Gravitation Lecture Notes

Introduction

• Gravitational Force: It is a central force, acting between objects m1 and m2.
• Formula: ( F = \frac{Gm_1m_2}{r^2} )
  • ( G ): Gravitational constant ( 6.67 \times 10^{-11} , \text{Nm}^2/\text{kg}^2 )

Gravitational Intensity & Potential

• Gravitational Intensity: ( E = \frac{Gm}{r^2} )
• Gravitational Potential: ( V = -\frac{Gm}{r} )

Acceleration Due to Gravity (g)

• On Earth's surface: ( g = \frac{GM}{R^2} )
• At a height: ( g' = g \left(1 - \frac{2h}{R} \right) )
• At a depth: ( g' = g \left(1 - \frac{d}{R} \right) )

Satellite Motion

• Orbital Velocity: ( v_o = \sqrt{\frac{GM}{r}} )
• Escape Velocity: ( v_e = \sqrt{2gR} )
• Time Period: ( T = 2\pi \sqrt{\frac{r^3}{GM}} )

Kepler's Laws

1. Law of Orbits: The orbits of planets are elliptical.
2. Law of Areas: Covers equal area in equal time.
3. Law of Periods: ( T^2 \propto r^3 )

Questions

• Center of mass questions: Formula and examples for the center of mass.
• Questions on direct equations of gravitational force and acceleration.

Important Points

• Gravity is highest at the surface.
• The effect of gravity changes with height and depth.
• Formulas for a satellite's orbital and escape velocities.

These notes cover important topics, formulas, and questions related to gravitation. This information will be beneficial for your upcoming exam.