Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Mechanics → Gravitational force ↓


Satellites and their orbits


Satellites are objects that orbit a planet or star. In our daily lives, satellites perform many functions, such as helping us forecast the weather, providing directions via GPS, broadcasting TV signals, and much more. Understanding how satellites move involves understanding their orbits, which are governed by the laws of gravity in physics.

Understanding classes

Orbit is the path that an object follows when it moves around another object due to gravity. The motion of a satellite around a planet can be understood from the laws of gravity and motion. Let's start with some basic concepts:

Gravity is the force that pulls two objects toward each other. The gravitational force between two objects depends on their masses and the distance between them. It can be described by Newton's law of universal gravitation:

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

Where:

  • F is the gravitational force between the two objects.
  • G is the gravitational constant, approximately (6.674 times 10^{-11} , text{Nm}^2/text{kg}^2).
  • m 1 and m 2 are the masses of the two objects.
  • r is the distance between the centers of the two objects.

Types of classes

Circular orbits

A circular orbit is one in which the satellite moves around the planet at a constant speed in a circular path. For a circular orbit, the gravitational force provides the centripetal force needed to keep the satellite in motion. The formula for centripetal force is:

        F_c = (m * v^2) / r
    F_c = (m * v^2) / r

Where:

  • F c is the centripetal force.
  • m is the mass of the satellite.
  • v is the velocity of the satellite.
  • r is the radius of the orbit.

For a satellite moving in a circular orbit, the gravitational force is equal to the centripetal force:

        G * (m e * m) / r^2 = (m * v^2) / r
    G * (m e * m) / r^2 = (m * v^2) / r

where m e is the mass of the Earth, and we can solve for the satellite's velocity v:

        v = sqrt(G * m e / r)
    v = sqrt(G * m e / r)

Elliptical orbits

An elliptical orbit is an oval-shaped path. Most natural satellites, such as the Moon, follow elliptical paths. Kepler's first law of planetary motion states that planets move in elliptical orbits with the Sun at one focus. Similarly, a satellite moves in an elliptical orbit with the planet at one focus.

Orbital elements

Several elements are used to define the size and shape of an orbit:

  • Semimajor axis (a): The longest radius of the ellipse, which represents half of the longest diameter.
  • Eccentricity (e): This measures how much an orbit deviates from being circular. A circular orbit has an eccentricity of 0, while an eccentricity close to 1 indicates a highly elongated orbit.
  • Inclination (i): The angle between the orbital plane and the equatorial plane of the planet.

Understanding geosynchronous orbits

The geosynchronous orbit is a high Earth orbit that allows satellites to match Earth's rotation. Located approximately 35,786 kilometers above Earth's equator, satellites follow an orbital period equal to Earth's rotation period, 24 hours. When a geosynchronous orbit just above the equator appears stationary relative to Earth's surface, it is called a geostationary orbit.

Orbital motion

The speed of a satellite in orbit depends on the gravitational pull of the planet and the altitude of the orbit. For a circular orbit, the speed can be calculated using:

        v = sqrt(G * m e / r)
    v = sqrt(G * m e / r)

Let's look at an example: If a satellite is 300 km above the Earth's surface, where the Earth's radius is about 6371 km, calculate its orbital speed. Substituting the values:

        r = 6371 km + 300 km = 6671 km = 6.671 x 10 6 mv = sqrt((6.674 x 10 -11 Nm 2 /kg 2) * (5.972 x 10 24 kg) / (6.671 x 10 6 m))
    r = 6371 km + 300 km = 6671 km = 6.671 x 10 6 mv = sqrt((6.674 x 10 -11 Nm 2 /kg 2) * (5.972 x 10 24 kg) / (6.671 x 10 6 m))

After performing the calculations, the estimated orbital speed is about 7.8 km/s.

Factors affecting satellite orbits

Several factors affect satellite orbits:

  • Gravity: The primary force affecting orbit. Different gravities of planets mean different orbits for satellites.
  • Atmospheric drag: When satellites pass through the upper layers of a planet's atmosphere, they encounter resistance, slowing them down.
  • Solar radiation pressure: Photons from the Sun can push satellites, slightly changing their path.

Misalignments or slight changes caused by these factors may require adjustments using onboard thrusters to maintain the intended orbits.

Conclusion

Understanding the orbits of satellites involves understanding the balance of forces acting on satellites and ensuring that they follow the desired paths around planets or stars. Applications such as GPS, communications, and weather forecasting rely heavily on our knowledge of orbits in mechanics. The harmony of gravitational forces and the mechanics involved ensures that these satellites perform their functions efficiently.


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Satellites and their orbits

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