📘 Newton’s Law of Universal Gravitation
Newton's Law of Universal Gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The Universal Attraction
Before Isaac Newton, scientists thought the rules for motion on Earth were different from the rules for motion in the heavens. Newton’s great insight was that the same force causing an apple to fall to the ground is the force that keeps the Moon in orbit around the Earth.
The Gravitational Equation
The magnitude of the gravitational force ($F_g$) between two objects can be calculated using the following formula:
\[F_G = G \frac{m_1 m_2}{r^2}\]Where:
$F_G$ is the force of gravity (Newtons, N).
$G$ is the Universal Gravitational Constant ($6.674 \times 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2$).
$m_1$ and $m_2$ are the masses of the two objects (kilograms, kg).
$r$ is the distance between the centers of the two masses (meters, m).
The Inverse Square Law
One of the most critical aspects of this law is the inverse square relationship with distance. Because the distance ($r$) is squared in the denominator:
If you double the distance between two objects ($\times 2$), the force becomes one-fourth as strong ($1/2^2$).
If you triple the distance ($\times 3$), the force becomes one-ninth as strong ($1/3^2$).
If you cut the distance in half ($\times 0.5$), the force becomes four times stronger ($1/0.5^2$).
Interactive: Universal Gravitation Vocabulary
Test your knowledge of the variables and concepts that define the pull of gravity.
Match the variables and concepts of Universal Gravitation to their correct descriptions.
💡 Quick Concept Check:
If the mass of one object is doubled and the distance between the objects is also doubled, what happens to the gravitational force?