Gravitational Force Calculator
Calculate the gravitational force between two masses using Newton’s law of gravitation.
Gravitational Force (F)
Calculation Details
Newton's Law of Universal Gravitation
Newton's law of universal gravitation states that every point mass attracts every other point mass 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, expressed as F = G·m₁·m₂/r², governs the motion of planets, moons, and falling objects alike.
The Formula
- F — gravitational force in newtons (N)
- G — gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg²
- m₁, m₂ — the two masses in kilograms (kg)
- r — distance between the centers of the masses in meters (m)
Worked Example
For the Earth (m₁ = 5.972 × 10²⁴ kg) and the Moon (m₂ = 7.348 × 10²² kg) separated by r = 3.844 × 10⁸ m, the gravitational force is approximately 1.98 × 10²⁰ N.
References
The formula and physical constants used in this calculator are based on established physics principles and verified sources:
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Note: This calculator uses Newton's classical law of universal gravitation and treats the masses as point masses or uniform spheres. It does not account for general relativistic effects, non-spherical mass distributions, or tidal forces. Results are intended for educational and estimation purposes.