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escape velocity = √(2GM)/R

So say for instance I plug this in to the escape velocity of the earth

I am going to say the radius is 4001 miles so I it would take a mile above the earth to escape (4001 * 1600) = 6401600 meters

escape velocity = √((2)(6.674*10^-11)(6.0*10^24)/(6401600)

= 11185.08934 m/s

This obviously isn't the speed you need to escape the earths gravity a mile off of its surface because we have left earth already with much lower speeds. This is so fast we would get a little time dilation, can someone tell me what I am doing wrong?

Thanks in advanced.