What is Escape Velocity and How does it Work?

An object must have a certain level of velocity to achieve orbit around a celestial body such as Earth. Breaking free of such an orbit requires even more velocity. Astrophysicists use the rotational velocity of the Earth to accelerate rockets and launch them beyond the reach of the gravity of earth when designing rockets to travel to other planets or out of the solar system entirely. Escape velocity is the speed required to break free of an orbit. In this article, you will learn about what is escape velocity and how it works, also its relation with orbital velocity.

What is escape velocity?

The velocity required by a body to escape the gravitational field of the Earth is known as escape velocity. It is common knowledge that an object projected upward returns to the ground after reaching a certain height. This is due to the downward force of gravity. The object rises to a greater height with increased initial velocity before falling back. If we keep increasing the object’s initial velocity, it will eventually stop returning to the ground. It will break free from gravity’s grip. The initial velocity with which an object exits the Earth’s gravitational field is known as E.V. In rocket science and space travel, v_e 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). The escape velocity depends on the mass and size of the object from which something is attempting to flee. A pebble’s v_e from Earth is the same as that of the Space Shuttle.

How escape velocity works?

Escape velocity, like orbital velocity, varies with object distance from a center of gravity. In practice, the higher the altitude of the rocket above Earth, the less velocity is required to orbit the Earth and to get out of the Earth’s gravitational field entirely. One reason communications satellites can orbit the Earth without constantly expending energy is that they are located miles above the surface. A commercial aircraft, on the other hand, which flies much closer to the planet’s surface, must constantly exert energy to stay aloft. According to the same principle, a rocket flying far from the earth’s surface requires less energy to achieve v_e than a rocket flying close to the earth.

How to calculate escape velocity?

The escape velocity of an object is determined by its orbital velocity. You can calculate the velocity required to escape orbit and the gravitational field controlling that orbit by multiplying the velocity required to maintain orbit at a given altitude by the square root of 2 (approximately 1.414). Consider a spaceship that is currently orbiting the Earth in the context of human space exploration. If it runs its engine long enough, it will eventually reach a high enough speed to escape the planet’s gravity. v_e is simply the square root of two, or 41 percent faster than orbital speed. The escape velocity formula is given as:

V_e = (2GM / r )^1/2

This formula is derived from the factor that the gravitational force of earth is equal to the centripetal force of the object revolving around it. Of course, centripetal force is necessary for an object to remain in circular motion, so:

(1/2) m v² = (G M m) / r

V² = 2GM / r

V_e = (2GM / r )^1/2

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Escape velocity of Earth

The theoretical value of v_e of Earth on surface is 11.2 km per second (6.96 miles per second). The v_e on the moon’s surface is approximately 2.4 km per second (1.49 miles per second). These figures aren’t particularly significant in practice. Rockets do not escape Earth’s gravity by launching from the ground. Rather, astronomical engineers launch these rockets into orbit, then use orbital velocity as a slingshot to propel the rocket to its required v_e. Furthermore, these velocities do not take atmospheric resistance into account, which would increase the required velocity to escape the planet’s gravitational field. This is yet another reason why rocket scientists launch spacecraft into orbit before attempting v_e.

Do you know about the escape velocity of black hole? The escape velocity of a Black Hole from its surface (i.e., the event horizon) is exactly c, the speed of light. Actually, the prediction of the existence of black holes was based on the idea that objects with v_e equal to “c” could exist.

Difference between Orbital Velocity and Escape Velocity

What is orbital velocity? Orbital velocity is the speed required to enter an orbit around a celestial body, such as a planet or star, whereas v_e is the speed required to exit that orbit. To maintain orbital velocity, you must travel at a constant speed that aligns with the rotational velocity of the celestial body and which is fast enough to overcome the gravitational pull of the orbiting object toward the body’s surface.

The curved surface of a planet, star, or other celestial body allows for orbital velocity. An object in orbit moves in a straight line, whereas the body it orbits curves. As a result, as long as the orbiting object maintains the proper speed, the constant curvature of the orbited body prevents it from falling all the way to the surface. Because of the principle of inertia, it is easier to maintain a constant speed in space than it is on Earth. One of Sir Isaac Newton’s laws of inertia states that unless acted on by an outside force, an object in motion tends to stay in motion. A flying object encounters many air molecules within the Earth’s atmosphere, which slows the object’s speed as it flies through the sky. As you travel beyond Earth’s atmosphere, the air becomes voider, with fewer molecules to counteract an orbiting object’s forward velocity.

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Relation between orbital and escape velocity

In astrophysics, the relation between escape velocity and orbital velocity is written as:

V_o = v_e / √2

Or v_e = √2 v_o

Where, v_o is orbital velocity and v_e is escape velocity. This implies that escape velocity is directly proportional to orbital velocity. That means for any massive body- If v_o increases, the v_e will also increase and vise-versa. If v_o decreases, the escape velocity will also decrease and vise-versa.