6.5 Newton's Law of Gravity Notes

Newton's Law of Gravity

• Isaac Newton developed the concept of gravity as a universal force affecting all objects in the universe.

• The same force that causes an apple to fall also keeps the moon in orbit.

Universal Law of Gravitation

• Every object attracts every other object with a force that varies based on:

  • The mass of the objects (directly proportional to the product of their masses).

  • The distance between them (inversely proportional to the square of the distance).

  • Mathematically, $F = G \frac{m<em>1 m</em>2}{r^2}$ where:

  • $F$ is the gravitational force,

  • $G$ is the gravitational constant ($G = 6.67 \times 10^{-11} \text{ N m}^2 / \text{kg}^2$),

  • $m<em>1$ and $m</em>2$ are the masses, and

  • $r$ is the distance between the centers of the masses.

Inverse Square Law

• As distance $r$ increases, gravitational force decreases dramatically:

  • Doubling the distance reduces the force by a factor of four (i.e., gravity behaves according to an inverse square relationship).

Inverse Relationship Concept

• If $y$ is inversely proportional to $x^2$, we can express this as:

  • $y = \frac{a}{x^2}$

  • If $x$ increases by a factor of $c$, $y$ decreases by a factor of $c^2$.

Gravitational Force Examples

• The gravitational force between ordinary objects is typically small unless one or both masses are large (e.g., Earth).

• Weight on other celestial bodies varies due to different gravitational accelerations (e.g., on the moon or other planets).

  • $g<em>{moon} = 1.62 \text{ m/s}^2$ and $g</em>{Earth} = 9.8 \text{ m/s}^2$.

Calculating Gravitational Force

• The gravitational force can be calculated for a person on Earth using:

  • $F = G \frac{M<em>{Earth} m</em>{person}}{R_{Earth}^2}$, where the mass of Earth and radius are involved.

Variation in Gravity

• Earth's gravity varies slightly due to its uneven density, but this variation is generally negligible for basic calculations.

Orbiting Objects

• Objects in orbit are not weightless but are in free fall.

• The period of orbit and gravitational force can be correlated using gravitational biomechanics.