Gravity, orbits and the Solar System

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課程筆記

Big idea: gravity, orbits and the solar system

Key concept: Systems. Gravity supplies the inward force that changes an orbiting object's velocity direction. A circular orbit can have constant speed while the object accelerates.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Orbital models help predict satellite and planetary motion.

The Earth, Moon & Sun

Earth rotates on its axis once every 24 hours, causing day and night.
Earth orbits the Sun once every 365 days (one year).
Earth's axis is tilted at 23.5° from the vertical, causing the seasons.
The Moon is a natural satellite orbiting Earth approximately every 27.3 days relative to distant stars; it rotates once per orbit so the same side always faces Earth.
Moon phases result from reflected sunlight; order: new moon → first quarter → full moon → last quarter.
Day and night are caused by Earth's rotation; seasons are caused by the combination of Earth's orbit and axial tilt.

The apparent path of the Sun across the sky at noon during different seasons

The Solar System

The Solar System consists of the Sun, eight planets, dwarf planets, moons, asteroids, and comets.
Planets in order from Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.
Inner planets (Mercury, Venus, Earth, Mars) are rocky and small; outer planets (Jupiter, Saturn, Uranus, Neptune) are gaseous and large.
Asteroids are rocky objects found mainly in the Asteroid Belt between Mars and Jupiter.
Comets are icy objects with highly elliptical orbits; they develop a tail when near the Sun.
Dwarf planets (e.g., Pluto) have weaker gravity and cannot clear their orbits of debris.

The Solar System

Formation of the Solar System

The Solar System formed about 4.5 billion years ago from a nebula (cloud of dust and gas).
Gravity pulled the nebula together; the Sun formed at the centre, and an accretion disc of leftover matter formed around it.
In the hot inner region, only metals and rocky materials could solidify → inner rocky planets.
In the cool outer region, light gases (H, He) condensed → outer gas giants.
Accretion is the process where particles stick together under gravity to form larger objects.

Light Speed Calculations

Light travels at 3 × 10⁸ m/s in a vacuum.
Time for light to travel a distance: time = distance / speed of light.
Light from Sun takes 8 minutes to reach Earth, ~3 minutes to Mercury, ~5 hours to outer Solar System.
Light from the nearest star (Proxima Centauri) takes 4 years to reach Earth.

Gravitational Field Strength

Gravitational field strength at a planet's surface depends on its mass and radius.
Greater mass → stronger gravitational field; greater distance from planet → weaker field.
The Sun contains >99% of the Solar System's mass, so its gravity keeps planets in orbit.
As distance from Sun increases, orbital speed decreases and orbital period increases.

Orbital Speed Equation

For a circular orbit, orbital speed v = 2πr / T, where r is orbital radius and T is orbital period.
Orbital radius is measured from the centre of the orbited body.
Ensure units: convert km to m, minutes to seconds as needed.
Example: Earth's orbital speed ≈ 30 km/s (from data table).

Elliptical Orbits

Planets have slightly elliptical orbits; comets have highly elliptical orbits.
The Sun is at one focus of the ellipse (not the centre).
As a comet approaches the Sun, its speed increases (KE increases, GPE decreases).
As it moves away, its speed decreases (GPE increases, KE decreases); energy is conserved.

Think like a scientist

Analyse planetary data to compare orbital periods at different average distances from the Sun; never look directly at the Sun.
Comparison: the planet's average orbital distance. Outcome: the orbital period.
Control: compare planets orbiting the same central star. 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

Orbital models help predict satellite and planetary motion.
Real orbits are often elliptical, so a circular-orbit approximation has limits.
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 planets listed is the gaseous planet which is closest to the Sun?
Easy
- AJupiter
- BMars
- CSaturn
- DUranus
2.Which of the following objects are described as orbiting the Sun? 1. Asteroids 2. Comets 3. Galaxies 4. Moons
Easy
- A1 and 2 only
- B1, 2 and 3
- C1, 2, and 4
- D1, 2, 3 and 4
3.What creates the periodic nature of the seasons?
Medium
- AThe tilting of the Earth's axis
- BThe orbiting of the Earth around the Sun
- CThe combination of the orbiting of the Earth around the Sun and the Earth's tilting axis
- DThe change in temperature of the Sun
4.Which of the following statements about the strength of a gravitational field is correct?
Medium
- AAt the surface of a planet it depends on the diameter of the planet
- BAround a planet it decreases as the distance from the planet increases
- CAround a planet it increases as the distance from the planet increases
- DAt the surface of a planet it depends on the mass of the planet
5.Which type of object orbits the Sun?
Easy
- Aan interstellar cloud of gas and dust
- Ba comet
- Ca galaxy
- Danother star
6.
Which line in the table best describes the angle of the Earth’s axis from the vertical, and the effect of this tilt?
Angle of tilt Effect of tilt
A 23.4° Rising and setting of the Sun
B 23.4° Changing of the seasons
C 66.6° Rising and setting of the Sun
D 66.6° Changing of the seasons
Medium
- AA
- BB
- CC
- DD
7.
Which line in the table correctly identifies the length of one year, one day and daylight hours during an equinox, all as experienced on Earth?
One Earth year / days One Earth day / hours Daylight hours during an equinox / hours
A 356 8 8
B 364 12 12
C 365 12 8
D 365 24 12
Easy
- AA
- BB
- CC
- DD
8.Extended tier only Which of the following statements about orbits is true?
Medium
- AAll planets, minor planets and comets have elliptical orbits
- BThe Sun is at the centre of an elliptical orbit
- COnly comets and minor planets have elliptical orbits
- DAn object in an elliptical orbit has a constant orbital radius

複習筆記

## Big idea: gravity, orbits and the solar system - **Key concept: Systems.** Gravity supplies the inward force that changes an orbiting object's velocity direction. A circular orbit can have constant speed while the object accelerates. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Orbital models help predict satellite and planetary motion. ## The Earth, Moon & Sun - Earth **rotates** on its axis once every **24 hours**, causing day and night. - Earth **orbits** the Sun once every **365 days** (one year). - Earth's axis is tilted at **23.5°** from the vertical, causing the **seasons**. - The Moon is a **natural satellite** orbiting Earth approximately every **27.3 days** relative to distant stars; it rotates once per orbit so the same side always faces Earth. - Moon phases result from reflected sunlight; order: new moon → first quarter → full moon → last quarter. - Day and night are caused by Earth's rotation; seasons are caused by the combination of Earth's orbit and axial tilt. ## The Solar System - The Solar System consists of the **Sun**, eight planets, dwarf planets, moons, asteroids, and comets. - Planets in order from Sun: **Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune**. - Inner planets (Mercury, Venus, Earth, Mars) are **rocky and small**; outer planets (Jupiter, Saturn, Uranus, Neptune) are **gaseous and large**. - **Asteroids** are rocky objects found mainly in the **Asteroid Belt** between Mars and Jupiter. - **Comets** are icy objects with **highly elliptical orbits**; they develop a tail when near the Sun. - **Dwarf planets** (e.g., Pluto) have weaker gravity and cannot clear their orbits of debris. ## Formation of the Solar System - The Solar System formed about **4.5 billion years ago** from a **nebula** (cloud of dust and gas). - Gravity pulled the nebula together; the **Sun** formed at the centre, and an **accretion disc** of leftover matter formed around it. - In the hot inner region, only **metals and rocky materials** could solidify → **inner rocky planets**. - In the cool outer region, **light gases (H, He)** condensed → **outer gas giants**. - **Accretion** is the process where particles stick together under gravity to form larger objects. ## Light Speed Calculations - Light travels at **3 × 10⁸ m/s** in a vacuum. - Time for light to travel a distance: **time = distance / speed of light**. - Light from Sun takes **8 minutes** to reach Earth, ~**3 minutes** to Mercury, ~**5 hours** to outer Solar System. - Light from the nearest star (Proxima Centauri) takes **4 years** to reach Earth. ## Gravitational Field Strength - Gravitational field strength at a planet's surface depends on its **mass** and **radius**. - Greater mass → stronger gravitational field; greater distance from planet → weaker field. - The Sun contains **>99%** of the Solar System's mass, so its gravity keeps planets in orbit. - As distance from Sun increases, **orbital speed decreases** and **orbital period increases**. ## Orbital Speed Equation - For a circular orbit, orbital speed **v = 2πr / T**, where r is orbital radius and T is orbital period. - Orbital radius is measured from the **centre** of the orbited body. - Ensure units: convert km to m, minutes to seconds as needed. - Example: Earth's orbital speed ≈ **30 km/s** (from data table). ## Elliptical Orbits - Planets have **slightly elliptical** orbits; comets have **highly elliptical** orbits. - The Sun is at one **focus** of the ellipse (not the centre). - As a comet approaches the Sun, its **speed increases** (KE increases, GPE decreases). - As it moves away, its **speed decreases** (GPE increases, KE decreases); energy is conserved. ## Think like a scientist - Analyse planetary data to compare orbital periods at different average distances from the Sun; never look directly at the Sun. - **Comparison:** the planet's average orbital distance. **Outcome:** the orbital period. - **Control:** compare planets orbiting the same central star. 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 - Orbital models help predict satellite and planetary motion. - Real orbits are often elliptical, so a circular-orbit approximation has limits. - **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.

Solar System Composition: Identify and order the eight planets, distinguish between inner rocky and outer gas giants, and describe the locations and characteristics of asteroids, comets, and dwarf planets.
Orbital Data Analysis: Analyze planetary data tables to identify trends, anomalies, and make predictions about planetary properties.
Solar System Formation: Explain the accretion model for the formation of the Solar System from a nebula, including the role of gravity and temperature in forming inner rocky and outer gaseous planets.
Earth, Moon & Sun Motions: Describe the rotation and orbit of Earth, the orbit and phases of the Moon, and explain day/night, seasons, and the apparent motion of the Sun.
Light Speed Calculations: Light travels at **3 × 10⁸ m/s** in a vacuum.
Gravitational Field Strength: Gravitational field strength at a planet's surface depends on its **mass** and **radius**.
Orbital Speed Equation: For a circular orbit, orbital speed **v = 2πr / T**, where r is orbital radius and T is orbital period.
Designing scientific inquiries: Plan a fair comparison: Analyse planetary data to compare orbital periods at different average distances from the Sun; never look directly at the Sun.
Evaluating evidence and impacts: Orbital models help predict satellite and planetary motion. Real orbits are often elliptical, so a circular-orbit approximation has limits.
The Earth, Moon & Sun: Earth **rotates** on its axis once every **24 hours**, causing day and night.
The Solar System: The Solar System consists of the **Sun**, eight planets, dwarf planets, moons, asteroids, and comets.
Formation of the Solar System: The Solar System formed about **4.5 billion years ago** from a **nebula** (cloud of dust and gas).
Elliptical Orbits: Planets have **slightly elliptical** orbits; comets have **highly elliptical** orbits.
rotates: Earth **rotates** on its axis once every **24 hours**, causing day and night.
24 hours: Earth **rotates** on its axis once every **24 hours**, causing day and night.
orbits: Earth **orbits** the Sun once every **365 days** (one year).

字卡

Which of the planets listed is the gaseous planet which is closest to the Sun?

Jupiter Jupiter is the first gas giant from the Sun; Mars is rocky, Saturn and Uranus are further out.

Which of the following objects are described as orbiting the Sun? 1. Asteroids 2. Comets 3. Galaxies 4. Moons

1 and 2 only Asteroids and comets orbit the Sun; galaxies are much larger systems, and moons orbit planets, not the Sun directly.

What creates the periodic nature of the seasons?

The combination of the orbiting of the Earth around the Sun and the Earth's tilting axis Seasons are caused by both the Earth's tilted axis and its orbit around the Sun; neither alone is sufficient.

Which of the following statements about the strength of a gravitational field is correct?

Around a planet it decreases as the distance from the planet increases Gravitational field strength decreases with distance from a planet; it depends on the planet's mass, not diameter.

Which type of object orbits the Sun?

a comet Comets orbit the Sun; interstellar clouds and galaxies are much larger, and other stars are separate systems.

Which line in the table best describes the angle of the Earth’s axis from the vertical, and the effect of this tilt? | Angle of tilt | Effect of tilt | |---------------|----------------| | A 23.4° | Rising and setting of the Sun | | B 23.4° | Changing of the seasons | | C 66.6° | Rising and setting of the Sun | | D 66.6° | Changing of the seasons |

B The Earth's axis is tilted about 23.5° from the vertical; this tilt, combined with orbital motion, causes seasons.

Which line in the table correctly identifies the length of one year, one day and daylight hours during an equinox, all as experienced on Earth? | One Earth year / days | One Earth day / hours | Daylight hours during an equinox / hours | |-----------------------|-----------------------|------------------------------------------| | A 356 | 8 | 8 | | B 364 | 12 | 12 | | C 365 | 12 | 8 | | D 365 | 24 | 12 |

D One Earth year is about 365 days, one day is 24 hours, and at an equinox day and night are equal (12 hours each).

Extended tier only Which of the following statements about orbits is true?

All planets, minor planets and comets have elliptical orbits All these bodies have elliptical orbits; the Sun is at one focus, not the centre, and orbital radius varies.

Extended tier only The orbit of the Earth around the Sun can be thought of as following a circular path with a circumference of 942 × 10⁶ km. What is the approximate orbital speed of the Earth?

100 000 km/h Orbital period T = 365 days = 8760 h. Speed = distance/time = 942×10⁶ km / 8760 h ≈ 107,500 km/h, closest to 100,000 km/h.

Extended tier only Comets travel faster within the Solar System than they do when they are outside it. Which of the following gives the correct reason for this?

Comets closer to the Sun transfer gravitational potential energy to kinetic energy due to conservation of energy. As a comet approaches the Sun, gravitational potential energy is converted to kinetic energy, increasing speed.

Select the combination which best defines and describes an accretion disc. 1. Gases rotating around a star 2. Ring of rocky material 3. Leads to formation of orbiting planets 4. Explains the range of elements in rocky planets 5. Explains the range of elements in the parent star

1, 3 and 4 An accretion disc is a rotating disc of gas and dust around a young star; planets form from it, and its composition explains the elements in rocky planets, not the star.

The Earth and Moon are held together by a gravitational force acting between them. Which row describes possible changes to the mass of the Earth and the distance between the Earth and the Moon that would cause the gravitational force to increase? | Mass of Earth | Distance between Earth and Moon | |---------------|----------------------------------| | A Double | Drop to one quarter | | B Stay the same | Stay the same | | C Halve | Stay the same | | D Drop to one quarter | Double |

A Gravitational force is proportional to the product of masses and inversely proportional to the square of distance. Doubling mass and reducing distance to 1/4 increases force by 2 × 16 = 32 times.

The table shows data for four planets. | Planet | Distance from Sun / million km | Orbital speed / km/s | |---|---|---| | Mercury | 58 | 47.9 | | Venus | 108 | 35.0 | | Earth | 150 | 29.8 | | Mars | 228 | 24.1 | Which planet has the greatest orbital speed?

Mercury Orbital speed decreases with distance from the Sun. Mercury is closest, so it has the highest orbital speed (47.9 km/s).

The orbital radius of Neptune is 4.5 × 10¹² m and its orbital period is 5.2 × 10⁹ s. What is its orbital speed?

5.4 × 10³ m/s Orbital speed v = 2πr / T = 2π × 4.5×10¹² / (5.2×10⁹) ≈ 5.4×10³ m/s.

A space probe travels from Earth to Mars. The distance from the Sun to Earth is 1.5 × 10¹¹ m and to Mars is 2.3 × 10¹¹ m. Light travels at 3.0 × 10⁸ m/s. How much longer does it take for light from the Sun to reach Mars than to reach Earth?

270 s Time to Earth = 1.5×10¹¹ / (3.0×10⁸) = 500 s. Time to Mars = 2.3×10¹¹ / (3.0×10⁸) ≈ 767 s. Difference = 267 s ≈ 270 s.

Which of the following lists the planets in order of increasing distance from the Sun?

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune The correct order from the Sun is Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

How would you design the inquiry for gravity, orbits and the solar system?

Analyse planetary data to compare orbital periods at different average distances from the Sun; never look directly at the Sun. Compare the planet's average orbital distance; record the orbital period; compare planets orbiting the same central star.

What limitation matters when applying gravity, orbits and the solar system?

Real orbits are often elliptical, so a circular-orbit approximation has limits.

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Angle of tilt	Effect of tilt
A 23.4°	Rising and setting of the Sun
B 23.4°	Changing of the seasons
C 66.6°	Rising and setting of the Sun
D 66.6°	Changing of the seasons

Mass of Earth	Distance between Earth and Moon
A Double	Drop to one quarter
B Stay the same	Stay the same
C Halve	Stay the same
D Drop to one quarter	Double

Planet	Distance from Sun / million km	Orbital speed / km/s
Mercury	58	47.9
Venus	108	35.0
Earth	150	29.8
Mars	228	24.1
Jupiter	778	13.1