Differences between revisions 1 and 17 (spanning 16 versions)
 ⇤ ← Revision 1 as of 2021-07-16 07:03:19 → Size: 10 Editor: KeithLofstrom Comment: ← Revision 17 as of 2021-07-16 08:09:26 → ⇥ Size: 1316 Editor: KeithLofstrom Comment: Deletions are marked like this. Additions are marked like this. Line 1: Line 1: =E<μ/r= #format jsmath= 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.|| $\large G$ || 6.67408e-11 || m³/kg/s² || Gravitational constant |||| $\large M$ || 5.972e24 || kg || Mass of Earth |||| $\large \mu = G M$ || 398600.4418 || km³/s² || Standard gravitational parameter of Earth |||| $\large R$ || 6378 || km || Equatorial radius of Earth |||| $day$ || 86400 || s || solar day (longer than sidereal day) |||| $\large\omega = 2\pi/day$ || 7.292158e-5 || radians/s || Earth sidereal rotation rate ||and surface radius $\large R$. The '''standard gravitational parameter''' $\large \mu$ for the planet is the product of the gravitational constant $\large G$ and $\large M$ : $\large \mu ~=~ G M$. The gravity at the surface of the planet is $\large g(R) ~=~ \mu / R^2$, and the gravity at radius $\large r$ above the surface is $\large g(r) ~=~ \mu / r^2$.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.

 \large G 6.67408e-11 m³/kg/s² Gravitational constant \large M 5.972e+24 kg Mass of Earth \large \mu = G M 398600 km³/s² Standard gravitational parameter of Earth \large R 6378 km Equatorial radius of Earth day 86400 s solar day (longer than sidereal day) \large\omega = 2\pi/day 7.29216e-05 radians/s Earth sidereal rotation rate

and surface radius \large R . The standard gravitational parameter \large \mu for the planet is the product of the gravitational constant \large G and \large 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 \large r above the surface is \large g(r) ~=~ \mu / r^2 .

For an

E<μ÷r (last edited 2021-07-17 07:19:46 by KeithLofstrom)