CIE iGCSE Co-ordinated Sciences-P6.2.1 The Sun as a star- Study Notes- New Syllabus
CIE iGCSE Co-ordinated Sciences-P6.2.1 The Sun as a star – Study Notes
CIE iGCSE Co-ordinated Sciences-P6.2.1 The Sun as a star – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.
Key Concepts:
CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics
The Sun and Astronomical Distances
(a) The Sun is the Closest Star to the Earth
The Sun is the nearest star to Earth, located at an average distance of about 150 million km (1 Astronomical Unit, AU).
- Other stars appear much dimmer even if they are larger and more luminous, because they are at much greater distances.
- The next closest star system, Alpha Centauri, is about 4.37 light-years away — far further than the Sun.
- This explains why the Sun dominates the sky, providing almost all the light and heat for life on Earth.
(b) Astronomical Distances in Light-Years
A light-year (ly) is the distance light travels in one year in a vacuum.
- Since the speed of light is \( 3.0 \times 10^{8} \, \text{m/s} \), one light-year is:
- \( 1 \, \text{ly} = 3.0 \times 10^{8} \times (60 \times 60 \times 24 \times 365) \, \text{m} \).
- This gives \( 1 \, \text{ly} \approx 9.46 \times 10^{15} \, \text{m} \), or about \( 9.46 \times 10^{12} \, \text{km} \).
- Light-years are used because distances between stars and galaxies are too large to express conveniently in kilometres or metres.
- For example, the nearest galaxy, Andromeda, is about 2.5 million light-years away.
Example
Calculate how far light travels in one year, given that the speed of light is \( 3.0 \times 10^{8} \, \text{m/s} \).
▶️Answer/Explanation
Step (1): Time in one year = \( 365 \times 24 \times 60 \times 60 = 31,536,000 \, \text{s} \).
Step (2): Distance = speed × time = \( 3.0 \times 10^{8} \times 31,536,000 \).
Step (3): Distance = \( 9.46 \times 10^{15} \, \text{m} \).
Final Answer: One light-year is about \( 9.46 \times 10^{15} \, \text{m} \) (or \( 9.46 \times 10^{12} \, \text{km} \)).
Calculating the Time Taken for Light to Travel Across the Solar System
Light travels at a constant speed in a vacuum: \( c = 3.0 \times 10^{8} \, \text{m/s} \).
- The time taken for light to travel a certain distance is given by:
- \( t = \dfrac{d}{c} \), where \( d \) is the distance and \( c \) is the speed of light.
- This calculation is useful for estimating how long it takes sunlight to reach planets and other objects in the Solar System.
- Since distances in the Solar System are very large, results are often expressed in minutes or hours, not seconds.
Example :
The average distance from the Sun to Earth is 1 Astronomical Unit (AU) = \( 1.496 \times 10^{11} \, \text{m} \). How much Sunlight takes to reach Earth.
▶️Answer/Explanation
Step (1): Formula → \( t = \dfrac{d}{c} \).
Step (2): Substitute → \( t = \dfrac{1.496 \times 10^{11}}{3.0 \times 10^{8}} \).
Step (3): \( t = 498.7 \, \text{s} \).
Step (4): Convert to minutes → \( \dfrac{498.7}{60} \approx 8.3 \, \text{minutes} \).
Final Answer: Sunlight takes about 8 minutes 20 seconds to reach Earth.
Example :
The average distance from the Sun to Jupiter is 5.2 AU = \( 7.78 \times 10^{11} \, \text{m} \).How much Sunlight takes to reach Jupiter.
▶️Answer/Explanation
Step (1): Formula → \( t = \dfrac{d}{c} \).
Step (2): Substitute → \( t = \dfrac{7.78 \times 10^{11}}{3.0 \times 10^{8}} \).
Step (3): \( t = 2.59 \times 10^{3} \, \text{s} \).
Step (4): Convert to minutes → \( \dfrac{2590}{60} \approx 43.2 \, \text{minutes} \).
Final Answer: Sunlight takes about 43 minutes to reach Jupiter.
(a) The Sun’s Mass and Planetary Orbits
- The Sun contains about 99.8% of the total mass of the Solar System.
- This enormous mass means the Sun exerts a strong gravitational pull on all other bodies (planets, dwarf planets, asteroids, comets).
- The gravitational force provides the centripetal force required to keep planets moving in nearly circular orbits around the Sun.
- Thus, the Sun’s mass directly explains why planets orbit the Sun and not each other.
(b) Defining Orbital Speed
The orbital speed of a planet or satellite is the average speed</strong it travels along its orbital path.
- The formula for orbital speed is:
- \( v = \dfrac{2 \pi r}{T} \)
- Where:
- \( v \) = orbital speed (m/s)
- \( r \) = orbital radius (distance from the centre of the orbit, in m)
- \( T \) = orbital period (time taken for one complete orbit, in seconds)
- This comes from: Speed = Distance / Time, where the orbital distance for one revolution is the circumference \( 2 \pi r \).
Example:
Calculate Earth’s Orbital Speed around the Sun
Earth’s orbital radius ≈ \( 1.496 \times 10^{11} \, \text{m} \).
Orbital period = 1 year = \( 365 \times 24 \times 3600 = 3.156 \times 10^{7} \, \text{s} \).
▶️Answer/Explanation
Step (1): Use formula → \( v = \dfrac{2 \pi r}{T} \).
Step (2): Substitute values → \( v = \dfrac{2 \pi (1.496 \times 10^{11})}{3.156 \times 10^{7}} \).
Step (3): \( v \approx \dfrac{9.40 \times 10^{11}}{3.156 \times 10^{7}} \).
Step (4): \( v \approx 2.98 \times 10^{4} \, \text{m/s} \).
Final Answer: Earth’s orbital speed ≈ 29,800 m/s (about 30 km/s).
(a) Gravitational Force Keeping Planets in Orbit
- The planets orbit the Sun because of the gravitational attraction between the Sun and the planets.
- This force acts as the centripetal force, pulling planets towards the Sun and preventing them from moving in a straight line.
- Without this gravitational pull, planets would move off in a straight line into space due to inertia.
- The balance between the planet’s forward motion and the Sun’s gravitational pull results in a stable orbit.
- The strength of this force can be described by Newton’s law of gravitation: \( F \propto \dfrac{1}{r^{2}} \), where \( r \) is the distance between the planet and the Sun.
(b) Variation of Gravitational Strength and Orbital Speed
- The Sun’s gravitational field becomes weaker as the distance from the Sun increases.
- This means that planets further from the Sun experience less gravitational pull.
- As a result, outer planets orbit the Sun more slowly compared to inner planets.
- Orbital speed can be calculated using \( v = \dfrac{2 \pi r}{T} \), and since \( T \) increases with distance, \( v \) decreases.
- Inner planets (e.g. Mercury, Venus, Earth) have higher orbital speeds than outer planets (e.g. Jupiter, Neptune).
Example:
Compare the given Orbital Speeds , Mercury is at an average distance of \( 5.8 \times 10^{10} \, \text{m} \) from the Sun with a period of 88 days, while Neptune is at \( 4.5 \times 10^{12} \, \text{m} \) with a period of 165 years.
▶️Answer/Explanation
Step (1): Formula → \( v = \dfrac{2 \pi r}{T} \).
Step (2): Mercury → \( T = 88 \times 24 \times 3600 = 7.6 \times 10^{6} \, \text{s} \).
\( v = \dfrac{2 \pi (5.8 \times 10^{10})}{7.6 \times 10^{6}} \approx 4.8 \times 10^{4} \, \text{m/s} \).
Step (3): Neptune → \( T = 165 \times 365 \times 24 \times 3600 = 5.2 \times 10^{9} \, \text{s} \).
\( v = \dfrac{2 \pi (4.5 \times 10^{12})}{5.2 \times 10^{9}} \approx 5.4 \times 10^{3} \, \text{m/s} \).
Final Answer: Mercury’s orbital speed ≈ 48,000 m/s, Neptune’s orbital speed ≈ 5,400 m/s.
This shows that inner planets move much faster in their orbits than outer planets.
The Sun as a Medium-Sized Star
- The Sun is classified as a main-sequence star of medium size compared to other stars in the Universe.
- It has a diameter of about 1.39 × 106 km and a mass of about 2.0 × 1030 kg.
- The Sun’s composition is approximately 74% hydrogen, 24% helium, and about 2% heavier elements (oxygen, carbon, iron, etc.).
- In its core, hydrogen nuclei undergo nuclear fusion to form helium, releasing huge amounts of energy.
- This energy is emitted as electromagnetic radiation across a wide range of wavelengths.
Energy Radiation by the Sun
- The Sun emits energy across the entire electromagnetic spectrum, but most of its energy is concentrated in three regions:
- Infrared (IR): Heat radiation, responsible for warming the Earth’s surface.
- Visible light: The spectrum of colours from red to violet, enabling vision and photosynthesis.
- Ultraviolet (UV): Higher-frequency radiation, responsible for tanning, vitamin D production, but also harmful effects like skin damage.
- The Sun’s radiation spectrum peaks in the visible range, making it appear bright to the human eye.
- This distribution of energy follows from the Sun’s surface temperature, about 5,800 K.
Example
Why does the Sun appear yellowish-white to the human eye, and why is visible light such a significant part of its emission?
▶️Answer/Explanation
Step (1): The Sun’s surface temperature (~5800 K) means it behaves approximately like a black body radiator.
Step (2): According to Wien’s displacement law, the wavelength at which emission is maximum is given by:
\( \lambda_{\text{max}} = \dfrac{2.9 \times 10^{-3}}{T} \).
Step (3): Substituting \( T = 5800 \, \text{K} \):
\( \lambda_{\text{max}} = \dfrac{2.9 \times 10^{-3}}{5800} \approx 5.0 \times 10^{-7} \, \text{m} \).
Step (4): This wavelength lies in the green-yellow part of the visible spectrum, where the human eye is most sensitive.
Final Answer: The Sun appears yellow-white because its peak radiation is in the visible region, and visible light makes up a major part of its emission.
Stars Powered by Nuclear Reactions
- Stars, including the Sun, shine because they generate huge amounts of energy in their cores through nuclear reactions.
- These reactions release energy in the form of electromagnetic radiation (infrared, visible, ultraviolet) and kinetic energy of particles.
- In the early stage, when the star becomes stable, the main process is the fusion of hydrogen nuclei into helium nuclei.
- Fusion reactions require extremely high temperatures and pressures, as positive hydrogen nuclei repel each other due to electrostatic forces.
- The energy released prevents further gravitational collapse this balance creates a stable main-sequence star.
Hydrogen Fusion in Stable Stars
- The dominant reaction in stars like the Sun is the proton–proton chain reaction.
- Simplified reaction: \( 4 \, ^{1}_{1}H \; \rightarrow \; ^{4}_{2}He + 2 \, e^{+} + 2 \, \nu_{e} + \text{energy} \)
- Here, four hydrogen nuclei (protons) combine to form one helium nucleus, releasing positrons, neutrinos, and large amounts of energy.
- This process releases energy because the mass of the helium nucleus is slightly less than the mass of the four protons; the missing mass is converted to energy according to Einstein’s equation:
- \( E = \Delta m c^{2} \)
Example
Explain why the Sun does not collapse under its own gravity despite its enormous mass.
▶️Answer/Explanation
Step (1): Gravity tends to pull all the matter of the Sun inward, trying to cause collapse.
Step (2): In the Sun’s core, hydrogen fusion produces a continuous outward pressure from the release of energy and radiation.
Step (3): This outward thermal and radiation pressure exactly balances the inward pull of gravity.
Step (4): The Sun is therefore in hydrostatic equilibrium a stable state.
Final Answer: The Sun does not collapse because the outward pressure from fusion balances inward gravitational forces.