Escape Velocity of Earth

When you throw a ball up into the air, why doesn’t it fly through the atmosphere and escape into outer space? This is because gravity pulls it back down. Then how does a rocket fly into outer space? It can fly into outer space because it is travelling with a very high velocity. This velocity is called escape velocity. The escape velocity of celestial bodies like planets and their natural satellites (the moon for us) is the minimum velocity that has to be achieved by an object, to escape the gravitational sphere of influence (pull or force or attraction) of the celestial body. At this velocity, the sum of the gravitational potential energy and kinetic energy of the system will be equal to zero.

What is Escape Velocity?

Escape velocity is defined as the speed at which an object travels to break free from either the planet’s or moon’s gravity and leave without any development of propulsion. 

Escape Velocity Equation

Escape velocity equation is obtained  by equating the kinetic energy of an object with mass m and travelling with a velocity of v and gravitational potential energy of the same object.

\( v_c = \sqrt {\frac {2GM}{r}}\)

where,

  • vc is the escape velocity
  • G is the universal gravitational constant
  • M is the mass of the celestial object whose gravitational pull has to be superseded
  • r is the distance from the object to the centre of mass of the body to be escaped
From this relation it is obvious that escape velocities for larger planets (or celestial bodies) is greater since it will have a larger mass compared to smaller planets with a lower mass (having less gravity in comparison).
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Escape Velocity of Earth

For earth, the acceleration due to gravity, g = 9.8 m/s2

The radius of the earth, R = 6.4 × 106 m

The escape velocity of the earth, ve = √2 × 9.8 × 6.4 × 106

Therefore, ve = 11.2 × 103 m/s = 11.2 km/s

On earth, the escape velocity is around 40,270 kmph, which is around 11,186 m/s.
For example, when a spacecraft is launched into outer space, the velocity attained by this should be greater than the escape velocity so that the rocket doesn’t fall back onto earth. And guess what, the escape velocity is different at the poles of the earth compared to that from the equator because the radius is slightly more at the equator.
It is said that it is impossible to escape a black hole because the gravitational field inside the event horizon is so huge that the calculated velocity is greater than the speed of light!

Escape Velocity of Different Objects

Following is the table with escape velocity of different celestial bodies:

Body Escape Velocity in km/s
Sun 618 km/s
Moon 2.38 km/s
Earth 11.2 km/s
Jupiter 59.5 km/s
Ceres 0.64 km/s

Check the below video to understand how escape velocity works:

Frequently Asked Questions

What does escape velocity depends on?

Escape velocity depends on the mass and radius of the celestial body.

What is the difference between orbital velocity and escape velocity?

The difference between orbital velocity and escape velocity is that orbital velocity is the speed that is required to reach the orbit of a planet or star whereas escape velocity is the speed which is required to leave the orbit.

How is escape velocity and orbital velocity related?

Escape velocity is a function of orbital velocity for an object. Escape velocity is derived by considering the product of orbital velocity and square root of 2. Also, the gravitational field that controls the orbit can be obtained.

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