Newton's Law of Universal Gravitation Calculator

What is Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravitation is a fundamental principle in physics that describes the gravitational attraction between any two objects with mass in the universe. It 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 them.

Formula

The mathematical expression of Newton's Law of Universal Gravitation is:

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

Where:

• \( F \) is the gravitational force between the two masses (in Newtons, N)
• \( G \) is the gravitational constant (\( 6.67430 \times 10^{-11} \text{ N(m/kg)}^2 \))
• \( m_1 \) and \( m_2 \) are the masses of the two objects (in kilograms, kg)
• \( r \) is the distance between the centers of the masses (in meters, m)

Calculation Steps

Let's calculate the gravitational force between the Earth and the Moon:

1. Given:
   • Mass of Earth (\( m_1 \)) = \( 5.97 \times 10^{24} \text{ kg} \)
   • Mass of Moon (\( m_2 \)) = \( 7.34 \times 10^{22} \text{ kg} \)
   • Average distance between Earth and Moon (\( r \)) = \( 3.84 \times 10^8 \text{ m} \)
2. Apply Newton's Law of Universal Gravitation: \[ F = G \frac{m_1 m_2}{r^2} \]
3. Substitute the known values: \[ F = (6.67430 \times 10^{-11}) \frac{(5.97 \times 10^{24})(7.34 \times 10^{22})}{(3.84 \times 10^8)^2} \]
4. Perform the calculation: \[ F \approx 1.98 \times 10^{20} \text{ N} \]

Example and Visual Representation

Let's visualize Newton's Law of Universal Gravitation for the Earth-Moon system:

This diagram illustrates:

• The Earth (blue) and Moon (green) represented to scale
• The average distance between their centers (red dashed line)
• The gravitational force acting between them (yellow arrow)