The space shuttle is launched with a velocity of 17 500 mi/h parallel to the tangent of the earth’s surface at point P and then travels around the elliptical orbit. When it reaches point A, its engines are turned on and its velocity is suddenly increased. Determine the required increase in velocity so that it enters the second elliptical orbit. Take G = 34.4(10^-9)ft⁴/lb · s⁴, M_e = 409(10²¹) slug, and r_e = 3960mi, where 5280 ft = mi.

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P 1500 mi P 4500 mi A