Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Gravitational force ↓


Newton's law of universal gravitation


Newton's law of universal gravitation is one of the cornerstones of classical mechanics. It describes the gravitational attraction between two bodies with mass. Before diving into this concept, let's learn the historical context and the basics of gravity.

Historical context

The story of the theory of gravity begins with Sir Isaac Newton, an English mathematician and physicist. In the late 17th century, Newton proposed the law of universal gravitation in his work Philosophiae Naturalis Principia Mathematica. This law was revolutionary because it laid the foundation for modern physics and astronomy.

Interpretation of the law

Newton's law of universal gravitation states:

Every point mass attracts every other point mass in the universe with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Let us analyse this statement:

  • Point mass: In physics, a "point mass" is an idealized object of mass concentrated at a point in space.
  • Proportional to the product of mass: The gravitational force increases with the mass of the objects. The heavier the objects, the greater the gravitational force.
  • Inversely proportional to the square of the distance: The gravitational force weakens with the square of the distance separating the masses. This means that if the distance between two bodies is doubled, the gravitational force becomes one-fourth stronger.

The equation of Newton's law of universal gravitation is given as:

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

Where:

  • F is the gravitational force between the two masses.
  • 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.

A visual representation

To understand Newton's law of universal gravitation, consider the following illustration, which shows the forces between two masses m1 and m2:

M1 M2 R F

In this illustration:

  • The blue circle represents the first mass m1.
  • The red circle represents the second mass m2.
  • The dashed line represents the distance r between the centers of the two masses.
  • The solid green line shows the gravitational force F acting on the two masses, pointing toward each other.

Real-life examples

Example 1: Earth and Moon

Consider the Earth and the Moon. They both have mass and are at a fixed distance from each other. The gravitational force between them is what keeps the Moon in orbit around the Earth. Using Newton's law of universal gravitation:

F = G * (m_earth * m_moon) / r^2

If we know the mass of the Earth, the mass of the Moon and the distance between them, we can calculate the force of gravity.

Example 2: Falling apple

An apple falling from a tree is a classic example that inspired Newton. When the apple falls toward the Earth, it is actually being pulled by the Earth's gravity. Likewise, the apple exerts an equally small force on the Earth, which is negligible due to the Earth's enormous mass.

Implications of the law

Newton's law of universal gravitation has many important implications. Let us discuss some of them:

1. Classes

An important consequence of Newton's laws is the explanation of orbital motion. Planets orbit the Sun due to the gravitational force exerted by the Sun. Similarly, satellites orbit the Earth due to the gravitational force.

2. Jowar (Sorghum)

The gravitational force of the moon and the sun affects the Earth's oceans, causing high and low tides. The moon's gravitational effect is stronger because it is closer to Earth.

3. Weight

The weight of an object is the force of gravity acting on it. This is why you weigh less on the Moon than you do on Earth; the Moon's gravitational force is weaker.

Boundaries

Although Newton's law of universal gravitation is incredibly powerful and useful for many calculations, it does have its limitations:

1. Large masses and distances

When dealing with very large masses or distances, the results predicted by Newton's laws may be less accurate. Einstein's general theory of relativity provides a more complete explanation in these cases.

2. Precision

For extremely precise calculations, especially those involving atomic particles, quantum mechanics provides a more suitable framework.

Conclusion

Newton's law of universal gravitation fundamentally changed our understanding of the universe. It allows us to calculate the gravitational forces between any two masses. Despite its limitations, the law remains an important part of physics education and real-world applications, forming the basis of many fields, including physics, engineering, and astronomy.

Understanding this law gives us insight into the forces that govern the motion of the planets and everyday events, and emphasizes the beauty and simplicity of how the universe works.


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Newton's law of universal gravitation

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