Escape Velocity Converter
Instantly convert escape velocity with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Escape Velocity Converter
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Formula: v_escape = sqrt(2 * G * M / R)
Worked example โ Escape velocity from Mars is about 5.03 km/s or 18,100 km/h
Formula
v_escape = sqrt(2 * G * M / R)
Escape velocity equals the square root of twice the gravitational constant (G = 6.674e-11) times the body mass (M in kg) divided by its radius (R in meters). This formula comes from setting kinetic energy equal to gravitational potential energy and solving for velocity.
Worked Examples
Example 1: Escape Velocity from Mars
Problem:Calculate the escape velocity from the surface of Mars (mass = 6.417e23 kg, radius = 3.3895e6 m).
Solution:v = sqrt(2 * G * M / R) v = sqrt(2 * 6.674e-11 * 6.417e23 / 3.3895e6) v = sqrt(2.528e7) = 5,027 m/s
Result:Escape velocity from Mars is about 5.03 km/s or 18,100 km/h
Example 2: Escape Velocity from Jupiter
Problem:Find the escape velocity from Jupiter (mass = 1.898e27 kg, radius = 6.9911e7 m).
Solution:v = sqrt(2 * G * M / R) v = sqrt(2 * 6.674e-11 * 1.898e27 / 6.9911e7) v = sqrt(3.621e9) = 60,177 m/s
Result:Escape velocity from Jupiter is about 60.2 km/s or 216,600 km/h
Frequently Asked Questions
What is escape velocity and why does it matter?
Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without any further propulsion. It is derived from the balance between kinetic energy and gravitational potential energy. For Earth, escape velocity is approximately 11.186 km/s or about 40,270 km/h. This speed determines the energy requirements for launching spacecraft into interplanetary trajectories and is fundamental to mission planning in aerospace engineering.
Does escape velocity depend on the direction of launch?
No, escape velocity is a scalar quantity that depends only on the mass and radius of the celestial body, not on the direction of travel. Whether launched straight up, horizontally, or at any angle, the same speed is needed to escape the gravitational field. However, launching eastward near the equator provides a small velocity boost from Earth's rotation of about 465 m/s, which is why most spaceports are located near the equator.
Why does the Moon have a much lower escape velocity than Earth?
The Moon's escape velocity is about 2.38 km/s compared to Earth's 11.19 km/s because escape velocity depends on the ratio of mass to radius. The Moon has roughly 1.2% of Earth's mass but about 27% of its radius. Since escape velocity scales with the square root of mass divided by radius, the Moon's much smaller mass dominates the calculation, resulting in an escape velocity about five times lower than Earth's.
How is escape velocity related to whether a body can hold an atmosphere?
A celestial body retains an atmosphere when its escape velocity significantly exceeds the average thermal velocity of gas molecules. The thermal velocity of a molecule depends on temperature and molecular mass. If gas molecules frequently reach speeds near the escape velocity, they gradually leak into space through a process called Jeans escape. This is why the Moon and Mercury have essentially no atmosphere while Earth and Venus retain thick ones.
References
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