E < μ/r
Climbing out of the Earth's gravity well requires energy, but a launch loop on the rotating Earth can launch to infinity with less than the classical μ/r gravitational escape energy. The difference is taken from the rotational energy of the Earth itself.
Assume a spherical planet with mass M and surface radius R. The standard gravitational parameter μ for the planet is the product of the gravitational constant G and M : \large \mu ~=~ G M . The gravity at the surface of the planet is \large g(R) ~=~ \mu / R^2 , and the gravity at radius r above the surface is \large g(r) ~=~ \mu / r^2 .
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