Gravitational Force Calculator

How to Calculate Gravitational Force

The gravitational force calculator is a powerful tool based on Newton's law of universal gravitation. It allows you to determine the gravitational force between two objects, calculate the mass of one object given the force and the other object's mass, or find the distance between two objects given their masses and the gravitational force between them.

What is the Formula?

The formula for gravitational force 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 (approximately 6.674 × 10^-11 N·m²/kg²)
• \(m_1\) 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)

What are the calculation steps?

1. Identify the known parameters and the parameter you need to calculate.
2. Ensure all units are consistent (e.g., masses in kg, distance in m).
3. Apply the appropriate formula based on what you're calculating:
   • For gravitational force: \(F = G \frac{m_1 m_2}{r^2}\)
   • For mass (e.g., \(m_2\)): \(m_2 = \frac{Fr^2}{Gm_1}\)
   • For distance: \(r = \sqrt{\frac{Gm_1m_2}{F}}\)
4. Substitute the known values into the formula and solve for the unknown parameter.

Example Calculation

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

Given:

• Mass of Earth (\(m_1\)) = 5.97 × 10²⁴ kg
• Mass of Moon (\(m_2\)) = 7.34 × 10²² kg
• Average distance between Earth and Moon (\(r\)) = 3.84 × 10⁸ m
• Gravitational constant (\(G\)) = 6.674 × 10^-11 N·m²/kg²

Step 1: Identify the formula for gravitational force

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

Step 2: Substitute the known values

\(F = (6.674 × 10^{-11}) \frac{(5.97 × 10^{24})(7.34 × 10^{22})}{(3.84 × 10^8)^2}\)

Step 3: Calculate the result

\(F ≈ 1.98 × 10^{20} \text{ N}\)

Therefore, the gravitational force between the Earth and the Moon is approximately 1.98 × 10²⁰ N.

Diagram of Gravitational Force

The following diagram illustrates the key components of gravitational force:

This diagram shows two masses (\(m_1\) and \(m_2\)) separated by a distance \(r\). The gravitational force \(F\) acts between these masses, attracting them towards each other. The magnitude of this force depends on the masses of the objects and the square of the distance between them, as described by Newton's law of universal gravitation.