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
(v_{e}) 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 v_{e}
= (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 



