Newton's Law of Universal Gravitation

What is Newton's Law of Universal Gravitation?

Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass 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 formula for this gravitational force is:

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

• $F$ is the gravitational force between the objects (in newtons, N).
• $G$ is the universal gravitational constant $(6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2)$.
• $m_1$ and $m_2$ are the masses of the objects (in kilograms, kg).
• $r$ is the distance between the centers of the two masses (in meters, m).

Understanding the Universal Gravitational Constant $G$

The universal gravitational constant $G$ is a key part of the equation. It is a constant value that helps us calculate the gravitational force between two masses anywhere in the universe.

Examples

Example 1: Calculating Gravitational Force

Let's calculate the gravitational force between two objects: a 5 kg mass and a 10 kg mass that are 2 meters apart.

• $m_1 = 5 \text{ kg}$
• $m_2 = 10 \text{ kg}$
• $r = 2 \text{ m}$

Using the formula:

$$F = G \frac{m_1 m_2}{r^2} = 6.674 \times 10^{-11} \frac{5 \times 10}{2^2}$$

$$F = 6.674 \times 10^{-11} \frac{50}{4}$$

$$F = 6.674 \times 10^{-11} \times 12.5$$

$$F = 8.3425 \times 10^{-10} \text{ N}$$