?

Gravitational force pulling inwards and thermal pressure pushing outwards In a stable star, gravitational forces pull inwards and thermal pressure from fusion reactions pushes outwards, balancing each other.

A star with a mass 15 times that of the Sun is in its stable phase. What will be its final evolutionary stage?

Neutron star A star of 15 solar masses is a high-mass star (more than about 8 solar masses), so after the supernova it leaves behind a neutron star; only the very highest-mass stars collapse further into a black hole.

The Hubble constant is 2.2 × 10^−18 per second. What is the approximate age of the Universe in seconds?

4.5 × 10¹⁷ s Age ≈ 1/H0 = 1/(2.2×10^−18) = 4.545×10¹⁷ s ≈ 4.5×10¹⁷ s.

How would you design the inquiry for stars, cosmology and scientific evidence?

Use teacher-provided galaxy spectra to compare measured redshift with independently estimated distance. Compare the galaxy distance in the dataset; record the spectral redshift; compare shifts of the same identified spectral line.

What limitation matters when applying stars, cosmology and scientific evidence?

A redshift-distance relationship has scatter and measurement limits; individual nearby galaxies need not follow the overall trend.

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歷屆試題

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即將推出

Galaxy	Distance from Earth (m)
A	1.0 × 10²³
B	5.0 × 10²²
C	2.0 × 10²³
D	8.0 × 10²²