PhysicsChapter 1: Gravitation
Escape Velocity
Definition
Escape velocity is the minimum initial speed required for an object to escape permanently from a gravitational field without further propulsion, reaching infinity with zero speed in the ideal model.
Important Result
Consider object mass `m` launched from radius `R`. Initial total energy: Ei = ½mve² − GMm/R At minimum escape condition, at infinity: `U=0` `K=0` so: Ef=0 By energy conservation: ½mve² − GMm/R = 0 Therefore: ½mve² = GMm/R Cancel `m`: ve² = 2GM/R Thus: ve = √(2GM/R) Since surface orbital speed is: vo = √(GM/R) therefore: ve = √2 vo Escape velocity is independent of the escaping object’s mass. For Earth’s surface, ignoring atmosphere and Earth rotation: approximately: **11.2 km/s**
Formula / Key Relation
**ve = √(2GM/R)**
Exam preparation
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Review the key facts, formulas and checks before you move on.Escape Velocity
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ESCAPE
- `ve=√(2GM/R)`
- Earth ≈ 0
60-second revision
- Mass of escaping object cancels.
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