Circular Orbital Velocity⚠ unverified
Physics / Mechanics · Compute the speed required for a circular orbit
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass | mass | kg | 1.0 | Mass of the central (gravitating) body |
| radius | radius | m | 1.0 | Orbital radius measured from the centre of the body |
| G | G | N*m^2/kg^2 | 1.0 | Universal gravitational constant |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | v | m/s | Orbital speed for a circular orbit, in metres per second (m/s) |
The science & history
Understanding the Parameters
-
$M$ — only the central mass appears under the point-mass / spherical symmetry assumption (test mass $m$ cancels).
-
$r$ — larger orbits are slower ($v \propto 1/\sqrt{r}$).
-
$G$ — SI value $\approx 6.674\times 10^{-11}$. The live calculator default
1.0is a numeric placeholder, not physical $G$. -
$v$ — inertial speed for a circular path; direction is tangential.
Derivation (Approaching a Proof)
Gravity supplies centripetal force for mass $m$ in a circular orbit:
$$\frac{G M m}{r^{2}} = \frac{m v^{2}}{r}.$$
Cancel $m$ (and one $r$):
$$v^{2} = \frac{G M}{r} \quad\Rightarrow\quad v = \sqrt{\frac{G M}{r}}.$$
Escape needs $\sqrt{2}$ times this speed — see Escape Velocity. Related: Gravitational Force, Centripetal Force.
History
Newton’s law of gravitation plus circular motion recovers Kepler’s period–radius relation ($T^{2} \propto r^{3}$). Circular-orbit speed is the first design number in orbital mechanics.
Related Concepts: Escape Velocity, Gravitational Force, Centripetal Force, Angular Momentum
Notes: Registry calculator circular-orbital-velocity (unverified). Two-body reduced to fixed
central $M$; circular, non-relativistic. Set $G$ correctly in SI — default is not CODATA $G$.