Introduction

Escape velocity is a minimal speed an object must achieve to break free from the gravitational pull of a celestial body without offering further thrust. The concept is significant in fields such as astrophysics, aerospace engineering, and space exploration.

Formula Of Escape Velocity

It is derived from the principles of energy conservation, namely gravitational potential energy and kinetic energy. The escape velocity is:

Where,

V = escape velocity

G = gravitational constant is  

M = mass of the planet

R = radius from the center of gravity

An expression for escape velocity that is specially useful at the surface on the body is

Where g is the acceleration due.

Thus escape velocity can also be written as,

In m/s it is expressed and the earth escape velocity is 11,200 m/s.

The formula of escape velocity is applied in finding out the escape velocity of any body or any planet if mass and radius is known.

Solved Examples

Example 1

Find the escape velocity of Jupiter if the radius is 7149 Km and the mass is    1.898 × Kg

Solution:

Given,

Mass M = 1.898 × Kg,

Radius R = 7149 Km

Gravitational Constant G =

Escape Velocity is given as

Vesc = √2GM / R

=√2 x    x 1.898 ×  / 7149

              50.3 km/s

 

Example 2

Determine the escape velocity of the moon if Mass is 7.35 × 10 22 Kg and the radius is 1.5 ×m.

Solution:

Given

M = 7.35 × 10 22 Kg,

R = 1.5 × m

The escape Velocity formula is given by

Vesc = √2GMR

          = √2×   ×7.35×10^22 / 1.5× 

          = 7.59 ×m/s

 

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