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| Deletions are marked like this. | Additions are marked like this. |
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| = E < μ÷r = | = E < μ/r = |
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| Climbing out of a gravity well requires energy. | 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. |
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| Assume a spherical planet with mass $M$ and surface radius $r$. The '''standard gravitational parameter''' $$\mu$$ is the product of the gravitational constant $G$ and $M$ : $\mu = G M $ | Assume a spherical planet with mass $M$ and surface radius $R$. The '''standard gravitational parameter''' $\mu$ for the planet is the product of the gravitational constant $G$ and $M$ : $\mu ~=~ G M $. The gravity at the surface of the planet is $ g(R) ~=~ \mu / R^2 $, and the gravity at radius $r$ above the surface is $ g(r) ~=~ \mu / r^2 $. For an |
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 \mu for the planet is the product of the gravitational constant G and M : \mu ~=~ G M . The gravity at the surface of the planet is g(R) ~=~ \mu / R^2 , and the gravity at radius r above the surface is g(r) ~=~ \mu / r^2 .
For an