Gravitation - Important Formulas, Definitions, and Examples | 11th Physics

Chapter 5: Gravitation

Chapter 5: Gravitation

Formulas: Gravitational force, Universal law of gravitation, Gravitational constant, Free fall, Gravitational potential energy, Escape velocity

Introduction

Gravitation is the force of attraction between two objects with mass. This chapter discusses the fundamental principles of gravitation, including Newton's universal law of gravitation, gravitational potential energy, and concepts related to free fall, escape velocity, and orbits.

1. Universal Law of Gravitation

Definition:

According to Newton’s law of universal gravitation, every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Key Concepts:

  • Formula: F = G (m₁ × m₂) / r² where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between them.
  • Gravitational Constant (G): Its value is 6.67 × 10⁻¹¹ Nm²/kg².

2. Gravitational Potential Energy

Definition:

Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. It is given by the work done to bring an object from infinity to a point in the gravitational field.

  • Formula: U = -G (m₁ × m₂) / r

Applications:

  • Understanding energy conservation in gravitational systems.
  • Potential energy plays a key role in orbital mechanics and free-fall scenarios.

3. Free Fall

Definition:

Free fall is the motion of an object under the influence of gravitational force only, with no other forces acting on it. The acceleration experienced by an object during free fall is called acceleration due to gravity (g).

  • Value of g on Earth: g ≈ 9.8 m/s²
  • In free fall, the object's velocity increases uniformly as it descends towards the Earth.

4. Escape Velocity

Definition:

Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet or other massive body without further propulsion.

  • Formula: vₑ = √(2GM/r) where vₑ is the escape velocity, G is the gravitational constant, M is the mass of the planet, and r is its radius.
  • For Earth, the escape velocity is approximately 11.2 km/s.

5. Satellites and Orbits

Orbital Motion:

Satellites move around the Earth in circular or elliptical orbits due to the balance between gravitational force and their inertia. The velocity required to maintain a stable orbit is called orbital velocity.

  • Formula: vorbital = √(GM/r) where vorbital is the orbital velocity, M is the mass of the Earth, and r is the distance of the satellite from the Earth's center.
  • Geostationary satellites revolve around the Earth in 24 hours, staying fixed over one location.

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