# ESCAPE VELOCITY FORMULA

What is escape velocity?

Escape Velocity is the minimum velocity required by a body to be projected overcome the gravitational pull of the earth. It is the minimum velocity required by an object to escape the gravitational field that is, escape the land without ever falling back. An object that has this velocity at the earth’s surface will totally escape the earth’s gravitational field ignoring the losses due to the atmosphere.

For example, a spacecraft leaving the surface of Earth needs to go at 7 miles per second, or around 25,000 miles per hour to leave without falling back to the surface.

Escape velocity formula is given as

$V_{esc}\,&space;=\,\sqrt{\frac{2GM}{R}}$

Wherein,

Vesc = escape velocity,

G = gravitational constant is 6.673 × 10-11m3kg-1s-2,

M = mass of the planet,

R = radius from center of gravity

Acceleration due to gravity formula is given by

$V_{esc}\,&space;=\,gR^{2}$

Where, g is acceleration due to gravity of earth.

Hence Escape velocity is also given by

$V_{esc}\,&space;=\,\sqrt{2gR}$

It is expressed in m/s and escape velocity of earth is 11,200 m/s.

Escape velocity formula is applied in finding escape velocity of anybody or planet, if mass and radius is known.

Example 1

Determine the escape velocity of the Jupitor if its radius is 7149 Km and mass is 1.898 × 1027 Kg.

Solution:

Given: Mass M = 1.898 × 1027 Kg,

Gravitational Constant G = 6.673 × 10-11m3kg-1s-2

Escape Velocity is given as

Vesc = √2GM / R

=√2 x 6.673 × 10-11 x  1.898 × 1027 Kg / 7149

50.3 km/s

Example 2

Determine the escape velocity of the moon if Mass is 7.35 × 1022 Kg and radius is 1.5 × 106 m.

Solution:

Given

M = 7.35 × 1022 Kg,

R = 1.5 × 106 m

Escape Velocity formula is given by

Vesc = √2GMR

= √2×6.673×10−11×7.35×1022 / 1.5×106

= 7.59 × 105 m/s