Newton's Law of Universal Gravitation
The foundation for this understanding lies in Newton's Law of Universal Gravitation. This law states that every object in the universe attracts every other object with a force that is:
* Proportional to the product of their masses: The more massive the objects, the stronger the gravitational attraction.
* Inversely proportional to the square of the distance between their centers: The farther apart the objects, the weaker the gravitational force.
The Key Insight:
The crucial point here is that gravity is a force, and forces cause accelerations. The acceleration due to gravity (g) is the acceleration an object experiences because of Earth's gravitational pull. While the gravitational force between Earth and an object is directly proportional to the object's mass, the *acceleration* is not. Here's why:
1. Force and Mass: Newton's Second Law of Motion states that force (F) is equal to mass (m) times acceleration (a): F = ma.
2. Force of Gravity: The force of gravity (Fg) between Earth and an object is given by Fg = G * (m1 * m2) / r², where:
* G is the gravitational constant
* m1 is the mass of Earth
* m2 is the mass of the object
* r is the distance between their centers.
3. Combining the Equations: Substituting Fg into F = ma, we get: G * (m1 * m2) / r² = m2 * a.
4. Canceling Mass: Notice that the mass of the object (m2) appears on both sides of the equation. When you cancel it out, you are left with: G * m1 / r² = a.
Conclusion:
This final equation shows that the acceleration due to gravity (a) is independent of the object's mass. It only depends on the mass of Earth (m1) and the distance between their centers (r). This explains why all objects, regardless of their mass, fall at the same rate near the Earth's surface.
Important Note: This explanation applies in a vacuum where air resistance is negligible. In reality, air resistance affects objects with different shapes and sizes differently, causing them to fall at slightly different rates.
