What Is Earth's Escape Velocity

JEE Escape Velocity

By definition, escape velocity is the minimum velocity an object must larn to escape the gravitational pull of the world without falling dorsum. The concept of escape velocity has huge significance in the field of space science. So let us delve into this a little deeper.

We know, that if nosotros throw a body upwardly, it falls back after rising for a while by the gravitational pull of the earth. Gravity decelerates the body progressively at the rate of thousand 1000/s² (acceleration due to gravity) until its velocity becomes 0 at the highest point. After exhausting its initial upwards velocity, the torso begins to now accelerate at the rate g merely downwards i.e. towards the surface of the earth and falls back.

However, if we were to impart sufficient velocity to the torso such that the torso crosses the gravitational field of the world without exhausting its velocity, it would exist able to escape into space.

How To Calculate Escape Velocity?

A good way to calculate the escape velocity is to use the principle of conservation of energy.

If the earth's gravitational field extends to a height, h above the world's surface, body'due south potential free energy at that superlative would exist.

P.Eastward. = GMm/(R + h)

where Thou is the universal Gravitational constant

G is the mass of the world

m is the mass of the torso

and R is the radius of the earth.

Since, h<<R, we tin simplify the potential energy to the following expression.

P.East. = GMm/R

Allow's say the escape velocity of the body is 5. The body must have greater energy than its gravitational binding free energy.

\(\begin{array}{l}\frac{i}{2}mv^2=G\frac{Mm}{R}\cease{array} \)

therefore,

\(\begin{array}{l}v=\sqrt{\frac{2GM}{R}}\terminate{array} \)

Equally y'all can run into, this velocity is independent of the mass of the body and therefore, the aforementioned for all bodies. On putting the values of G, One thousand, R in the expression, we get

five = 11.2 Km/s

Escape Velocity

Frequently Asked Questions on Escape Velocity

Define escape velocity.

The minimum speed required to project a body vertically upward from the surface of the globe so that it never returns to the surface of the world is called escape speed.