Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Mechanics → Gravitational force ↓


Newton's law of universal gravitation


Newton's law of universal gravitation is a fundamental principle in physics that describes the gravitational force between two objects. It was formulated by Sir Isaac Newton in 1687 and laid the foundation for classical mechanics. This law describes how objects in the universe attract each other, depending on their mass and the distance between them.

Interpretation of the law

According to Newton's law of universal gravitation, every point mass in the universe attracts every other point mass with a force along the line connecting them. This force is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law can be expressed mathematically as follows:

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

Where:

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

Let us study each of these components in more detail and understand the implications of this law.

Gravitational constant (G)

The gravitational constant, denoted by G, is a key parameter in the law of universal gravitation. Its value is very small, indicating that gravitational forces are much weaker than, for example, electromagnetic forces. The constant helps to calculate the gravitational force when the mass and distance are known.

Since the value of G is very small, it requires massive bodies like planets or stars to experience significant gravitational forces. This is why we only feel the gravity of the Earth on a daily basis, not the gravity of smaller objects around us.

Mass of the objects (m1 and m2)

The masses of both objects play a vital role in determining the gravitational force. The greater the mass, the stronger the gravitational force. This means that larger celestial bodies like planets and stars have a substantial gravitational pull compared to smaller objects.

For example, the mass of the Earth creates the gravitational force that keeps the Moon in orbit. Similarly, the enormous size of the Sun keeps the planets of the Solar System in their respective orbits. We can visualize this using the mass and force relationship:

m1 m2 F

Distance between objects (r)

Distance also plays an equally important role in determining the force of gravity. The force decreases rapidly as the distance between two objects increases. The nature of the inverse-square law means that if the distance is doubled, the gravitational force becomes one-fourth.

For example, the gravitational force between the Earth and the Moon is less than the gravitational force between the Earth and a satellite orbiting much closer to it. We can visualize this concept with a simple diagram:

Earth moon r = 384,400 km

Gravitational force (F)

The force of gravity is what keeps planets, moons and artificial satellites in orbit. It is also the reason we stay firmly rooted to Earth. This force is always attractive, which means it pulls objects toward each other, not pushes them away.

The implications of the force of gravity are very wide. It governs the motion of celestial bodies, controls the tides on Earth due to the gravity of the Moon, and affects light and time in phenomena such as gravitational lensing and general relativity.

Examples of Newton's law of universal gravitation

Example 1: Earth and Moon

The Earth and the Moon are two massive bodies located relatively close together in space. The gravitational force between these two celestial bodies keeps the Moon in orbit around the Earth. Consider the following:

  • The mass of the Earth, m1, is approximately 5.972 × 10^24 kg.
  • The mass of the Moon, m2, is about 7.342 × 10^22 kg.
  • The average distance between the Earth and the Moon is about 384,400 km, which is equivalent to 384,400,000 m.

By applying Newton's law of universal gravitation, we can calculate the force of gravity:

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

Enter values:

F = (6.674 × 10^-11) * (5.972 × 10^24 * 7.342 × 10^22) / (384,400,000)^2

This calculation results in a gravitational force equal to about 1.992 × 10^20 N, which is enough to keep the Moon in a stable orbit around the Earth.

Example 2: You are on Earth

The force of gravity between you and the Earth is what gives you weight. This force is often referred to as "weight" and is given by:

Weight = m * g

Where:

  • m is your mass.
  • g is the acceleration due to gravity on Earth, approximately 9.8 m/s^2.

Suppose your mass is 70 kg. The gravitational force acting on you will be:

Weight = 70 * 9.8 = 686 N

This means that you apply a gravitational force of 686 N on the Earth and the Earth also applies the same force on you.

Conclusion

Newton's law of universal gravitation is a cornerstone of understanding the motion of celestial bodies and the forces at work in our universe. It helps us understand gravitational interactions from microscopic to astronomical scales.

This simple but profound law explains why planets orbit stars, how moons orbit planets and why objects fall toward each other. Its universality means it applies everywhere in the universe, making it a fundamental principle in the study of physics.

As we continue to explore the universe and discover new phenomena, the fundamental understanding provided by Newton's laws will remain an essential tool in solving the mysteries of gravity and motion.


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Newton's law of universal gravitation

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