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Escape Velocity
If a body is thrown upwards fast enough, it never comes back down: it has escaped from the planet.  
The velocity needed to do this is called the escape velocity (ve) of the planet.  
   
As the body is moving away from the planet, it is losing kinetic energy and gaining potential energy.  
   
To completely escape from the gravitational attraction of the planet, the body must be given enough kinetic energy to take it to a position where its potential energy is zero.  
 
The potential energy U possessed by a body of mass m in a gravitational field is given by  
 
If the field is due to a planet of mass M and radius R, then a mass, m, on the surface of the planet possesses potential energy given by:  
 
As the body is moving away from the planet, K.E lost is equal to P.E. gained  
 
If U is to change from     to zero, then the change, ΔU is given by
 
 
 
 
 
For the earth, this gives ve = (about) 11kms-1  
 
The escape velocity can also be given in terms of g (the gravitational field strength or acceleration due to gravity) at the surface of the planet:  
as shown here, we have  
which gives us  
   
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