Science & Technology

Learn How Escape Velocity Works and How to Calculate Escape Velocity

Written by MasterClass

Sep 9, 2019 • 4 min read

It takes a certain level of velocity for an object to achieve orbit around a celestial body such as Earth. It takes even greater velocity to break free of such an orbit. When astrophysicists design rockets to travel to other planets—or out of the solar system entirely—they use the rotational velocity of the Earth to speed up the rockets and launch them beyond the reach of Earth’s gravity. The speed required to break free of an orbit is known as escape velocity.

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What Is Escape Velocity?

Escape velocity, as it applies to rocket science and space travel, is the velocity required for an object (such as a rocket) to escape the gravitational orbit of a celestial body (such as a planet or a star).

How Does Escape Velocity Work?

Much like orbital velocity, escape velocity varies based on the distance that an object is from a center of gravity. In practical terms, the higher the rocket’s altitude is above Earth, the less velocity will be required to:

  • Orbit the Earth
  • Escape Earth’s gravitational field altogether

One reason that communications satellites can orbit the earth without constantly expending energy is that they subsist at an altitude miles above Earth. By contrast, a commercial aircraft, which flies much closer to the planet’s surface, must constantly exert energy to remain in the sky. By this same principle, it takes comparatively less energy for a rocket far from the earth’s surface to achieve escape velocity than it would if the rocket were flying close to the earth.

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How Do You Calculate Escape Velocity?

Escape velocity is a function of the orbital velocity of an object. If you take the velocity required to maintain orbit at a given altitude and multiply it by the square root of 2 (which is approximately 1.414), you will derive the velocity required to escape orbit and the gravitational field controlling that orbit.

In the context of human space exploration, consider a spaceship currently orbiting the earth. If it fires its engine long enough, it will eventually go fast enough to fly away into deep space, escaping the planet’s gravity. That speed, called escape velocity, is simply the square root of 2, or 41 percent faster than orbital speed.

What Is the Escape Velocity of the Earth?

In theoretical terms, the escape velocity at the surface of Earth is 11.2 km per second (6.96 miles per second). The escape velocity on the surface of the moon is roughly 2.4km per second (1.49 miles per second).

In practical application, these numbers aren’t terribly important. Rockets don’t go escape Earth’s gravity by launching directly from the surface. Rather, astronomical engineers first send these rockets into orbit and then use orbital velocity as a slingshot to propel a rocket to its necessary escape velocity. Furthermore, the escape velocities listed above do not account for atmospheric resistance, which would actually increase the required velocity needed to escape the planet’s gravitational field. This is yet one more reason why rocket scientists first put spacecraft into orbit before gunning for escape velocity.

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What Is the Difference Between Escape Velocity and Orbital Velocity?

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Orbital velocity is the speed required to achieve orbit around a celestial body, such as a planet or a star, while escape velocity is the speed required to leave that orbit. Maintaining orbital velocity requires traveling at a sustained speed that:

  • Aligns with the celestial body’s rotational velocity
  • Is fast enough to counteract the force of gravity pulling the orbiting object toward the body’s surface

Orbital velocity is made possible by the curved surface of a planet, star, or other celestial body. An orbiting object tends to move in a straight line, whereas the body it is orbiting curves. As such, the constant curvature of the orbited body prevents the orbiting object from falling all the way to the surface, provided that the orbiting object maintains the proper speed.

In space, it is easier to maintain a constant speed than it is on earth, due to the principle of inertia. One of Sir Isaac Newton’s laws of inertia states that an object in motion tends to stay in motion unless acted on by an outside force. Within the earth’s atmosphere, a flying object encounters many air molecules, which cumulatively slow the speed of that object as it flies through the sky. As you journey beyond Earth’s atmosphere, the air becomes more vacuous, with fewer molecules to counteract the forward velocity of an orbiting object.

Learn more about orbital velocity in our complete guide here.

Want to Learn More About Space Exploration?

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