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Escape velocity
Intermediate
Minimum speed to leave a planet without returning.
v_e = √(2GM/R)Escape speed v_e = √(2GM/R) is the minimum speed to reach infinity with zero speed left, ignoring air. It follows from ½mv² = GMm/R.
Earth 11.2 km/s, Moon 2.4 km/s, Sun 618 km/s.
It's independent of the direction and the object's mass.
In more detail
Escape velocity is the minimum speed needed to leave a planet's gravitational pull without further propulsion. It is v = sqrt(2GM/R) and does not depend on the mass of the escaping object.
Real-world uses
- Rocket designers calculate escape velocity to plan launches.
- Astronomers estimate whether gas can escape a planet or moon.
- Rocket engineers calculate the minimum speed needed to leave Earth, which sets the size of the fuel tanks and the engines.
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Frequently asked questions
Do I need to reach escape velocity to leave Earth?
Only to escape entirely. Rockets can reach orbit at lower speeds.
Does escape velocity depend on direction?
No, for a spherical planet, the minimum escape speed is the same in all directions.
Does a rocket need to keep burning at escape speed?
No. If it reaches escape speed with no further thrust needed, it will coast away, ignoring drag and other bodies.
Related topics in Gravitation & Orbits
Gravitational potential · Field of a spherical shell · Field inside a uniform sphere · Escape velocity of Earth · Orbital velocity · Satellite energy