Gravitation
1. Universal Law of Gravitation
- Every object attracts every other object with a force.
- Force is directly proportional to product of masses and inversely proportional to square of distance between them.
- Formula: F = G × (m₁ × m₂) / r²
2. Gravitational Constant (G)
- Value: G = 6.674 × 10⁻¹¹ N·m²/kg²
- G is universal and does not change.
3. Acceleration Due to Gravity (g)
- g = GM / R²
- It is the acceleration experienced by a body due to Earth’s gravity.
- Standard value: g ≈ 9.8 m/s² near the Earth's surface.
4. Variation of g
- With Altitude: g decreases with height above the Earth.
- With Depth: g decreases linearly with depth.
- With Latitude: g is maximum at poles and minimum at equator due to Earth's rotation.
5. Gravitational Potential Energy
- Energy due to position in gravitational field.
- U = -GMm / r
6. Escape Velocity
- Minimum velocity required to escape Earth's gravity without returning.
- vₑ = √(2gR) or √(2GM / R)
- Value on Earth ≈ 11.2 km/s
7. Orbital Velocity
- Velocity required to stay in orbit around Earth.
- v₀ = √(GM / r)
- Less than escape velocity.
8. Satellites
- Natural or artificial objects orbiting a planet.
- Time period of satellite (T): T = 2π√(r³ / GM)
- Geostationary satellites have period of 24 hours and remain fixed over one location.
9. Weightlessness
- Condition when there is no normal force acting on a body.
- Experienced in free fall or in orbiting satellites.