Key Concepts: Escape Velocity

What is Escape Velocity?

• The minimum speed an object needs to escape a gravitational field without further propulsion.
• At escape velocity, the object reaches infinity with zero speed (KE → 0 as PE → 0).

Formula

v_esc = √(2GM/r)

• From Earth's surface: v_esc ≈ 11.2 km/s.
• Independent of the escaping object's mass.
• Depends on the mass M and radius r of the body you're escaping from.

Derivation

• Set total energy = 0 (just barely escaping): ½mv² − GMm/r = 0 → v = √(2GM/r).

Comparison

• Escape velocity = √2 × orbital velocity at the same radius.
• Moon: ~2.4 km/s. Jupiter: ~60 km/s. Sun: ~618 km/s.