Astrophysics

Units

  • Units to be used:

    • kilogram (kg) → unit of mass, a measure of the amount of matter in an object

    • metre (m) → unit of distance/length, used to measure size or separation in space

    • metre/second (m/s) → unit of speed or velocity, describing how fast something moves

    • metre/second² (m/s²) → unit of acceleration, describing the rate of change of velocity

    • newton (N) → unit of force, defined as the force needed to accelerate 1 kg at 1 m/s²

    • second (s) → unit of time

    • newton/kilogram (N/kg) → unit of gravitational field strength, the force acting on 1 kg of mass

Motion in the universe

  • The universe:

    • A very large collection of billions of galaxies

    • Continues to expand since the Big Bang

  • A galaxy:

    • A large collection of billions of stars, along with gas, dust, and sometimes black holes

    • Held together by gravity

    • Our solar system is located in the Milky Way galaxy, which is a spiral-shaped galaxy

  • Gravitational field strength (g):

    • The strength of gravity varies depending on location

    • On Earth, g ≈ 9.8 N/kg

    • It is weaker on the Moon (about 1/6th of Earth’s g) because the Moon is smaller and less massive

    • Larger planets, like Jupiter, have much stronger gravitational field strengths

  • Gravitational force causes:

    • Moons to orbit planets → moons are held in stable orbits around their planets due to gravitational attraction; they usually have almost circular paths

    • Planets to orbit the Sun → the Sun’s very large mass creates a strong gravitational pull that keeps the planets moving in nearly circular orbits rather than flying off in straight lines

    • Artificial satellites to orbit the Earth → satellites, such as communication or weather satellites, are kept in orbit by Earth’s gravity; without gravity they would move off into space

    • Comets to orbit the Sun → comets follow highly elliptical orbits; gravity from the Sun pulls them back after they travel to the far reaches of the solar system

  • Differences in orbits:

    • Moons orbit planets in nearly circular orbits and remain bound closely to the planet

    • Planets orbit the Sun in almost circular orbits and remain in the same plane (the ecliptic)

    • Comets orbit the Sun in very elongated elliptical orbits, spending most of their time far from the Sun and only briefly close to it

  • Orbital speed formula:

    • The orbital speed remains nearly constant as the distance from the centre doesn’t change

      • Orbital speed = (2 × π × orbital radius) ÷ time period

      • v = 2πr / T

      • This means the speed of an orbiting object depends on its orbital radius and how long it takes to complete one orbit

Stellar evolution

  • Star classification:

    • Stars can be classified according to their colour

    • Star colour depends on surface temperature:

      • Blue stars → hottest, temperatures above 25,000 K

      • White → very hot, between 10,000–25,000 K

      • Yellow → medium temperature, around 6,000 K (e.g. the Sun)

      • Orange → cooler, around 4,500 K

      • Red → coolest, temperatures below 3,500 K

  • Evolution of stars similar to the Sun:

    • Nebula → cloud of gas and dust pulled together by gravity

    • Protostar → region contracts, temperature rises, nuclear fusion begins

    • Main sequence star → stable stage lasting billions of years, fusion of hydrogen into helium provides energy, outward radiation pressure balances inward pull of gravity

    • Red giant → hydrogen runs out, core contracts and outer layers expand, helium fusion begins, star becomes cooler and redder in colour

    • White dwarf → outer layers drift away forming a planetary nebula, leaving behind a small hot dense core that slowly cools over billions of years

  • Evolution of stars more massive than the Sun:

    • Nebula → massive protostar → main sequence star

    • Red supergiant forms after hydrogen fuel runs out

    • Core collapses, leading to a violent supernova explosion, releasing huge amounts of energy

    • After explosion:

      • Neutron star forms if the core left is dense and compact but not extremely massive

      • Black hole forms if the remaining core is extremely massive and gravity prevents even light escaping

  • Brightness of a star:

    • Brightness can be measured by apparent magnitude (how bright a star looks from Earth) and absolute magnitude (how bright it would appear at a standard distance of 10 parsecs)

    • Absolute magnitude allows fair comparison of stars without the effect of distance

    • A lower magnitude value means a brighter star (e.g. -1 is brighter than +5)

  • Hertzsprung–Russell (HR) diagram:

    • Shows relationship between surface temperature (x-axis, decreasing to the right) and absolute magnitude/brightness (y-axis, increasing upwards)

    • Main features:

      • Main sequence stars form a diagonal band from hot/bright (top left) to cool/dim (bottom right)

      • Red giants appear in the upper right (cool but very bright due to large size)

      • White dwarfs appear in the lower left (hot but dim due to small size)

Drawn HR diagram:

Simplified digital HR diagram:

Cosmology

  • Evolution of the universe:

    • The Big Bang theory suggests the universe began around 13.8 billion years ago from a single, extremely hot and dense point

    • All matter, space and time originated in this event

    • The universe has been expanding ever since, and galaxies are moving apart from each other

    • In the earliest moments, particles formed, then atoms, leading to stars and galaxies forming over time

  • Evidence for the Big Bang theory:

    • Red-shift:

      • Light from distant galaxies is shifted towards the red end of the spectrum, showing they are moving away from us

      • The more distant the galaxy, the greater the red-shift, meaning it is moving away faster → this indicates that the universe is expanding

    • Cosmic microwave background radiation (CMB):

      • Faint radiation detected in every direction of the sky

      • It is the leftover heat from the Big Bang, stretched into microwave wavelengths as the universe expanded

      • Its uniform presence provides very strong evidence that the universe began in a hot, dense state

  • Doppler effect with waves:

    • If a wave source moves relative to an observer, the frequency and wavelength change

    • Approaching source → frequency appears higher, wavelength shorter (blue-shift in light)

    • Receding source → frequency appears lower, wavelength longer (red-shift in light)

    • This effect applies to both sound and light waves

  • Equation for red-shift:

    • change in wavelength / reference wavelength = velocity of galaxy / speed of light

    • Δλ (New - original) / λ₀ (Original) = v / c (3×10 to the power of 8)

    • Used to calculate how fast galaxies are moving away from us

  • Red-shift observations:

    • Light from galaxies further away shows a greater red-shift

    • This means that the universe is not only expanding, but galaxies that are more distant are receding at faster speeds

  • Red-shift as evidence for expansion:

    • Since galaxies are moving apart in all directions, it suggests that space itself is stretching

    • This supports the Big Bang model rather than a static universe

    • It also suggests that in the past, all matter and space were concentrated at a single point

  • Future of the universe:

    • The ultimate fate depends on the total amount of matter and energy

    • Possibilities include:

      • Continuous expansion forever

      • Slowing down but never stopping

      • Eventually collapsing back in a "Big Crunch" if there is enough mass and gravity

Expansion example:

  • Original:

  • Expansion:

  • Expansion from different point of view