Escape Velocity
Escape Velocity
\[v_e = \sqrt{\frac{2GM}{R}}\]
Variables
ve = escape velocity (m/s)
G = gravitational constant (6.67430×10^-11 N·m²/kg²)
M = mass of planet or celestial body (kg)
R = distance from center of mass (m)
Description
What is this formula?
The escape velocity equation calculates the minimum velocity required for an object to escape the gravitational field of a celestial body without additional propulsion.
When to use it
Use this formula when analyzing rockets, spacecraft launches, planetary missions, orbital mechanics, or gravitational escape problems.
Example
Calculate the escape velocity from Earth.
Data:
G = 6.67430×10^-11 N·m²/kg²
M = 5.972×10^24 kg
R = 6.371×10^6 m
Formula:
ve = √((2*G*M)/R)
Substitution:
ve = √((2*6.67430×10^-11*5.972×10^24)/(6.371×10^6))
Result:
ve ≈ 11186 m/s
Applications
Aerospace engineering, orbital mechanics, rocket science, astrophysics, planetary exploration, and space mission analysis.
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