Escape velocity

Introduction

Escape velocity is the speed required for a body to escape the gravitational field or gravitational centre of attraction without the need for additional velocity or acceleration. The escape velocity reduces with altitude.

In other words, escape velocity can be defined as the minimum velocity a body must have to escape the gravitational attraction potential of a planet. The escape velocity is different for different planets depending upon the gravitational pull, which functions in the planet’s mass and its radius.

Escape velocity of earth:

In astronomy and space research, escape velocity is the velocity at which a body can escape from a gravitational centre of attraction without further acceleration. The velocity required to maintain a circular orbit at the same altitude is equal to the square root of 2 (or around 1.414) times the escape velocity. If atmospheric resistance were ignored, the escape velocity at the Earth’s surface would be around 11.2 kilometres (6.96 miles) per second. At its surface, the less massive Moon’s escape velocity is around 2.4 km per second. 

The mass and size of the object from which something is attempting to flee determine the escape velocity. A pebble has the same escape velocity as the Space Shuttle when it leaves the Earth.

Escape velocity equation:

The features of the escaping item have no bearing on the escape velocity formula. The mass and radius of the heavenly body in question are the only factors that matter:

       Ve = ✓(2GM/R)

The planet’s mass is M, its radius is R, and the gravitational constant is G. G = 6.674 10-11 Nm²/kg² is the value.

The second cosmic velocity formula is derived directly from the law of conservation of energy. The item possesses some potential energy PE and some kinetic energy KE at the time of launch. As a result, the energy at launch LE can be expressed as follows:

 PE + KE = -GMm/R + 1/2mV²

Where m is the mass of the beginning item and v is the escape velocity.

When the item finally makes it away from the planet, it is so far away that its potential energy is zero. It can likewise move at nearly no speed, therefore its kinetic energy is also zero. That is to say, the total ultimate energy equals:

                       PE + KE = 0+0 = 0

Because the entire energy must be conserved, the starting energy must be equal to zero as well. We can simplify the first equation as follows:

                    0 = -GMm/R + 1/2mV²

                             ✓(2GM/R) = v

Simply follow these steps and you’ll have it figured out in no time;

• Find out how much mass the planet has. The mass of the Earth, for example, is 5.9723 x 10²⁴ kg.
• Calculate the planet’s radius. The radius of the Earth, for example, is 6,371 kilometres.
• Substitute these numbers for v = ✓(2GM/R) in the escape velocity equation.
• Calculate the outcome. In the case of Earth, the escape velocity is 11.2 kilometres per second.
• Use our escape velocity calculator to see if the answer is right.

Definition of escape velocity equation:

Only when an object’s kinetic energy equals its gravitational potential energy can it escape a celestial body of mass M. 12mv2 is the kinetic energy of an object with mass m travelling at a velocity v. By definition, the gravitational potential energy of this item is a function of its distance r from the celestial body’s centre.

Gives this as GMm/r, where G is the gravitational constant whose value is. When we combine the two, we obtain:

                   ½ mv² = GMm/r

                    v = ✓(GM/r)

Different values of M and r can be substituted in this equation to determine the escape velocity of various celestial bodies. Because of the dependency on r, things that are high above the body’s surface have an easier time escaping than those that are sitting on it. This is clear since the gravitational force of a planet weakens as we move away from its surface.

Finally, the equation shows that the escape velocity of a planet is independent of its mass. This may seem contradictory, but in order to escape, a dinosaur or a turtle must travel at 11.2 km/s (ignoring air resistance). However, because acceleration is a function of mass, even though the dinosaur departs at the same speed as the turtle, getting it to 11.2 km/s is far more difficult than getting the turtle to the same speed.

Conclusion:

• The minimal velocity at which a body must travel to escape the earth’s gravitational field is called escape velocity.
• Assume that we throw a ball and it falls back. This is owing to the gravitational attraction imposed on the ball by the earth’s surface, which causes the ball to be drawn towards the earth’s surface.
• If we increase the velocity to the point where the thrown object never falls back, we have achieved our goal.

This speed is referred to as escape velocity.

The ball is tossed aloft, but because of gravity, it falls to the ground.

The same ball is flung at a high enough velocity to escape the earth’s gravitational pull and not return. This speed is referred to as escape velocity.

Need of escape velocity:

The only force acting on you is gravity, therefore your escape velocity is determined after the rocket engines (or whatever drove you to 11km/s) have ceased firing. Imagine yourself well above the Earth’s atmosphere, speeding away from the planet. The gravitational attraction of the Earth slows you down, but as you get further away from it, the pull diminishes. If you were travelling faster than the escape velocity, Earth’s gravitational pull would ultimately bring you to a halt, and you would then fall back to Earth. The escape velocity is the speed at which you can avoid this fate and continue travelling indefinitely, albeit you’d have to go much faster if you wanted to reach the stars in your lifetime.