Gravitational Force- Escape Velocity

This force is responsible for the attraction of any two objects with mass to one another. Attractive is the term used to describe the gravitational force because it always tries to bring masses together rather than pushing them apart. As a matter of fact, every object, including you, is pulling on every other object throughout the entire universe!

The bare minimum velocity at which a moving body (such as a rocket) must travel in order to escape the gravitational field of a celestial body (such as the earth) and move outward into space is called the escape velocity.

Force and Gravity 

There are numerous forces at work in the universe, as well as numerous pushes and pulls. Furthermore, we are constantly pulling or pushing something, even if it is only a rock or a stick in the ground. However, in physics, there are four fundamental forces from which everything else is derived, and these are as follows: Aside from that, the weak force, the strong force, the gravitational force, and the electromagnetic force are all known as the four fundamental forces.

Furthermore, the gravitational force is something that attracts any two objects that have a similar mass to one another. Furthermore, this gravitational force attracts because it is always attempting to pull masses together and is never attempting to pull masses apart. Newton’s Universal Law of Gravitation states that all objects, including you, pull all other objects in the entire universe, and this is known as the Law of Universal Gravitation.

The Formula for Gravitational Force

The gravitational force formula is also referred to as Newton’s law of gravitation because it was discovered in 1687. In addition, it specifies the magnitude of the force between the two objects in question. Furthermore, the gravitational force formula includes the gravitational constant, which has a value of 

G = 6.67×10-11 m3 kg-1 s-2

and is denoted by the symbol G. Furthermore, the gravitational force is measured in Newtons (N).

Derivation of the Gravitational Force Formula

The gravitational force between two objects (N = kg.m/s2) is denoted by the symbol Fg.

The gravitational constant (G = 6.67*10-11Nm2/kg2 ) is denoted by the letter G.

The first object’s mass, expressed in kilograms, is denoted by the symbol m1.

m2 = is the mass of the second object, which is also measured in kilogrammes.

The distance between the objects is expressed in metres by the symbol r.

According to Newton’s thought experiment, he imagined himself as the commander of a cannon on the summit of a very high mountain summit. Depending on how the cannon is loaded with gunpowder and fired, the following scenarios may occur.

Unless the cannon is fired at a high rate, the cannon will fall to the ground in a projectile motion.

If the speed of the cannonball at that particular altitude is equal to the speed of the Earth’s orbital rotation, the cannonball will continue to revolve around the Earth in a fixed orbit.

If the cannonball’s speed is greater than the orbital velocity but less than the Earth’s escape velocity, the cannonball will continue to revolve around the planet in an elliptical orbit until it reaches the escape velocity of the Earth.

Depending on whether or not the speed is equal to or greater than the escape velocity, the cannonball will leave the Earth on a parabolic or hyperbolic trajectory.

What is the mechanism by which planets revolve around the Sun? 

The gravity of the Sun, on the other hand, keeps the planets in their fixed orbits around it. The Moon orbits the Earth as a result of the gravitational pull of the Earth on the Moon, which is due to the same reason. But, if the Sun is attracting the Earth, why doesn’t the Earth fall into the Sun, or why doesn’t the Moon collide with the Earth, as the theory suggests?

According to this explanation, Earth moves at a speed parallel to the gravitational force exerted on it by the Sun. As a result, the planets move sideways in addition to being attracted to the Sun, which keeps them moving in specific orbits around the Sun. In a similar vein, the Moon revolves around the Earth without collapsing inside it.

Examples Of Gravity

The gravitational force that exists between the Sun and the Earth.

The Moon’s gravitational pull is responsible for the tides that occur in the oceans.

The gravitational force that holds all of the gases in the Sun together.

The force that is exerting its influence on us causes us to walk on the ground rather than float in the air.

What is the definition of Escape Velocity?

A spacecraft’s escape velocity is defined as the speed at which an object travels in order to break free from the gravitational pull of the planet or moon and leave without developing any form of propulsion.

The Equation of Escape Velocity

The escape velocity equation is obtained by equating the kinetic energy of an object with mass m and travelling with a velocity of v with the gravitational potential energy of the same object, and then multiplying the result by a factor of two.

where,

The escape velocity is denoted by vc.

G is the gravitational constant of the universe.

M denotes the mass of the celestial object whose gravitational pull must be overcome in this equation.

The distance between the object and the centre of mass of the body to be escaped is denoted by the letter r.

It follows from this relationship that the escape velocities of larger planets (or celestial bodies) are greater than those of smaller planets with a lower mass because the larger planets (or celestial bodies) have a greater mass (having less gravity in comparison).

On Earth, the escape velocity is approximately 40,270 kmph, which is approximately 11,186 metres per second.

A spacecraft, for example, should achieve a velocity greater than that of its escape velocity when launched into outer space in order to avoid re-entering the atmosphere and crashing back onto the planet. And, guess what? The escape velocity at the poles of the earth differs from that at the equator because the radius at the equator is slightly larger than at the poles.

A black hole is said to be unreachable because the gravitational field inside the event horizon is so powerful that the calculated velocity is greater than the speed of light.

Conclusion

The minimum speed required for a free, non-propelled object to escape from the gravitational influence of a primary body and reach an infinite distance from it is known as escape velocity or escape speed. It is commonly stated as an ideal speed, which ignores the effects of atmospheric friction. Despite the fact that the term “escape velocity” is commonly used, it is more accurately described as a speed rather than a velocity because it is independent of direction; the escape speed increases with the mass of the primary body and decreases with the distance between the primary body and the escape velocity.