Gravitation

Gravitation for IIT-JEE and NEET

1. Newton’s Law of Universal Gravitation:

  • The Foundation: This law states that every particle 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 centres.   
    • F is the gravitational force
    • G is the universal gravitational constant (6.674 x 10⁻¹¹ N m²/kg²)
    • m1 & m2 are the masses of the two objects
    • r is the distance between their centres
    • Equation: F = G (m₁m₂)/r²

  • JEE Focus: You’ll need to apply this equation in various scenarios, including calculating the force between celestial bodies, finding the gravitational field strength, and analyzing the motion of satellites.

2. Gravitational Field and Potential:

  • Field: A region where a mass experiences a gravitational force. It’s a vector quantity, with both magnitude and direction.
    • Field Strength (g): The force per unit mass experienced by a small test mass placed in the field. g = F/m
  • Potential (V): The work done per unit mass in bringing a small test mass from infinity to a point in the field. It’s a scalar quantity.
    • Relationship: g = -dV/dr (the negative gradient of the potential)
  • JEE Focus: Expect problems involving calculating field strength and potential at different points, understanding the relationship between them, and analyzing the motion of particles in gravitational fields.

3. Kepler’s Laws of Planetary Motion:

  • Empirical Laws: These laws, based on observations, describe the motion of planets around the Sun.
    • 1st Law: Planets move in elliptical orbits with the Sun at one focus.
    • 2nd Law: The line joining a planet to the Sun sweeps out equal areas in equal times.
    • 3rd Law: The square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit.
  • JEE Focus: You might need to apply these laws to solve problems related to planetary motion, orbital periods, and orbital velocities.

4. Gravitational Potential Energy:

  • Concept: The energy possessed by an object due to its position in a gravitational field.
  • Equation: U = -G (m₁m₂)/r (for two point masses)
  • Gravitation for IIT-JEE and NEET: You’ll encounter problems involving calculating the potential energy of objects in different configurations, analysing energy conservation in gravitational systems, and determining escape velocities.

5. Satellite Motion:

  • Orbital Velocity: The velocity required for a satellite to maintain a stable orbit around a celestial body.
  • Geostationary Satellites: Satellites that remain stationary above a particular point on the Earth’s surface.
  • JEE Focus: Expect problems involving calculating orbital velocities, orbital periods, and the conditions for geostationary orbits.

Formula Sheet

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