Equations
Escape speed
Gravitation · id escape_velocity
v_{esc} = \sqrt{\frac{2 G M}{r}}
| Symbol | Quantity | Unit | Meaning | Usual range |
|---|---|---|---|---|
v | escape speed | m/s | Minimum launch speed to escape to infinity | 0 to 1e+07 |
G | gravitational constant | m^3/(kg*s^2) | Newton's constant of gravitation | |
M | central mass | kg | Mass of the central body | 1 to 1e+32 |
r | distance from center | m | Launch distance from the body's center | 1 to 1e+13 |
Assumptions
- No air resistance
- Non-rotating spherical body
Valid when
- Speeds far below the speed of light
Look-alikes
Speed of a circular orbit has exactly the same variables, so only the question's words tell them apart. To get this one, use one of: black hole, escape speed, escape velocity, launch, rocket. A question that says neither gets an answer flagged as ambiguous.
Found by
Questions with these words retrieve this equation: escape velocity, escape speed, rocket, launch, planet, black hole.
Source
OpenStax University Physics Volume 1, Chapter 13 (reference; entry written by the project). License: MIT. Entry confidence: 0.99.