Gravitational Force Calculator

Mass 1 (M) (kg) Mass 2 (m) (kg) Gravitational constant (G) (m³/kg⋅s²) Distance (R) (m)

The gravitational force calculator helps you calculate the gravitational force of the given objects.

Enter the masses of both objects, the gravitational constant ( you can keep the default value), and the distance to find the gravitational force.

This calculator uses Newton’s universal law of gravitation. i.e. the force of attraction between any two bodies is inversely proportional to the square of the distance between them and directly proportional to the product of their masses.

F = GMm/R²

F is the Gravitational force
M and m are the masses of two objects
R is their center-to-center distance.
G is the gravitational constant that equals 6.674×10⁻¹¹ N·m²/kg².

You might want to calculate the impulse or gravitational potential energy.

What is Gravitational Force?

Gravitational force is the attractive force that acts between any two objects with mass in the universe. This force is always attractive, meaning it pulls objects towards each other. The strength of the gravitational force depends on two main factors: the masses of the objects involved and the distance between them.

Newton’s law of universal gravitation states that every object in the universe attracts every other object 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. This relationship can be expressed mathematically as:

F = G × (M × m) / R²

Where:

F is the gravitational force (measured in Newtons, N)
G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N·m²/kg²)
M and m are the masses of the two objects (measured in kilograms, kg)
R is the distance between the centers of the two objects (measured in meters, m)

The Importance of Gravitational Force in Physics

Gravitational force plays a fundamental role in various aspects of physics and our understanding of the universe:

Celestial Mechanics: It governs the motion of planets, moons, and other celestial bodies in our solar system and beyond.
Tides: The gravitational pull of the Moon and Sun causes the rise and fall of ocean tides on Earth.
Satellite Orbits: Understanding gravitational force is crucial for planning and maintaining satellite orbits for communication and navigation systems.
Space Exploration: Calculating gravitational forces is essential for planning space missions and determining spacecraft trajectories.
Structure of the Universe: Gravitational force is responsible for the formation and evolution of galaxies, stars, and planets.

How to Calculate Gravitational Force

To calculate the gravitational force between two objects, you need to know three key pieces of information:

The mass of the first object (M)
The mass of the second object (m)
The distance between the centers of the two objects (R)

Once you have these values, you can use the formula mentioned earlier:

F = G × (M × m) / R²

Let’s break down the steps to calculate gravitational force:

Determine the masses of both objects in kilograms (kg).
Measure the distance between the centers of the objects in meters (m).
Use the gravitational constant G, which is approximately 6.674 × 10⁻¹¹ N·m²/kg².
Multiply the two masses together.
Divide the result by the square of the distance.
Multiply this value by the gravitational constant G.

The final result will give you the gravitational force in Newtons (N).

Using the Gravitational Force Calculator

While it’s important to understand the underlying principles and calculations, using a gravitational force calculator can significantly simplify the process and reduce the chance of errors. Here’s how to use the gravitational force calculator provided above:

Enter the mass of the first object (M) in kilograms in the “Mass 1” field.
Enter the mass of the second object (m) in kilograms in the “Mass 2” field.
The gravitational constant (G) is pre-filled with the standard value, but you can adjust it if needed.
Enter the distance between the centers of the two objects in meters in the “Distance” field.
Click the “Calculate” button.

The calculator will then display the gravitational force acting between the two objects in Newtons (N).

Examples of Gravitational Force Calculations

To better understand how the gravitational force calculator works and to illustrate its practical applications, let’s consider two examples:

Example 1: Gravitational Force Between Earth and the Moon

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

Mass of Earth (M) = 5.97 × 10²⁴ kg
Mass of Moon (m) = 7.34 × 10²² kg
Average distance between Earth and Moon (R) = 384,400,000 meters

Using the gravitational force calculator:

Enter 5.97e24 in the “Mass 1” field.
Enter 7.34e22 in the “Mass 2” field.
Leave the gravitational constant as is.
Enter 384400000 in the “Distance” field.
Click “Calculate”

The calculator should return a result of approximately 1.98 × 10²⁰ N. This enormous force is what keeps the Moon in orbit around the Earth and influences our tides.

Example 2: Gravitational Force Between Two People

Now, let’s calculate the gravitational force between two people standing 1 meter apart:

Mass of Person 1 (M) = 70 kg
Mass of Person 2 (m) = 65 kg
Distance between them (R) = 1 meter

Using the gravitational force calculator:

Enter 70 in the “Mass 1” field.
Enter 65 in the “Mass 2” field.
Leave the gravitational constant as is.
Enter 1 in the “Distance” field.
Click “Calculate”

The calculator should return a result of approximately 3.03 × 10⁻⁷ N. This tiny force demonstrates why we don’t notice gravitational attraction between everyday objects – it’s incredibly weak compared to other forces we experience, like friction or the normal force.

Factors Affecting Gravitational Force

Understanding the factors that influence gravitational force can help us interpret the results from our calculator more effectively:

Mass: The gravitational force is directly proportional to the product of the masses involved. Doubling the mass of one object will double the gravitational force, while doubling the mass of both objects will quadruple the force.
Distance: The gravitational force is inversely proportional to the square of the distance between the objects. This means that as objects get farther apart, the force decreases rapidly. For example, doubling the distance reduces the force to one-quarter of its original value.
Gravitational Constant: This universal constant ensures that the units in the equation balance out and provides the correct scale for the force. Its small value (approximately 6.674 × 10⁻¹¹ N·m²/kg²) is why gravitational forces between everyday objects are so weak.

Limitations and Considerations

While the gravitational force calculator is a powerful tool, it’s important to understand its limitations and consider certain factors:

Point Masses: The calculator assumes that the objects are point masses or perfect spheres with evenly distributed mass. For objects with irregular shapes or mass distributions, the results may be approximate.
Relativistic Effects: At very high masses or velocities, or in strong gravitational fields, Newton’s law of universal gravitation becomes less accurate, and Einstein’s theory of general relativity should be used instead.
Multiple Body Systems: The calculator only considers the force between two objects. In systems with three or more bodies, the gravitational interactions become more complex and may require more advanced computational methods.
Scale Considerations: Due to the vast range of masses and distances in the universe, be mindful of using appropriate units and scientific notation when entering values into the calculator.

Applications of Gravitational Force Calculations

Understanding and calculating gravitational forces has numerous practical applications across various fields:

Astronomy: Predicting the motion of planets, moons, and asteroids, and planning space missions.
Geology: Studying Earth’s internal structure through gravitational anomalies.
Engineering: Designing satellites and spacecraft that can maintain stable orbits or trajectories.
Physics Education: Teaching students about fundamental forces and celestial mechanics.
Climate Science: Understanding the Earth-Moon system’s influence on tides and long-term climate patterns.