Use this interactive calculator to compute the gravitational force between two objects based on
Newton’s Law of Universal Gravitation.
Input the masses (in kilograms, grams, or pounds) and the distance (in meters, kilometers, or miles)
between their centers to get the gravitational force in Newtons (N).
Formula: \[ F = G \cdot \frac{m_1 \cdot m_2}{r^2} \] Where \( G = 6.67430 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)
Output:
Visualization: Force vs Distance
What is Gravitational Force and How Does the Calculator Work?
Gravitational force is the attractive force that exists between any two masses in the universe. It was first described mathematically by Sir Isaac Newton in his Law of Universal Gravitation. This fundamental force keeps planets in orbit, causes tides on Earth, and gives us our body weight.
Gravitational Force Calculator Formulas and Equations
1. Newton’s Law of Gravitation:
\[ F = G \cdot \frac{m_1 \cdot m_2}{r^2} \]
2. Weight on Earth:
\[ W = m \cdot g \]
3. Gravitational acceleration at a planet’s surface:
\[ g = \frac{G \cdot M}{R^2} \]
How to Use the Gravitational Force Calculator (Step-by-Step Guide)
- Enter the Mass 1 and select its unit (kg, g, lb).
- Enter the Mass 2 and select its unit.
- Enter the Distance between the two centers and choose the unit (m, km, mi).
- Click Calculate to compute the gravitational force.
- Use the preset buttons for Earth–Moon or Earth–Sun examples.
- Check the formula derivation and Force vs Distance chart for deeper insights.
Gravitational Force Calculator Example (Earth & Moon)
Let’s calculate the gravitational force between:
- Earth: 5.972e24 kg
- Moon: 7.348e22 kg
- Distance: 3.844e8 m
Substituting values into the formula: \[ F = (6.67430 \times 10^{-11}) \cdot \frac{(5.972 \times 10^{24})(7.348 \times 10^{22})}{(3.844 \times 10^8)^2} \]
Result: \( 1.9821 \times 10^{20} \, N \)
Important Notes When Using the Gravitational Force Calculator
- The calculation assumes point masses or spherically symmetric objects.
- Use scientific notation (e.g., 5.972e24) for large numbers.
- Distance must be greater than 0 to avoid division by zero.
- This calculator uses Newtonian mechanics — relativistic effects are not included.
Real-Life Uses and Applications of Gravitational Force
- Astronomy: Predicting planetary orbits and interactions.
- Space Exploration: Planning rocket launches and space missions.
- Tides: Understanding the effect of Moon and Sun on Earth’s oceans.
- Sports Science: Ball flight, jumps, and projectile motion analysis.
- Engineering: Designing stable structures considering weight and load.
Key Applications
- Explains planetary orbits and satellite motion
- Used in space trajectory planning
- Helps calculate weight variation on different planets
Benefits of This Calculator
- Simple inputs with unit conversion
- Step-by-step substitution and derivation
- Force vs Distance interactive chart
- Preset real-world examples
- Educational for students, teachers, and engineers
FAQs
What is the gravitational constant?
\( G = 6.67430 \times 10^{-11} \, Nm^2/kg^2 \). It defines the strength of gravity between two bodies.
Does gravitational force ever become zero?
No, but it decreases with the square of the distance. At very large distances, it becomes negligible.
How is weight related to gravitational force?
Weight is simply the gravitational force Earth exerts on a body: \( W = m \cdot g \).
Can this calculator be used for satellites?
Yes, you can input the mass of Earth and the satellite along with their orbital distance to find the force. their orbital distance, you can calculate the gravitational force acting on the satellite.