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|But what is the mean free path? The hydrogen may collide with another H of OH or O or H₂O and lose some energy. MoreLater||But what is the mean free path? The hydrogen may collide with another H of OH or O or H₂O and lose some energy.
The deployment of 100MT of SBSP (25 TW) using LOX/LH rockets could result in as much as 40 MT of plume molecules in retrograde orbits.
Other "rockets" might use electrically superheated hydrogen, or ion engines (though there is not nearly enough xenon and krypton for that). Laser ablation thrusters are possible, but those make a dog's breakfast of hot, poorly collimated molecules and ions compared to "clean" hydrogen-based thrust.
Let's focus on LOX/LH chemical engines with an oxidizer:fuel mass ratio of 5:1, resulting in a 15:1 mass ratio of H₂O and H₂ plume molecules. For 40 MT of plume, that is 1.67e36 H₂0 molecules, and 1e36 H₂ molecules. They will be emitted over years, but many may persist.
5 O(16) + 8 H₂ -> 5 H₂O + 3 H₂ = 90 AMU of H₂O and 6 AMU of H₂
The collision cross section of H₂0 is 15.5e-20 m² and the collision cross section of H₂ is 5.75e-20 m², so the total collision cross section of the entire plume is 2.6e17 + 0.58e17 m² = 3.16e17m² = 3.16e11 km², equivalent to a spherical shell 160,000 km in diameter. The atoms are in elliptical orbits, with a starting apogee at GEO; they will frequently collide with each other and spread into a rotating cloud.
MoreLater, including guestimate of how the atoms will scatter downwards into the atmosphere, and outwards to escape, but mostly form into a swirling donut of retrograde gas molecules and atoms with approximately the same (WAG) angular momentum and a sizeable fraction of the mass of the original plume constellation.
Photodissociation, Photoionization of H₂ and H₂O
The minimum photodissociation energy of H₂O is 5.118 eV (242.2 nm, near UV), to OH and H . Excess energy can create highly excited states of both, but also send the reaction products at high velocities in opposite directions ... the H faster than escape velocity. The spectrum-averaged OH ejection velocity is 1.05 km/s and the H ejection velocity is 17.85 km/s, according to Crovisier(1989) as mentioned by Wu and Chen (numbers on p7416. Velocity Distributions of H Atoms and OH Radicals, JGR 98 E4 7415-7435 1993).
However, if the reaction products ionize (from the initial energy excess, or solar UV), they will be trapped in the Earth's magnetic field, with diamagnetic plasma effects weakening the field and reducing cosmic ray shielding.
According to H.U.Keller ( p670, The Intepretation of Ultraviolet Observations of Comets, Space Science Reviews 18 (1976) 641-684 ) the photodissociation energy of OH is 261 nm (4.75eV) with a kinetic energy of 0.4eV (8.5 km/s H), increasing to kinetic energy of 4eV at 150nm (14.7 km/s H). Lyman alpha is 121.6 nm, 10.2eV, so the H velocity is above 15 km/s.
But what is the mean free path? The hydrogen may collide with another H of OH or O or H₂O and lose some energy.