Escape Velocity

Escape Velocity

When an object moves far above the Earth's surface, calculating its Gravitational Potential Energy becomes a bit more difficult:

                                                    1        1
    GPE(B) - GPE(A)  =   G*M(earth)*m(object) * (  ----  -  ---- )
                                                   R(A)     R(B)

where

             G           is the universal gravitational constant
	     M(earth)    is the mass of the Earth
	     M(object)   is the mass of the object
	     R(A)        is the distance of point A from center of Earth
	     R(B)        is the distance of point A from center of Earth

One can use conservation of energy to calculate the speed an object needs at the Earth's surface to reach an infinite distance from the Earth. The escape velocity for the Earth turns out to be
```
                                    [  2*G*M(earth)  ]
           escape velocity  =  sqrt [  -----------   ]
                                    [    R(earth)    ]
```

Viewgraphs

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