Escape Velocity Calculator
Speed needed to break free from gravity.
Formula first
Overview
Escape velocity represents the minimum speed required for an object to overcome the gravitational pull of a celestial body and reach an infinite distance without additional propulsion. It is a critical threshold where the object's kinetic energy perfectly balances its gravitational potential energy, resulting in a total mechanical energy of zero.
Symbols
Variables
v = Escape Velocity, G = Grav Constant, M = Planet Mass, r = Radius
Apply it well
When To Use
When to use: Apply this equation when calculating the launch speed needed for a spacecraft to leave a planet or when analyzing the ability of a moon to retain an atmosphere. It assumes the object is a projectile without continuous thrust and ignores external forces such as atmospheric friction or the influence of other nearby celestial bodies.
Why it matters: This concept is essential for mission planning in aerospace engineering, as it determines the fuel and energy requirements for interplanetary travel. It also defines the physics of black holes, where the escape velocity at the event horizon exceeds the speed of light.
Avoid these traps
Common Mistakes
- Using diameter instead of radius.
- Mixing km and m.
One free problem
Practice Problem
Calculate the escape velocity from the surface of Earth, given Earth's mass is 5.97 × 10²⁴ kg and its radius is 6.37 ×10⁶ m.
Solve for:
Hint: Multiply 2, G, and M, then divide by r before taking the square root.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, Walker, Fundamentals of Physics
- Wikipedia: Escape velocity
- Britannica: Escape velocity
- NIST CODATA (for G value)
- Halliday, Resnick, Walker, Fundamentals of Physics (for equation and dimensional analysis)
- Atkins' Physical Chemistry (for dimensional analysis principles)
- Halliday, Resnick, Walker Fundamentals of Physics
- OCR A-Level Physics A — Gravitational Fields