(371) Newton's law of gravitation | Physics | Khan Academy

Overview of Earth's Mass and Gravity

  • The mass of the Earth is approximately 6 x 10²⁴ kilograms.

  • How is this mass calculated? Through Newton's Universal Law of Gravity.

Understanding Gravity

Definition of Gravity

  • Gravity is a force of attraction between any two masses in the universe.

    • Example: Earth and an apple attract each other.

  • According to Newton's Third Law, the apple also pulls back on the Earth with an equal and opposite force.

General Attraction

  • All masses in the universe attract each other due to gravity.

    • Examples:

      • You attract the Moon.

      • You attract other objects like apples and furniture.

Factors Influencing Gravity

Increasing Mass

  • If either mass increases, the force of gravity increases.

    • The force of gravity is directly related to the masses involved.

Increasing Distance

  • As the distance between two masses increases, the force of gravity decreases.

    • This can explain why we do not feel the gravity from distant massive objects; the force is too weak.

Newton's Law of Universal Gravitation

  • Newton derived a formula for gravitational force based on observations of celestial bodies:

Formula for Gravitational Force

  • The force of gravity (F) can be expressed as:

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

    • Where:

      • F = gravitational force

      • G = universal gravitational constant (approximately 6.67 x 10⁻¹¹ N m²/kg²)

      • m₁ = mass of the first object (Earth)

      • m₂ = mass of the second object (like an apple)

      • r = distance between the centers of the two masses

Implications of the Formula

  • The gravitational force is:

    • Directly related to the masses (m₁, m₂).

    • Inversely related to the square of the distance (r²) between them.

  • This relationship means:

    • Doubling the distance reduces the gravitational force to 1/4.

    • Tripling the distance reduces the gravitational force to 1/9.

Inverse-Square Law

  • Because gravitational force decreases with distance as an inverse square, noted as the inverse-square law.

    • Graphically, the force diminishes rapidly as distance increases, showing a curve downward.

Simplified Calculation Near Earth

  • For objects close to Earth:

    • Mass of Earth is denoted as M.

    • Mass of an object close to Earth is m.

  • The formula for gravitational force becomes:

    [ F = G \frac{M m}{r^2} ]

    • Where r approximates the radius of the Earth when the object is very close.

Conclusion

  • Understanding gravity's calculation helps in exploring how objects interact in the Earth's vicinity and beyond, forming the basis for physics related to celestial mechanics.