PHY101(Gravitation)

Course Overview

  • Institution: Osun State University

  • Faculty: Basic and Applied Sciences

  • Department: Physics

  • Course: General Physics

  • Code: PHY 101

  • Semester: 2024/2025 Harmattan Semester

  • Lecturer: I.A. Akanni (PhD)

Course Contents

  • Newton’s Law of Gravitation

  • Kepler’s Law of Planetary Motion

  • Gravitational Potential Energy

  • Escape Velocity

  • Satellites Motion and Orbits

Newton's Law of Gravitation

  • Definition: States that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

  • Formula: [ F = G \frac{m_1 m_2}{r^2} ]

    • Where: ( F ) = gravitational force, ( G ) = gravitational constant ( (6.67 \times 10^{-11} m^3 kg^{-1} s^{-2}) ), ( m_1 ), ( m_2 ) = masses, ( r ) = distance between centers.

Examples of Gravitational Force Calculation

  1. Earth and Moon: Calculate the gravitational force between Earth ( (m_1 = 6.0 \times 10^{24} kg) ) and Moon ( (m_2 = 7.4 \times 10^{22} kg) ) with ( r = 345,000 km ).

  2. Human on Earth: Calculate the force between Earth and a 70 kg man at the Earth's radius ( (6.38 \times 10^6 m) ).

Gravitational Field

  • Definition: Region where an object experiences gravitational attraction.

  • Characteristics:

    • Attractive force directed towards the center of mass.

    • Infinite range affecting all objects.

    • Varies with mass; greater for large masses (planets), negligible for small masses.

  • Gravitational Field Strength: ( g = \frac{F}{m} ) (force per unit mass).

Mass vs Weight

  • Mass:

    • Measure of matter; intrinsic, scalar quantity; constant everywhere.

  • Weight:

    • Force due to gravity; dependent on mass and gravitational field; vector quantity.

    • Example: Weight of a 10 kg stone on Earth vs Moon.

Kepler’s Laws of Planetary Motion

  1. First Law (Law of Orbits): Planets orbit the Sun in elliptical paths.

    • Ellipses: Defined by semi-major and semi-minor axes.

  2. Second Law (Law of Equal Areas): A line from the Sun to a planet sweeps equal areas in equal times.

  3. Third Law (Harmonic Law): The square of the period of a planet's orbit is proportional to the cube of its semi-major axis.

    • Formula: [ T^2 \propto a^3 ]

Gravitational Potential Energy

  • Definition: Energy possessed due to an object's position in a gravitational field.

  • Factors:

    • Mass (m), gravitational acceleration (g), height (h).

  • Formula: ( PE = mgh )

Escape Velocity

  • Definition: Minimum speed needed to break free from a planet's gravitational pull.

  • Formula: [ V_e = \sqrt{2GM/R} ] (where ( M ) is the mass of the planet and ( R ) is its radius).

Satellite Motion and Orbits

  • Definition: Bodies that revolve around a central body (Earth, Sun).

  • Types of Satellites:

    • Natural: Moon, comets.

    • Artificial: Weather satellites, communication satellites.

  • Orbital Motion: Involves gravitational force and centripetal force, with motion being circular or elliptical.