How this calculation works
The Newton's Universal Gravitation Calculator determines the mutual attractive gravitational force (F) in Newtons between any two masses across space based on Sir Isaac Newton's law of universal gravitation.
Mathematical formula and logic
F = G × (m₁ × m₂) / r², where G = 6.67430 × 10⁻¹¹ N·m²/kg² (Universal Gravitational Constant) and r is distance between centers of mass.
Worked example
Between Earth (5.972 × 10²⁴ kg) and the Moon (7.348 × 10²² kg) separated by 3.844 × 10⁸ meters: The gravitational pull is 1.982 × 10²⁰ Newtons, maintaining the Moon's stable elliptical orbit.
Calculation assumptions
- NIST/CODATA 2022 gravitational constant G = 6.67430 × 10⁻¹¹ N·m²/kg².
- Spherical mass distributions behaving as point masses at their centers of gravity.
Frequently asked questions
What is the Universal Gravitational Constant (G)?
G is an empirical physical constant (G = 6.67430 × 10⁻¹¹ N·m²/kg²) that quantifies the strength of gravitational attraction throughout the cosmos.
What is the difference between 'G' and 'g'?
Capital 'G' is the universal gravitational constant everywhere in the universe. Lowercase 'g' is local surface gravitational acceleration (e.g. 9.81 m/s² on Earth, 1.62 m/s² on the Moon).
What happens to gravity if the distance between objects is halved?
Because gravity follows the inverse-square law (1/r²), halving the distance increases the gravitational force by 2² = 4 times.
Do all objects with mass attract each other?
Yes, every object with mass exerts a gravitational pull on every other object in the universe, although the force is only noticeable when at least one object has planetary mass.
How did Henry Cavendish first measure G in 1798?
Cavendish measured G using a delicate torsion balance with lead spheres, famously allowing physicists to 'weigh the Earth' for the first time.
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