Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Gravitational force → Universal gravitation ↓


Kepler's laws of planetary motion


Kepler's laws of planetary motion describe how planets orbit around the Sun. These laws help us understand the motion of planets in our solar system. Let's take a detailed look at Kepler's three laws using simple language and visual aids.

Kepler's first law - the law of ellipses

According to the first law, the paths of the planets around the Sun are elliptical, with the Sun located at one of two foci.

Sun Focus 2 Planet Oval

The ellipse looks like a flattened circle. It has two focus points. The sum of the distances from any point on the ellipse to the two foci is constant. The sun sits at one focus, not at the center.

For example, imagine a planet, say Earth, revolving around the Sun. If you measure the total distance from Earth to both foci at any time, it will remain the same, so Earth's path remains elliptical.

Kepler's second law - the law of equal areas

The second law states that the imaginary line joining a planet and the Sun covers equal areas in equal intervals of time.

Area 1 = Area 2

This means that if you move a planet to two different positions in its orbit but at equal intervals of time, the area between the planet, the Sun and the path will remain the same. This law means that a planet moves faster when it is near the Sun and slower when it is far from it.

For example, when Earth is closest to the sun, such as during perihelion (around January 3), it travels faster than when it is farther away (during aphelion, around July 4). Still, the area covered over 30 days is the same at both times of year.

Kepler's third law - the law of harmony

The third law states that the square of the period of revolution of any planet is proportional to the cube of the semi-major axis of its orbit.

 t^2 ∝ a^3

Where:

  • T is the planet's orbital period (how long it takes to complete one orbit).
  • a is the semi-major axis, the average distance from the planet to the Sun.

This law shows a consistent relationship between the distance of the planets from the Sun and their orbital period. The farther a planet is from the Sun, the longer it takes to orbit.

For example, Earth is 1 astronomical unit (AU) from the Sun and takes about one year to complete one orbit. Mars, on the other hand, is about 1.52 AU from the Sun and takes about 1.88 years to complete one orbit. The ratio between the square of their period and the cube of their average distance is constant for all planets.

Applying Kepler's Laws

To better understand these rules, let’s apply them to a hypothetical scenario where you are an astronomer observing a newly-discovered two-planet system around a distant star.

Planet A has a semi-major axis of 1.5 AU and takes 2 years to orbit the star. Planet B orbits the same star at a distance of 3 AU.

Use of Kepler's third law:

T a ^2 / a a ^3 = T b ^2 / a b ^3

Substitute the known values for planet A:

(2 yr)^2 / (1.5 AU)^3 = T b ^2 / (3 AU)^3

Calculate:

4 / 3.375 = t b ^2 / 27

Solve for T B :

t b ^2 = (4 * 27) / 3.375
t b = √32
T b ≈ 5.66 years

This shows that Kepler's simple but profound laws help astronomers predict orbital dynamics and better understand our universe.

Kepler's legacy in understanding the universe

Kepler's laws laid the groundwork for Isaac Newton to derive the law of universal gravitation. These laws were important in the transition from ancient thought, especially the circular orbits proposed by Ptolemy, to elliptical orbits, providing a new understanding based on observations made by Tycho Brahe.

Through these laws, we understand why planets don't move in perfect circles and understand the complex motions and dances of celestial bodies in space, shaping the field of celestial mechanics. Kepler's brilliant mathematical descriptions echo throughout modern science, helping to chart the paths of planets, spacecraft, and satellites.

This study of motion extends beyond our solar system, and aids in the precise navigation of distant planets, star systems, and extraplanetary discoveries that intrigue the fields of astrophysics and cosmology.

In short, Kepler's laws are the backbone of planetary science, facilitating predictions and explanations of celestial behavior. Armed with this knowledge, we are better equipped to explore the mysteries of the universe and the ever-dynamic nature of space, connecting the orbits of the tiny worlds that shine within it.


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Kepler's laws of planetary motion

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