w2 NewtonsLawUniversalGravity

Newton's Law of Universal Gravity

Overview of the Law

• Newton's law of universal gravity describes the gravitational attraction between two masses.

• Fundamental principle: Every mass attracts every other mass.

• Example: An apple falling to the ground due to the Earth’s gravity.

Key Concepts

• Mass Interaction: Each object with mass exerts a gravitational force on other objects. This attraction is mutual.

• Force (F): The force of gravity between two masses is denoted as F.

Mathematical Expression

• The gravitational force (F) is modeled by the equation:

  F = G * (M1 * M2) / R^2

  Where:

  • F = gravitational force

  • G = gravitational constant (6.67 x 10^-11 m^3/kg/s^2)

  • M1 = mass of the first object

  • M2 = mass of the second object

  • R = separation distance between the centers of mass of the two objects

Component Explanation

• Direct Proportionality:

  • The force (F) is directly proportional to the product of the masses (M1 * M2).

  • Example: Mass of the Sun (~1.9 x 10^30 kg) and mass of the apple (150 g).

• Inverse Proportionality:

  • The force is inversely proportional to the square of the distance (R^2) separating the two masses.

  • If R increases, the gravitational force decreases by the square of the distance.

Units and Consistency

• Ensure all units are compatible with each other when performing calculations:

  • Masses should be in kilograms.

  • Distance should be in meters.

• The gravitational constant (G) has units: meters³/(kilograms·seconds²).

Practical Considerations

• To calculate gravitational forces in practical scenarios, consistent units must be applied.

• This principle will be referenced throughout the course for various applications.