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Mechanics
Mechanics

Escape Velocity

ve=2GMrv_e = \sqrt{\frac{2GM}{r}}

Minimum velocity to escape gravitational field.

Variables

v_e
Escape velocity
Minimum escape speed
m/s
G
Gravitational constant
6.674×10⁻¹¹
N·m²/kg²
M
Mass
Mass of body
kg
r
Radius
Starting distance
m

Derivation

Set total energy = 0: ½mv² - GMm/r = 0.

Your notes

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Common questions

What is the Escape Velocity formula?

Escape Velocity is written vₑ = √(2GM/r). Minimum velocity to escape gravitational field. It belongs to Mechanics, under Gravitation.

What are the units in vₑ = √(2GM/r)?

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

How is the Escape Velocity formula derived?

Set total energy = 0: ½mv² - GMm/r = 0. The result is vₑ = √(2GM/r).