Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate ↓


Astrophysics and cosmology


Astrophysics and cosmology are fields of physics that explore the vast universe beyond our planet Earth. These include understanding stars, galaxies, black holes, the beginning of the universe, and much more. In this lesson, we will discuss these topics in depth, breaking them down into understandable concepts.

What is astrophysics?

Astrophysics is the branch of astronomy that studies the physics of the universe. It includes the physical properties of celestial objects and the processes that control them. Astrophysics looks at the life cycle of stars, the formation of planets, and the behavior of matter in extreme conditions such as black holes and neutron stars.

Understanding the wires

Stars are massive celestial bodies composed primarily of hydrogen and helium that produce light and heat from nuclear fusion occurring in their cores. The life of a star can be roughly described as a cycle.

Stars begin as clouds of dust and gas. When these clouds collapse due to their own gravity, they form a protostar. If this protostar gathers enough mass, nuclear fusion begins. This is when hydrogen atoms merge to form helium, releasing energy in the form of light and heat.

Here's a simplified illustration of a protostar structure:

The energy produced counteracts the force of gravity, causing the star to become stable. Eventually, the star will exhaust its nuclear fuel, causing its death. Depending on the size of the star, it may become a white dwarf, a neutron star, or even collapse into a black hole.

Life cycle of stars

The life cycle of stars consists of different phases, and each phase lasts millions or billions of years:

  • Main sequence: Most stars, including our Sun, remain in this longest stage, where they burn hydrogen into helium.
  • Red giants or supergiants: After the hydrogen is exhausted, stars expand and cool, becoming red giants or supergiants.
  • Final stage: Small stars shed their outer layers to become white dwarfs. Massive stars explode as supernovae, potentially producing black holes or neutron stars.

Physics of stars

Stars are great physical systems where various physical processes take place. Let us discuss two important processes: nuclear fusion and gravitational equilibrium.

Nuclear fusion: The extreme temperature and pressure at the centre of a star causes hydrogen nuclei to collide and fuse to form helium. This is illustrated as follows:

4 H -> He + Energy

This process releases enormous amounts of energy, which keeps the star alive for millions of years.

Gravitational equilibrium: Also known as hydrostatic equilibrium, this is the balance between the inward pull of gravitational pull and the outward pressure from nuclear fusion. This is crucial to the stability of a star. The pressure from fusion at the core must counteract the gravitational forces trying to compress it.

What is cosmology?

Cosmology is the study of the entire universe. It attempts to understand the origin, evolution, structure, and ultimate fate of the universe. Cosmologists explore questions such as how the universe began, why it looks the way it does, and what will happen to it in the future.

The Big Bang Theory

The most prominent theory in cosmology is the Big Bang theory. It proposes that the universe began as an extremely hot and dense state about 13.8 billion years ago and has been expanding ever since.

To understand this concept, think of the universe as a balloon. When you pump air into it, the balloon (universe) expands. The galaxies inside the balloon move away from each other, just like the dots on the surface of a balloon when it is inflated.

As the universe expands, the distance between galaxies increases, but the galaxies themselves remain intact. This explains the redshift seen in light from distant galaxies, a phenomenon that supports the expansion of the universe.

Dark matter and dark energy

There are two mysterious things in the universe: dark matter and dark energy. Together, they make up about 95% of the total mass-energy fraction of the universe.

Dark matter: Although it cannot be seen directly with telescopes, dark matter exerts a gravitational force. It helps hold galaxies together and affects their rotation. Unlike ordinary matter, dark matter does not emit, absorb, or reflect light.

Dark energy: This is the force thought to be responsible for the accelerating expansion of the universe. Unlike dark matter which acts on a large scale within galaxies, dark energy acts on a cosmic scale, affecting the entire universe.

Key observations in cosmology

  • Cosmic Microwave Background (CMB): This is the radiation left behind by the Big Bang, providing a snapshot of the newborn universe about 380,000 years after its beginning.
  • Redshift of galaxies: The observed redshift of light from distant galaxies is an important support for the theory of an expanding universe. The greater the shift, the faster the galaxy is moving away.
  • Distribution of galaxies: The large-scale structure of the universe aligns galaxies into huge filaments and clusters, separated by voids. This distribution reflects the influence of both dark matter and dark energy.

Interrelation of astrophysics and cosmology

Astrophysics and cosmology are closely linked, because understanding different astronomical phenomena helps us understand the evolution and structure of the universe. For example, by studying star formation and supernovae, we learn about the creation and dispersal of elements. This knowledge is important for cosmological models that predict how the universe evolves over time.

Important concepts and their interrelationships

  • Nucleosynthesis in stars and the Big Bang: While Big Bang nucleosynthesis produced only lighter elements (hydrogen, helium, and small amounts of others), stars produce heavier elements through nuclear fusion. Understanding these processes helps describe the chemical composition of the universe.
  • Black holes and the fate of the universe: Black holes, which arise at the end of the life-cycle of massive stars, help us think about the fate of the universe because of their ability to distort spacetime and potentially accumulate mass.

Formulas and models used in astrophysics and cosmology

Various mathematical models and equations are used to describe and predict astrophysical and cosmological phenomena:

For stellar dynamics, Newton's laws of motion and the law of universal gravitation are important:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.

In cosmology, the Friedmann equations describe the expansion of the universe:

(dot{a}/a)^2 = 8πGρ/3 - kc^2/a^2 + Λc^2/3

where a is the scale factor, ρ is the density of matter, k is the curvature constant, Λ is the cosmological constant, and c is the speed of light.

Conclusion

Astrophysics and cosmology together help us understand the vast scale and mysteries of the universe. These sciences allow us to trace the history of the universe, from the birth of stars to the universe we see today, teaching us about the fundamental forces and elements that shape everything around us. By studying these fields, we gain insights necessary not just for scientific curiosity, but to understand our own place in the vast expanse of the universe.


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