Lectures
This page will provide the list of lectures, details and videos to each lectues.
Lectures Of PCA
In PCA, lectures can provide club members with valuable knowledge and skills to study specific topics that interest them, offering members a valuable experience in further research.
Lecture 1: Planetary Motion- Kepler’s Laws
Kepler's three laws describe how planets orbit the Sun. They describe how (1) planets move in elliptical orbits with the Sun as a focus, (2) a planet covers the same area of space in the same amount of time no matter where it is in its orbit, and (3) a planet's orbital period is proportional to the size of its orbit.​
Lecture 2: Newtonian Laws.
1st, 2nd and 3rd law….
The most commonly used Newtonian Laws in Astrophysics are usually Newton’s 2nd Law, F=MA, where the force, mass, and acceleration can be replaced by other components
Lecture 3: Newtonian Law- Gravity (Spherical Bodies).
Newton's Law of Universal Gravitation applies to spherical bodies. We will break down the inverse-square law and explain why the force of gravity between two objects acts as if all their mass is concentrated at a point at their center—a key concept known as the shell theorem. We will then apply this to calculate gravitational force, orbital velocity, and the motion of planets and satellites, providing the fundamental principles behind celestial mechanics.
Lecture 4:
Galileo’s Discoveries
Gallileo's Revelations explore the groundbreaking discoveries of Galileo Galilei, who transformed our understanding of the cosmos through early telescopic observation. We will discuss his critical findings, including the moons of Jupiter, the phases of Venus, and the rugged surface of our own Moon. We will analyze how these observations provided the first direct empirical evidence against the geocentric model of the universe and became a cornerstone of the Scientific Revolution, firmly supporting a heliocentric view of the solar system.
Lecture 5: Conservation Of Energy (All Orbits)
Conservation of Energy explores the fundamental principle of energy conservation as it applies to orbital mechanics. We will analyze how the total mechanical energy—the sum of kinetic and gravitational potential energy—remains constant for an object under the influence of gravity, regardless of its path. We will derive and apply the energy conservation equation to all four conic sections:
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Circular Orbits: Where kinetic and potential energy maintain a fixed relationship.
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Elliptical Orbits: How energy varies between perihelion and aphelion while the total remains constant.
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Parabolic Orbits: The special case of exactly zero total energy, defining the escape trajectory.
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Hyperbolic Orbits: Where excess positive kinetic energy results in unbound motion.
This approach provides a powerful and unified framework for understanding orbital paths, from satellites to comets.
Lecture 6:
Hyperbolic Trajectories & Gravitational Slingshots
Gravitational Slingshots will focus on the dynamics of unbound orbits under the influence of gravity, specifically hyperbolic trajectories and their practical application in gravitational slingshot maneuvers. We will begin by deriving the characteristics of hyperbolic paths from the energy-based approach to orbital mechanics, highlighting how a positive total energy results in open trajectories with distinct asymptotes. The discussion will then shift to the physics of gravitational assists—how spacecraft can gain or lose significant kinetic energy by passing through a planet's gravitational well. We will analyze the mechanics of these flybys, including the role of the planet's own orbital motion, and demonstrate how this technique is used to propel probes into the outer solar system or slow them for inner planetary encounters.
Lecture 7: Gravitational Energy, Potential Energy, Kinetic Energy, and Conservation Principle
This lecture will provide a unified treatment of energy in gravitational systems. We will begin by deriving the expression for gravitational potential energy, emphasizing its zero point at infinity and its application for both uniform and non-uniform fields. The focus will then shift to the relationship between this potential energy and kinetic energy for objects in motion under gravity, such as falling bodies, satellites, and escaping projectiles. By applying the principle of conservation of mechanical energy, we will analyze orbital velocities, escape speed, and energy transitions in various trajectories, reinforcing how potential energy converts to kinetic energy in a closed system. This framework is essential for understanding orbital dynamics and energy balances in astrophysical contexts.
Lecture 8:
Light - Planck’s Energy Formula
This lecture will explore the revolutionary concept of quantized energy that resolved the ultraviolet catastrophe and laid the foundation for quantum mechanics. We will begin by examining the limitations of classical physics in explaining blackbody radiation, leading to Max Planck’s groundbreaking proposal: that light is emitted or absorbed in discrete packets of energy called quanta. We will derive and analyze Planck’s energy formula, E=hν, where (E) is the energy of a photon, (h) is Planck’s constant, and (ν) is the frequency of light. The implications of this formula will be discussed in contexts such as:
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The photoelectric effect
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Atomic spectra
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Quantum nature of electromagnetic radiation
This lecture aims to bridge classical wave theory and the particle-like behavior of light, highlighting how Planck’s work fundamentally changed our understanding of energy and light at the atomic scale.
Lecture 9:
Angular Momentum in Physical Systems
This lecture will explore the fundamental conservation law of angular momentum and its pivotal role across various physical systems. We will begin by defining angular momentum mathematically for both a particle and a rigid body (L=r x p and L=Iw) emphasizing its vector nature and dependence on the choice of origin. The central principle of conservation—where no net external torque implies constant angular momentum—will be derived and applied to diverse phenomena:
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Planetary orbits and Kepler’s second law
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Spin of astronomical objects (neutron stars, galaxies)
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Gyroscopic motion and stability
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Quantum mechanical spin and intrinsic angular momentum
Through these examples, we will illustrate how angular momentum governs rotational dynamics, from galactic scales to subatomic particles, providing a unified framework for analyzing conserved quantities in isolated systems.
Lecture 10:
Stellar Spectroscopy: The Emission and Absorption of Light in Astrophysics
This lecture will explore how the quantum processes of light emission and absorption serve as the fundamental tools for decoding the universe. We will examine how atoms and molecules in astrophysical environments—from stellar atmospheres to interstellar clouds—interact with light to produce unique spectral fingerprints. The discussion will focus on:
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Formation of Absorption Lines: How photospheric photons passing through a star’s cooler outer atmosphere yield Fraunhofer lines, revealing composition, temperature, and density.
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Emission Line Nebulae: The physics behind glowing regions like HII zones and planetary nebulae, where ultraviolet radiation from hot stars ionizes gas, leading to recombination and line emission.
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Doppler Shifting: Using redshift and blueshift of spectral lines to measure radial velocity, orbital dynamics, and the expansion of the universe.
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Quantitative Spectroscopy: How line strength, width, and profile inform us of chemical abundance, gravitational fields, magnetic fields (Zeeman effect), and gas pressure.
This lecture will highlight how spectroscopy remains one of the most powerful instruments in astrophysics, allowing us to determine the physical properties, composition, and motion of celestial objects across the cosmos.
Lecture 11:
Stellar Radiation: Energy, Luminosity, and Flux
This lecture will explore the fundamental principles that allow astronomers to measure and classify the energy output of stars. We will begin by defining the core concepts of luminosity—the total energy a star radiates per second—and flux, which is the energy received per second per unit area here on Earth. This will naturally lead to the inverse square law of light, explaining how flux diminishes with distance. We will then apply these ideas to blackbody radiation, using Planck's law and the Stefan-Boltzmann law to understand how a star's luminosity depends on its surface temperature and radius. Finally, we will synthesize all these concepts by introducing the Hertzsprung-Russell (H-R) Diagram, using it as a powerful tool to classify stars by their luminosity and temperature, thereby revealing the patterns of stellar evolution, from main-sequence stars to giants and white dwarfs.
Lecture 12:
Redshift & Blueshift- The Doppler Effect in Light
This lecture will explore the critical astrophysical phenomenon of redshift and blueshift, which are manifestations of the Doppler Effect applied to electromagnetic waves. We will derive the relativistic Doppler formula to accurately describe how the observed wavelength and frequency of light from a source are altered by its motion relative to an observer. The discussion will cover key applications, including:
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Radial Velocity Measurements: Determining the approach (blueshift) or recession (redshift) of stars, galaxies, and other celestial objects.
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Hubble’s Law: Using cosmological redshift to measure the expansion rate of the universe and the distance to faraway galaxies.
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Gravitational Redshift: How light losing energy as it escapes a strong gravitational field (e.g., near a black hole) also causes a redshift, as predicted by general relativity.
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Exoplanet Detection: Indirectly detecting planets by observing stellar “wobbles” via subtle Doppler shifts in the host star’s spectrum.
This lecture will highlight how redshift and blueshift serve as essential tools for probing motion, distance, and the very structure of the universe on all scales.