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Mechanics
Mechanics

Orbital Velocity

v=GMrv = \sqrt{\frac{GM}{r}}

Velocity for circular orbit at radius r.

Variables

v
Orbital velocity
Circular orbit speed
m/s
G
Gravitational constant
6.674×10⁻¹¹
N·m²/kg²
M
Central mass
Mass being orbited
kg
r
Orbital radius
Distance from center
m

Derivation

Set gravitational force = centripetal force: GMm/r² = mv²/r.

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Common questions

What is the Orbital Velocity formula?

Orbital Velocity is written v = √(GM/r). Velocity for circular orbit at radius r. It belongs to Mechanics, under Gravitation.

What are the units in v = √(GM/r)?

In SI units, v is orbital velocity, measured in m/s; G is gravitational constant, measured in m³/(kg·s²); M is central mass, measured in kg; r is orbital radius, measured in m.

How is the Orbital Velocity formula derived?

Set gravitational force = centripetal force: GMm/r² = mv²/r. The result is v = √(GM/r).