Gravitational Force Calculator
Calculate the gravitational force between two masses using Newton's law of universal gravitation. Enter the masses and the distance between them to find the force of attraction. Perfect for physics students, educators, and science enthusiasts.
What Is Newton's Law of Universal Gravitation?
Newton's law of universal gravitation states that every particle of matter 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.
F = G × (m₁ × m₂) / r²
Where:
F = Gravitational force (newtons, N)
G = Gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
m₁ = Mass of the first object (kg)
m₂ = Mass of the second object (kg)
r = Distance between the centers of the two masses (m)
This law explains why planets orbit the sun, why the moon orbits Earth, and why objects fall to the ground. It is one of the most important principles in physics and astronomy.
How Does the Gravitational Force Calculator Work?
The calculator supports four modes:
- Force Mode: Enter two masses and the distance to calculate the gravitational force between them.
- Mass 1 Mode: Enter the force, mass 2, and distance to calculate mass 1.
- Mass 2 Mode: Enter the force, mass 1, and distance to calculate mass 2.
- Distance Mode: Enter the force and both masses to calculate the distance between them.
The calculator uses the derived formulas:
- m₁ = F × r² / (G × m₂)
- m₂ = F × r² / (G × m₁)
- r = √(G × m₁ × m₂ / F)
Why Use This Gravitational Force Calculator?
- Four Modes: Calculate force, mass 1, mass 2, or distance.
- Scientific Notation: Display very large or small numbers in scientific notation.
- Visual Chart: See how force changes with distance.
- Step-by-Step: Detailed breakdown of the calculation.
- Free & Private: No registration, no data storage.
❓ Gravitational Force Calculator FAQ
What is Newton's law of universal gravitation?
Newton's law of universal gravitation states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
What is the gravitational constant (G)?
The gravitational constant G is a fundamental physical constant with a value of approximately 6.674 × 10⁻¹¹ N·m²/kg².
What are the units of gravitational force?
Gravitational force is measured in newtons (N) in the SI system.
How do I calculate gravitational force between two objects?
Use the formula F = G × (m₁ × m₂) / r². Enter the two masses and the distance between them, and the calculator will compute the force for you.
What is the gravitational force between Earth and Moon?
The gravitational force between Earth (5.972 × 10²⁴ kg) and the Moon (7.348 × 10²² kg) at a distance of 3.844 × 10⁸ m is approximately 1.98 × 10²⁰ N.
How does distance affect gravitational force?
Gravitational force decreases with the square of the distance. If you double the distance, the force becomes one-quarter as strong.
How does mass affect gravitational force?
Gravitational force is directly proportional to the product of the two masses. If you double one mass, the force doubles.
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms. Weight is the force of gravity on an object, measured in newtons. Weight = mass × gravitational acceleration (g ≈ 9.81 m/s² on Earth).
What is the gravitational force between two 1 kg objects 1 meter apart?
F = G × (1 × 1) / 1² = 6.674 × 10⁻¹¹ N, which is a very small force.
Why is gravity weaker than other fundamental forces?
Gravity is the weakest of the four fundamental forces because the gravitational constant G is extremely small (6.674 × 10⁻¹¹). It only becomes significant when large masses are involved.
What is the acceleration due to gravity on Earth?
The acceleration due to gravity on Earth's surface is approximately 9.81 m/s². This can be derived from F = mg, where g = G × M_earth / R_earth².
Does gravity act at a distance?
Yes, gravity is a non-contact force that acts at a distance. According to Newton's law, the force acts along the line connecting the centers of the two masses.
Who discovered the law of universal gravitation?
Sir Isaac Newton discovered the law of universal gravitation in the 17th century, famously inspired by observing an apple fall from a tree.
Can I use this calculator for astronomy?
Yes. This calculator is perfect for calculating gravitational forces between planets, moons, stars, and other celestial bodies.
What is the significance of the inverse square law in gravity?
The inverse square law means that gravitational force falls off rapidly with distance. This is why planets close to the sun experience much stronger gravitational forces than distant planets.
How do I calculate the mass of a planet using gravity?
If you know the gravitational force between two objects and the distance between them, you can solve for one of the masses using the formula m = F × r² / (G × M).
Is gravity the same everywhere in the universe?
The gravitational constant G is the same everywhere in the universe. However, the strength of the gravitational field depends on the mass and distance of the objects involved.