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| Launch loops can launch vehicles as fast as escape velocity for "kinetic energy cost", without the expense of large rocket engines and fuel and fuel tanks. Escape velocity at 80 km altitude (6378 km equatorial radius) is | Launch loops can launch vehicles as fast as escape velocity for "kinetic energy cost", without the expense of large rocket engines and fuel and fuel tanks. Escape velocity at 80 km altitude ( $ r_{launch} =$ 458 km equatorial radius) is $ v_{escape} = \sqrt{ 2 * \mu_0 / r_{launch} } $ = 11.11 km/s, where $ \mu_0 $ is the Earth's standard gravitational parameter, 398600.4418 km^3^/s^2^. The Earth rotates at 0.47 km/s at launch loop altitudes, so the surface-relative escape velocity is 10.64 km/s . The kinetic energy cost is proportional mass and velocity squared, $ { 1 over 2 } m ~ v^2 , or 56.6 megajoules per kilogram. A kilowatt-hour (KWh) is 3.6 megajoules, and costs $0.125/kWh on my 2020 Oregon residential power bill, so the launch energy is 15.7 KWh/kg, and costs $1.97 at Oregon residential rates (rumor has it that Oregon's giant data centers - Google, Apple, Facebook - pay $0.08/kWh industrial rates). |
HEEO, High Eccentricity Earth Orbit
Launch loops can launch vehicles as fast as escape velocity for "kinetic energy cost", without the expense of large rocket engines and fuel and fuel tanks. Escape velocity at 80 km altitude ( r_{launch} = 458 km equatorial radius) is v_{escape} = \sqrt{ 2 * \mu_0 / r_{launch} } = 11.11 km/s, where \mu_0 is the Earth's standard gravitational parameter, 398600.4418 km3/s2. The Earth rotates at 0.47 km/s at launch loop altitudes, so the surface-relative escape velocity is 10.64 km/s . The kinetic energy cost is proportional mass and velocity squared, { 1 over 2 } m ~ v^2 , or 56.6 megajoules per kilogram. A kilowatt-hour (KWh) is 3.6 megajoules, and costs 0.125/kWh on my 2020 Oregon residential power bill, so the launch energy is 15.7 KWh/kg, and costs 1.97 at Oregon residential rates (rumor has it that Oregon's giant data centers - Google, Apple, Facebook - pay 0.08/kWh industrial rates).