Gravitational Force⚠ unverified
Physics / Mechanics · Compute the gravitational attraction between two point masses
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass1 | mass1 | kg | 1.0 | Mass of the first body |
| mass2 | mass2 | kg | 1.0 | Mass of the second body |
| distance | distance | m | 1.0 | Centre-to-centre separation between the bodies |
| G | G | N*m^2/kg^2 | 1.0 | Universal gravitational constant, in newton-metres squared per kilogram squared (N*m^2/kg^2), approximately ``6.674e-11 N*m^2/kg^2`` |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | F | N | Magnitude of the gravitational force, in newtons (N) |
The science & history
Understanding the Parameters
- $m_1$, $m_2$ — gravitational masses (equivalent to inertial mass in Newtonian theory).
- $r$ — force falls as $1/r^{2}$; doubles distance → quarter force.
- $G$ — $\approx 6.674\times 10^{-11}$ in SI. Registry default
1.0is not physical $G$. - $F$ — always attractive along the line of centres (magnitude only here).
Derivation (Approaching a Proof)
Newton’s inverse-square law is a fundamental postulate of classical gravity (later explained as curvature in GR). It is consistent with Kepler’s laws for planetary motion and with the surface weight $mg$ when $g = G M / R^{2}$ for a spherical body. Combining with Centripetal Force gives orbital speeds (Circular Orbital Velocity).
Near Earth: for $m_2 = m$, $m_1 = M_E$, $r = R_E$, $F \approx m g$ with $g \approx 9.8$ m/s².
History
Newton’s Principia (1687) unified celestial and terrestrial gravity under $F \propto m_1 m_2 / r^{2}$. Cavendish (1798) measured $G$ in the laboratory.
Related Concepts: Circular Orbital Velocity, Escape Velocity, Potential Energy, Centripetal Force, Newton's Second Law
Notes: Registry calculator gravitational-force (unverified). Point masses / spherical symmetry.
Set $G$ correctly in SI.