Answer:
Escape velocity: Measuring the gravitational strength of an object
The escape velocity is the exact amount of energy you would need to escape the gravitational clutches of an object with mass. Since all objects have mass, they all have a measureable gravitational strength. A good way to think about escape velocity is to think about a deep well (physicists like to think of this as an energy well). If you are at the bottom of the well and want to get out (to escape), you need enough energy to climb out. The deeper the well, the more energy you will have to expend in order to climb to
the top. If you have only enough energy to get half way out, you will eventually fall back to the bottom. The escape velocity is a way of measuring the exact amount of energy needed to reach the lip of the well -- and have no energy left over for walking away.
When a ball is thrown up into the air from the surface of the Earth, it does not have enough energy to escape. So it falls back down. How might we enable the ball to escape? Throw it harder, give it more energy. How hard must we throw it? Just hard enough to get over the top, over the edge of the well.
We can find this energy directly by saying that the kinetic energy of the thrown ball must exactly equal the 'potential energy' of the well. From basic physics we know that the potential energy for an object at a height above a surface is:
Epotential= GMm/R
where
G = Newton's universal constant of gravity = 6.67 x 10-11 N-m2/kg3
M = the mass of the 'attracting object' [the planet] [in units of kg]
m = the mass of the object trying to escape [e.g., me or a ball or a rocket or a molecule] [in kg]
R = the distance between the centers of objects M and m [in units of m]
note: provided we do everything in the same units, we don't have to worry about units
while the kinetic energy we know from above:
Ekinetic=0.5 m v2
where
m = mass of the moving object [in kg]
v = the velocity of object m [in m/sec]
If we set these two energies equal to each other, and solve for v, we find the exact velocity needed to escape from the energy well:
0.5 m v2= GMm/R
v= (2GM/R)0.5
and since this velocity is exactly what is needed to 'escape,' it is called the escape velocity:
vescape= (2GM/R)0.5
Explanation:
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