How do we find the earths escape velocity
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How do we find the earths escape velocity

[From: ] [author: ] [Date: 11-05-05] [Hit: ]
It is 2G, not G,because of the half in the formula for kinetic energy. To calculate escape velocity you equate kinetic energy lost (mv^2/2) with potential energy gained moving from the surface of the earth to infinity (GMm/r).......
I know the formula Ve=square root of 2G.M/r

if I know the circumference of earth (r) what is M and why is it 2G and not just G?

also, what is G anyway?

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The potential energy of a mass m at the earth's surface relative to infinitely far away, is -GMm/R where M is the mass of the earth, R is the radius of the earth, and G is the gravitational constant.

G is just the proportionality constant that appears in Newton's Law of Gravitation F = GMm/R^2.

So it takes an amount of energy GMm/R to move something from the surface to infinitely far away. If you ask the question, how much kinetic energy can I give something at the surface so that it will keep traveling forever, never turning around and falling back, then the answer is GMm/R of kinetic energy.

So you set the initial KE equal to that quantity: (1/2)mv^2 = GMm/R. If you rearrange to solve for v, you'll find that the speed is sqrt(2GM/R). If you have that much speed at the surface, then ignoring air resistance you have enough energy to escape to infinity.

As you can see, m cancels out. It doesn't matter what the mass of the object is. And you asked about the 2. It comes from the "1/2" that's part of the kinetic energy formula.

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r usually means radius not circumference!
M is mass of earth
G is universal constant of gravitation

It is '2G', not 'G', because of the 'half' in the formula for kinetic energy. To calculate escape velocity you equate kinetic energy lost (mv^2/2) with potential energy gained moving from the surface of the earth to infinity (GMm/r).
mv^2/2 = GMm/r
v^2 = 2GM/r
v = sqrt(2GM/r)
= 11180m/s
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