Calculate the attraction between two objects using Isaac Newton's Law of Universal Gravitation. This tool allows you to input masses and distances in various units to find the precise force of gravity in Newtons (N).
Force vs. Distance Visualization
Shows how gravitational force decreases as distance increases (Inverse Square Law)
What is the Gravitational Force Calculator?
The Gravitational Force Calculator is a specialized tool designed to compute the magnitude of the attractive force between two masses. Based on Sir Isaac Newton's Law of Universal Gravitation, this calculator bridges the gap between complex astrophysical calculations and everyday physics curiosity.
Whether you are calculating the force between the Earth and the Moon or the subtle pull between two bowling balls, this tool handles the massive scientific notation involved, ensuring accuracy without the manual math headache.
The Formula and Scientific Explanation
The calculation relies on the universal formula established in 1687:
Where:
- F is the gravitational force between the masses (measured in Newtons).
- G is the Gravitational Constant, approximately 6.674 × 10⁻¹¹ N·m²/kg².
- m₁ is the mass of the first object (kg).
- m₂ is the mass of the second object (kg).
- r is the distance between the centers of the two masses (m).
Practical Examples
Example 1: Earth and the Moon
The Earth has a mass of ~5.97 × 10²⁴ kg, and the Moon has a mass of ~7.35 × 10²² kg. They are roughly 384,400 km apart. Using our calculator, we find the force is approximately 1.98 × 10²⁰ Newtons. This massive force is what keeps the Moon in orbit.
Example 2: Two Humans
If two people, each weighing 70 kg, stand 1 meter apart, the gravitational force between them is roughly 0.000000327 Newtons. This is why we don't "feel" gravity from the people around us—the force is incredibly weak compared to the Earth's pull.
How to Use the Calculator Step-by-Step
- Enter Mass 1: Input the weight of the first object and select its unit (kg, Tons, Earth Masses, etc.).
- Enter Mass 2: Input the weight of the second object.
- Set the Distance: Enter how far apart the centers of the objects are. Note that for planets, this is the distance from core to core.
- Review the Result: The calculator updates in real-time to show the force in Newtons.
- Copy and Share: Use the "Copy Result" button to save your findings for your homework or research.
Key Factors Influencing Gravitational Force
| Factor | Relationship | Impact on Force |
|---|---|---|
| Mass (m) | Directly Proportional | Doubling one mass doubles the force. |
| Distance (r) | Inverse Square | Doubling the distance reduces the force to 1/4th. |
| G Constant | Universal | Remains constant throughout the known universe. |
Frequently Asked Questions (FAQ)
1. Why is G such a small number?
Gravity is actually the weakest of the four fundamental forces of nature. The small value of G (10⁻¹¹) reflects this inherent weakness.
2. Does gravity work in a vacuum?
Yes. Gravity does not require a medium (like air or water) to travel; it acts across the vacuum of space.
3. What is the difference between g and G?
'G' is the universal gravitational constant, while 'g' is the acceleration due to gravity on Earth (9.8 m/s²).
4. Can gravitational force be repulsive?
In classical Newtonian physics, gravity is always attractive. It only pulls objects together.
5. How does distance affect gravity the most?
Because distance is squared in the denominator, small changes in distance have a much larger impact on force than changes in mass.
6. Is gravity the same on all planets?
No. While G is the same, the mass and radius of planets differ, leading to different surface gravities.
7. What units does the result come in?
The standard unit of force is the Newton (N). One Newton is roughly the weight of a small apple.
8. Does weight change with gravity?
Yes. Mass is constant, but weight is the measure of gravitational force. You weigh less on the Moon because its mass is smaller than Earth's.