Gravitation-Variations In G-Escape Velocity

We can state escape velocity definition as the precise amount of energy that you require to get out of the gravitational grip of a massive object. Because all objects have mass, they all possess an observable gravitational force. 

One method to think about escape velocity is to consider the depth of a well (physicists tend to think of it as an energy reservoir). If you’re at one end of the well, and you want to climb out (to escape) you will require enough energy to be able to climb. The deeper your well is, the more energy you must expend for climbing up at the highest point. If you only have enough energy to walk about halfway up, then you will be back at the bottom. 

Escape velocity is a method for measuring the precise amount of energy required to get to the top of the well and there is no energy left to walk away. Now, let us look into what is escape velocity? What is its formula?

What is escape velocity?

Escape velocity is always determined when there is a large difference in the mass and size of both bodies. This means that either of them has an extremely massive mass and size when compared to the body which seeks to get out. Because the escape velocity is determined by the mass and size of the body that is pulling its gravitational pull trying to get out, the larger is the gap between the weights and dimensions that the body has, the greater is the escape velocity. 

There are some space bodies with enormous mass but have a smaller dimension e.g dark holes. For black holes, they are so densely high that the escape velocity is greater than what light travels at, and this means that light isn’t able to escape black holes.

How to derive escape velocity?

When a ball gets launched in the air from the ground of Earth, the ball does not contain enough force to get away. Therefore, it comes back to earth. What can we do to allow the ball to get away? Throw it more forcefully, give the ball more power. What is the maximum force we can throw it with? It should be just enough to get to the top.

You can determine this energy by stating that the energy of the throwing ball should be exactly the same as the potential energy as that of the well. From the basics of physics, we know that the potential energy of an object that is placed above the surface is:

Epotential= GMm/R

where

E is the potential energy

G is Newton’s universal constant of gravity. It is equal to 6.67 x 10-11 N-m2/kg3

M is the “attractive object’, i.e. the planet which we measure in kilograms

m is the weight or mass that the object is trying to get away which we measure in kilograms

R is the distance between centre of objects M and m which is measured in metres

While the kinetic energy is what we have learned from above:

Ekinetic= (½ ) m v2

in which

m = mass of the object that is moving [in kg] 

v is the velocity of object  [in m/sec]

When we make these two energy levels equal, and then solve for v, we can find the precise speed required to escape the well

(½ ) m v2= GMm/R

v= (2GM/R)1/2

and because this speed is precisely what is needed to escape, it is known as the escape velocity.

vescape= (2GM/R)1/2

Notice what a crucial parameter that is not included in the equation for escape velocity is the weight of the object that is moving. The escape velocity is dependent on the weight and size of the object that attempts to get away. 

Conclusion

The Escape Velocity is the speed at which an object must reach to escape the gravitational pull of the Earth. But it is not allowed to accelerate any further. This is the speed at which the object has to be launched in order that it can overcome the gravitational pull of the Earth and thus be capable of escaping to space. This means that the escape velocity must remain constant for the entire escape route and should not change when the object is in the grip of gravity force from the Earth.

The gravitational force of Earth will depend on the size and volume of the Earth and the escape velocity is determined by gravity’s pull of the Earth. This means that the escape velocity depends on the mass and size of the Earth.