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{m1 m2}{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 ),
m1 and m2 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{moon} = 1.62 \text{ m/s}^2 and g{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{Earth} m{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.