Escape Velocity

Escape Velocity:

Escape velocity is the minimum velocity at which a mass would have to project from the ground to escape the earth's gravitational field. Escape velocity, also known as escape velocity, is defined as: 

The minimum speed required for an object to break free from the gravitational pull of a massive object.

For example, if we think of the Earth as a massive body. Escape velocity is the minimum speed an object must reach to overcome the Earth's gravitational field and fly to infinity without falling back. It purely depends on the distance of the object from the massive body and the mass of the massive body. The greater its mass, the greater the distance, the greater the escape velocity.

For all massive bodies, such as planets and stars, which are spherically symmetric in nature, the escape velocity at any distance is mathematically expressed as:

where,

  • woe is the escape velocity
  • G is the universal gravitational constant.
  • M is the mass of the massive body (the body from which the object should escape)
  • r is the distance from the center of the massive body to the object

It may be noted here that the above relation does not depend on the mass of the object escaping from the massive body.

 Derivation of escape velocity

In general escape, velocity is achieved when an object is moving at a velocity at which the arithmetic sum of the object's gravitational potential energy and its kinetic energy is zero. This means that to reach infinity, the object would have to have more kinetic energy than gravitational potential energy. The easiest way to derive the formula is to use the concept of energy conservation. Suppose an object tries to escape a planet (which is uniformly circular in nature) by moving away from it.  The main force acting on such an object is the planet's gravity. As we know, kinetic energy (K) and gravitational potential energy (Ug) are the only two types of energy. Using the principle of energy conservation, we can write:

By the principle of conservation of energy, we can write:

 (K+Ug)i=(K+Ug)f

 Where,

 K=1/2mv2

 U=GMm/r

Here Ugf is zero as the distance is infinity and Kf will also be zero as the final velocity will be zero. Thus, we get:

The minimum velocity required to escape from the gravitational influence of a massive body is given by:

 The escape speed of the earth at the surface is approximately 11.186 km/s. That means “an object should have a minimum of 11.186 km/s initial velocity to escape from earth’s gravity and fly to infinite space.”

Ideally, if you can jump at an initial speed of 11,186 km/s, you can orbit in space!

Unit of escape velocity

The unit of escape velocity, or escape velocity, is meter per second (m.s-¹), which is also the SI unit of escape velocity.