Escape Velocity

Escape Velocity:
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if you throw an object straight up, it will rise until the the negative acceleration of gravity stops it, then returns it to Earth. Gravity's force diminishes as distance from the center of the Earth increases, however. So if you can throw the object with enough initial upward velocity so that gravity's decreasing force can never quite slow it to a complete stop, its decreasing velocity can always be just high enough to overcome gravity's pull. The initial velocity needed to achieve that condition is called escape velocity.
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From the surface of the Earth, escape velocity (ignoring air friction) is about 7 miles per second, or 25,000 miles per hour. Given that initial speed, an object needs no additional force applied to completely escape Earth's gravity

1/2 mv2 = GMm/R
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Where m is the mass of the object, M mass of the earth, G is the gravitational constant, R is the radius of the earth, and v is the escape velocity. It simplifies to:
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v = sqrt(2GM/R)
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or
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v = sqrt(2gR)
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Where g is acceleration of gravity on the earth's surface.
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The value evaluates to be approximately:
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11100 m/s
40200 km/h
25000 mi/h

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