Lecture 13 Physics

PH101 Lecture 13 Overview

• Date: 16/10/2024

• Instructor: Dr. Niamh Fitzgerald

• Location: School of Natural Sciences, Room PH231

Lecture Topics

1. Uniform Circular Motion and Centripetal Force (Sections 6.1-6.3)

   • Understanding circular motion and the forces acting on bodies moving in a circular path.

   • Key equations and applications of centripetal force.

2. Law of Universal Gravitation (Section 6.5)

   • Explanation of gravitational attraction between masses.

   • Detailed discussion of Newton's law of gravitation.

3. Kepler’s Laws and Satellite Motion

   • Overview of Kepler’s laws governing planetary motion.

   • Application of these laws to satellite dynamics.

Acceleration Due to Gravity

• Standard value of acceleration due to gravity on Earth: 9.80 m/s².

Understanding Gravity

• Newton’s Insight:

  • Questions the gravitational force applied to objects of varying masses (e.g., apple vs. Sun).

  • Exploration of the gravitational force between two masses.

Universal Gravitation

• Gravitational Attraction:

  • Occurs along the line joining the centers of mass of two bodies.

  • Equal force acts on both masses, consistent with Newton’s third law.

• Gravitational Force Equation:

  • [ F = G \frac{mM}{r^2} ]

  • Where:

    • G = Gravitational constant = ( 6.674 \times 10^{-11} ) N⋅m²/kg²

    • m, M = Masses of the objects

    • r = Distance between centers of mass.

Calculation of Gravitational Acceleration (g)

• Derivation using gravitation:

  • [ g = G \frac{M}{r^2} ]

  • Example Calculation:

    • For Earth:

      • [ g = \frac{G \cdot (5.98 \times 10^{24} kg)}{(6.38 \times 10^6 m)^2} = 9.80 m/s² ]

Example Problem 6.6

• Task:

  • (a) Calculate acceleration due to gravity at the distance of the Moon.

  • (b) Find centripetal acceleration needed to maintain Moon's orbit; compare it with gravitational acceleration derived.

  • Radius of Moon’s Orbit: ( 3.84 \times 10^8 m )

Gravitational Context in the Solar System

• Masses:

  • Mass of Earth: ( 5.972 \times 10^{24} kg )

  • Mass of Sun: ( 1.989 \times 10^{30} kg )

• Gravitational Acceleration on the Sun:

  • Radius of Sun: 696,340 km

  • Resulting Calculation:

    • [ g_{sun} = G \frac{M_{sun}}{r_{sun}^2} = 274 m/s² ]

Tidal Forces

• Tide Generating Forces:

  • Explanation of low and high tides influenced by gravitational effects of the Moon and Sun.

  • Dynamics of solar and lunar tides leading to resulting tidal patterns.

Summary of Key Concepts

• Newton’s Universal Law of Gravitation:

  • Universally applicable [ F = G \frac{mM}{r^2} ]

• Gravitational Constant:

  • G = ( 6.674 \times 10^{-11} ) N⋅m²/kg².