Calculator Math Papa

Calculate the gravitational force between two objects using Newton's Law of Universal Gravitation.

Understanding Gravitational Force

Gravitational force is a fundamental force of attraction that exists between any two objects with mass. It's the force that keeps planets in orbit around stars, moons around planets, and us firmly planted on the Earth. The strength of this force depends on the masses of the objects and the distance between their centers.

Newton's Law of Universal Gravitation

The mathematical relationship governing gravitational force was famously described by Sir Isaac Newton. His Law of Universal Gravitation states that every particle attracts every other particle in the universe with a force that is:

• Directly proportional to the product of their masses.
• Inversely proportional to the square of the distance between their centers.

This can be expressed by the following formula:

F = G * (m₁ * m₂) / r²

Where:

• F is the gravitational force between the two objects.
• G is the Gravitational Constant, a fundamental constant of nature. Its approximate value is 6.674 × 10⁻¹¹ N⋅m²/kg².
• m₁ is the mass of the first object.
• m₂ is the mass of the second object.
• r is the distance between the centers of the two objects.

Calculator Inputs Explained

• Mass of Object 1 (m₁): The mass of the first celestial body or object, measured in kilograms (kg).
• Mass of Object 2 (m₂): The mass of the second celestial body or object, measured in kilograms (kg).
• Distance between Centers (r): The distance separating the centers of the two objects, measured in meters (m).

Units of Measurement

For this calculator to provide an accurate result in Newtons (N), the standard unit of force in the International System of Units (SI), ensure your inputs are in the following units:

• Mass: Kilograms (kg)
• Distance: Meters (m)

The Gravitational Constant (G) is hardcoded into the calculator as 6.674e-11 N⋅m²/kg².

Use Cases

This calculator is useful for:

• Understanding the gravitational pull between celestial bodies like planets and stars.
• Estimating the force experienced by objects in space.
• Educational purposes to demonstrate Newton's Law of Universal Gravitation.
• Basic physics and astronomy calculations.

Example Calculation

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

• Mass of Earth (m₁): Approximately 5.972 × 10²⁴ kg
• Mass of Moon (m₂): Approximately 7.348 × 10²² kg
• Average Distance between Earth and Moon (r): Approximately 3.844 × 10⁸ m

Using the calculator with these values will yield the approximate gravitational force exerted by the Earth on the Moon (and vice-versa).