Escape velocity is the minimum launch speed an object needs to move away from a planet or moon without ever falling back, assuming no air resistance and no additional thrust after launch. It matters for rockets, space probes, and understanding why some worlds hold atmospheres while others lose gas to space. The idea is not about escaping the atmosphere, but escaping the gravitational pull of a body.
For Earth, escape velocity near the surface is about 11.2 km/s, while for the Moon it is about 2.38 km/s.
Key Facts
- Escape velocity is the speed needed so total mechanical energy is zero or greater.
- Energy condition for escape: 1/2mv^2 - GMm/r >= 0.
- Escape velocity formula: vesc = sqrt(2GM/r).
- Using surface gravity: vesc = sqrt(2gr) when g is the surface gravitational field and r is the body's radius.
- Escape velocity does not depend on the object's mass because m cancels from kinetic and gravitational potential energy.
- Typical values: Earth vesc = 11.2 km/s, Moon vesc = 2.38 km/s.
Vocabulary
- Escape velocity
- The minimum speed an object needs at a given distance from a body to escape its gravity without further propulsion.
- Gravitational potential energy
- The energy an object has because of its position in a gravitational field, given by U = -GMm/r for two masses.
- Total mechanical energy
- The sum of kinetic energy and potential energy, written as E = K + U.
- Gravitational constant
- The constant G that sets the strength of gravity in Newton's law, with value about 6.67 x 10^-11 N m^2/kg^2.
- Escape trajectory
- A path followed by an object whose speed is high enough that it will not return to the body under gravity alone.
Common Mistakes to Avoid
- Thinking escape velocity depends on the rocket's mass, which is wrong because the mass m cancels in the energy equation.
- Confusing escape velocity with orbital velocity, which is wrong because orbiting means continuously falling around the body while escaping means not returning.
- Using the planet's diameter instead of its radius in vesc = sqrt(2GM/r), which gives an incorrect speed because r is measured from the center of the body.
- Treating 11.2 km/s as the speed all rockets must have at liftoff, which is wrong because real rockets use continuous thrust, staging, and curved trajectories through the atmosphere.
Practice Questions
- 1 Use vesc = sqrt(2GM/r) to find the escape velocity from a planet with mass 6.0 x 10^24 kg and radius 6.4 x 10^6 m. Use G = 6.67 x 10^-11 N m^2/kg^2.
- 2 The Moon has escape velocity 2.38 km/s. What kinetic energy per kilogram is required for escape from the Moon's surface? Use K/m = 1/2v^2.
- 3 A small probe and a heavy capsule are launched from the same height above Earth with the same speed and no further thrust. Explain why their ability to escape is the same if air resistance is ignored.