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 ↓


Orbital mechanics and satellites


Orbital mechanics, also sometimes referred to as celestial or celestial mechanics, is the application of the laws of physics and mathematics to explain how celestial bodies move through space. When we talk about orbiting bodies such as satellites, planets, and comets, we get into the fascinating intersection of physics and astronomy.

Understanding gravity

First, it is important to understand what gravity is. Gravity is a force that attracts two bodies towards each other. A great example of this is how the Earth attracts an apple when it falls from a tree. This concept was discovered by Sir Isaac Newton.

Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This can be represented as the equation:

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

Where:

  • F is the force of attraction between two bodies.
  • G is the gravitational constant, approximately 6.674 × 10^-11 N(m/kg)^2.
  • m1 and m2 are the masses of the two bodies.
  • r is the distance between the centers of the two masses.

Classes explained

When we talk about orbits, we mean the path that a body takes when it revolves around another body due to the force of gravity. For example, the Moon orbits the Earth, and the Earth orbits the Sun. The orbit is generally elliptical in shape.

Let's imagine a classroom:

Primary bodies Satellite

In the figure above, the blue circle represents a planet, and the red circle represents a satellite. The path taken by the red circle is its orbit.

Types of classes

There are several types of orbitals, depending on their shape and orientation:

  • Circular orbits: These are the simplest type of orbits where the distance between the satellite and the body it orbits remains constant. The orbit is a perfect circle.
  • Elliptical orbits: Most orbital paths are elliptical, meaning they look like elongated circles or ovals. Satellites in elliptical orbits move closer and farther away from Earth at different points.
  • Geostationary orbits: In these orbits the satellite appears to stay over the same spot on the Earth's surface. This is because the satellite's orbital period matches the Earth's orbital period.
  • Polar orbits: These paths allow satellites to pass over Earth's poles, giving the satellite a view of every part of Earth as it rotates.

How do satellites stay in orbit?

The satellite stays in orbit because it is moving sideways so fast that the curve of its fall matches the curve of the Earth. Imagine you are throwing a ball. It travels in an arc before gravity pulls it to the ground. If you can throw the ball fast enough, its path will go further and further, and it will never hit the ground - that's an orbit.

throw Earth

Calculating orbital speed

The speed required for a satellite to remain in orbit is called its orbital speed. It can be calculated using the following formula:

v = √(G * M / r)

Where:

  • v is the orbital speed.
  • G is the gravitational constant.
  • M is the mass of the Earth (or the central celestial body).
  • r is the distance from the center of the Earth (or the central celestial body) to the satellite.

Example calculation

Let us calculate the speed a satellite must travel to maintain itself in low Earth orbit, about 200 kilometers above the Earth's surface.

  • The average radius of the Earth is about 6,371 km.
  • The mass of the Earth is approximately 5.972 × 10^24 kg.
  • The distance from the satellite r is 6,371 km + 200 km = 6,571,000 meters.

Plug these into the equation:

v = √(6.674 × 10^-11 N(m/kg)^2 * 5.972 × 10^24 kg / 6,571,000 m) = 7.8 km/s

Therefore, the satellite needs to maintain a speed of about 7.8 kilometers per second to remain in this orbit.

Kepler's laws of planetary motion

The motion of planets and satellites also obeys Kepler's laws of planetary motion, which can help us understand how objects travel in orbits:

  1. First Law (Law of Elliptical Orbit): This law states that the planets move in elliptical orbits with the Sun as their focal point.
  2. Second Law (Law of Equal Area): The line segment joining a planet and the Sun sweeps out equal area in equal time intervals. This means that when a planet comes near the Sun, its speed is fast and when it moves away from the Sun, its speed is slow.
  3. Third Law (Law of Harmony): The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit. This means that there is a predictable relationship between a planet's distance from the Sun and its orbital period.

Kepler's third law formula

Kepler's third law can be expressed mathematically as follows:

T^2 = k * r^3

Where:

  • T is the orbital period (the time it takes a planet or satellite to make one complete orbit).
  • k is a constant.
  • r is the semi-major axis (the average distance from the object to the central body).

Applications of orbital mechanics

Orbital mechanics is not just theory; it is practical and essential in a variety of fields:

  • Satellites: Understanding orbits is important for launching satellites, which have many applications including GPS, communications, weather monitoring, and Earth observation.
  • Space exploration: Space missions, including missions to other planets or moons, require detailed knowledge of orbital mechanics to ensure proper flight paths and mission success.
  • Astronomy: Studying the orbits of celestial objects helps astronomers understand the dynamics of our solar system and beyond.

Conclusion

Orbital mechanics unravels the dance of celestial bodies, uncovering the forces and principles that underpin the universe. From understanding why satellites stay in orbit to predicting the paths of planets, the mathematics and physics of orbits provide both theoretical and practical insights needed to harness satellite technology and expand our exploration of space.

As you continue your studies in physics, remember that the principles you learned about gravity and orbits are the fundamental basis of everything from the simplest spacecraft to the most far-reaching telescopes exploring the universe. The same rules that keep satellites in orbit also guide the journeys of stars across the universe.


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Orbital mechanics and satellites

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