Gravitational Force Calculator
Calculate gravitational force between any two objects using Newton's Law of Universal Gravitation
Calculate Gravitational Force
Quick Presets
First object mass (e.g., 5.972e24 for Earth)
Second object mass (e.g., 7.348e22 for Moon)
Distance between object centers (e.g., 3.844e8 for Earth-Moon)
Calculation Results
Formula: F = G × M₁ × M₂ / r²
G: 6.674 × 10^-11 N⋅m²/kg²
Distance: 3.844 × 10^8 m
Physical Insights
• This force acts equally on both objects (Newton's 3rd Law)
• Force decreases with the square of distance (inverse square law)
• Doubling distance reduces force by factor of 4
• This is an astronomical-scale force typical of planetary systems
Example: Earth-Moon System
Given Values
Earth's mass (M₁): 5.972 × 10²⁴ kg
Moon's mass (M₂): 7.348 × 10²² kg
Distance (r): 3.844 × 10⁸ m
G: 6.674 × 10⁻¹¹ N⋅m²/kg²
Calculation
F = G × M₁ × M₂ / r²
F = (6.674 × 10⁻¹¹) × (5.972 × 10²⁴) × (7.348 × 10²²) / (3.844 × 10⁸)²
F = (6.674 × 10⁻¹¹) × (4.387 × 10⁴⁷) / (1.478 × 10¹⁷)
F = 1.982 × 10²⁰ N
This enormous force keeps the Moon in orbit around Earth!
Universal Constants
Gravitational Constant (G)
6.67430 × 10⁻¹¹ N⋅m²/kg²
Universal constant of proportionality
Earth's Mass
5.972 × 10²⁴ kg
Mass of our planet
Sun's Mass
1.989 × 10³⁰ kg
Mass of our star
Key Concepts
Inverse Square Law
Force ∝ 1/r² - doubling distance quarters the force
Universal Attraction
Every mass attracts every other mass
Newton's 3rd Law
Equal and opposite forces on both objects
Orbital Mechanics
Gravity provides centripetal force for orbits
Understanding Newton's Law of Universal Gravitation
What is Gravitational Force?
Gravitational force is the attractive force between any two objects with mass. Formulated by Isaac Newton in 1687, the law states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of their separation distance.
The Universal Law
F = G × M₁ × M₂ / r²
Newton's Law of Universal Gravitation
- F: Gravitational force (N)
- G: Universal gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²)
- M₁, M₂: Masses of the two objects (kg)
- r: Distance between centers of mass (m)
Key Properties
- •Always Attractive: Gravitational force always pulls objects together, never pushes them apart.
- •Universal: Acts between all objects with mass, regardless of their composition or state.
- •Inverse Square: Force decreases rapidly with distance - double the distance, quarter the force.
- •Mutual: Each object experiences equal and opposite forces (Newton's 3rd Law).
Fun Fact: The gravitational force between you and this device is real but incredibly tiny - about 10⁻⁹ N for typical masses and distances!