Lecture on Gravity

Introduction

• Presented by Stanford University.
• Main focus on gravity, excluding the general theory of relativity, focusing on Newtonian gravity.
• Gravity is unique compared to electric and magnetic forces.

Newton's Equations

• Newton's First Law: An object will remain at rest or in uniform motion unless acted on by a force.
• Newton's Second Law: ( F = ma ) (Force equals mass times acceleration).
• Newton's Third Law: For every action, there is an equal and opposite reaction.
• Vector Nature of Forces: Forces have direction and magnitude (components in x, y, z directions).
• Mass Conservation: Mass is a scalar quantity that doesn't change unless externally altered.

Inertial Frames of Reference

• Defined by lack of acceleration when no forces act on an object.
• Example: In an inertial frame, a released pen stays still unless pushed.

Galilean Gravity

• Assumes a flat Earth for simplicity.
• Gravity points downwards and is constant near Earth's surface.
• Demonstrates that acceleration due to gravity is independent of mass.
• Equivalence Principle: Gravitational motion is independent of mass, but depends on the mass of the celestial body (e.g., Earth).

Newton's Law of Universal Gravitation

• Equation: ( F = \frac{GMm}{r^2} ), where G is the gravitational constant.
• Gravitational Constant (G): Approximately ( 6.7 \times 10^{-11} ) Nm²/kg², indicating gravity's relative weakness.
• Concept of Gravitational Attraction: Gravitational force is always attractive, pulling objects toward each other.

Tidal Forces

• Due to variations in gravitational field strength and direction.
• Example: Stretching and squishing effects due to Earth's curvature.

Gauss's Theorem

• Concept of Divergence: Represents the rate at which "stuff" spreads out from a point.
• Gauss's Theorem: Relates the divergence of a vector field within a volume to the flow across the boundary surface.

Gravitational Field

• Definition: Force field that dictates how masses influence each other.
• Similar to electric fields but related to mass instead of charge.
• Test Particles: Used to measure gravitational acceleration at different points.

Applications of Gauss's Theorem

• Gravitational Field Consistency: Outside a spherically symmetric mass, the gravitational field behaves as if all mass is concentrated at the center.
• Shell Theorem: Inside a spherical shell, the gravitational field is zero.
• Facilitates calculations of gravitational effects without needing complex distributions.

Conclusion

• The lecture concludes with an emphasis on understanding Gauss's theorem and its fundamental role in gravitational theory.