Light Pressure on Rocket Propellant Rarified Gas Plumes

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I'm often told that orbiting propellant gas plumes will be scattered out of orbit by light pressure. This is most unlikely; the scattering cross section of an isolated molecule is small, and light pressure is weak.

The accurate way to estimate scattering is to look up all the scattering linewidths and cross sections for each gas species and calculate the photon energy absorption rate (that is, the power) and divide by the speed of light - light pressure.

However, there is an easy way - look up. The gas between me and space is mostly nitrogen and oxygen, while a RP1-LOX propellant plume will be CO₂, CO, and H₂O, a small percentage of the gas column; still, the important fact is that the atmosphere above me is mostly transparent, delivering perhaps 1000 W/m² of sunlight, and stopping or scattering perhaps 300 W/m² of sunlight. That gas column produces a pressure around of 100,000 Pascals, so it masses about 10,000 kg/m². Regardless of the number of atoms and their individual properties, as an ensemble they scatter about 30 mW per kilogram, and that is with collision band broadening.

Isolated atoms will absorb even less, though they might remain ionized longer.

Light pressure is the power divided by the speed of light, so the light pressure is 30 mW / 3e8 m/s per kg, or an acceleration of 1E-10 m/s² . For an orbiting particle, that subtracts from the sunward velocity and adds to the spaceward velocity; for a 3000 m/s 24 hour orbit, that adds a 7e-10 velocity fraction per day, and distorts the orbit by about 4e-8 of the radius, or about 2 meters. That is enough to detect with sensitive interferometry, but it is not nearly enough to scatter gas molecules out of Earth orbit.

Forget light pressure. I could be off by a factor of a million, and the light pressure would still be laughably inadequate to send plume molecules to reentry or escape.

Ionization?

Ultraviolet radiation is a tiny fraction of sunlight energy, but one photon is enough to split chemical bonds and create ions. Ions may have a large capture cross section, but that does NOT help; ions with only a few electron-volts of kinetic energy move slowly, and have a small cyclotron radius even in the very weak magnetic fields above 4 Re. The exhaust plume from an apogee insertion burn will be approximately westward, and roughly perpendicular to the pole-to-pole magnetic field. The electrons and ions might have a small amount of north-south velocity, but they will move around the (imaginary) field lines helically, and bounce off the denser field nearer the poles, like their MeV cousins in the van Allen belt. So, ionized atoms won't even have the good grace to fall in an elliptical orbit into the atmosphere. Ionization makes propellant plume pollution worse.

A Big Future, if We AREN'T Stupid

If we launch a LOT of space objects (like solar power satellites) and create a LOT of orbiting propellant plume, than the flux per square meter will increase proportionally to the mass of the launched objects. For 40 TW of SSPS with a mass of 5 kg/KW, that is 2e11 kg of SSPS, associated with perhaps 1e11 kg of exhaust plume for an apogee injection ISP of 300 seconds. If only 1% of the plume remains in orbit, that is 200,000 tonnes of gas, vastly more than the few hundred tonnes that may be in retrograde orbit from launching the 2e5 kg (WAG) of geostationary satellites in orbit now. Whatever the erosion rate is today, it might be a million times larger per square meter of satellite area for a large SSPS constellation.

Of course we haven't seen huge amounts of damage - yet. The total damage cost goes up as the square of the mass in orbit.

No Gram Left Behind propellant plume management will be essential for a >10 million-tonne-per-year space-faring civilization. We already have evidence that the solid fuel apogee kick motors used for comsats decades ago peppered the LDEF experiment in LEO, creating a few micrometer pits per square meter.

Orbiting propellant plumes are incompatible with big spacefaring dreams. Delta V and propellant velocity must be managed so that plumes reenter, or are ejected into interplanetary space, even if this requires variable ISP so the plume trajectories are sure to impact the atmosphere,

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Rayleigh Scattering

Rayleigh scattering amplitude is multiplied by a 1-cos²θ term; the light pressure thrust term in line with the sunlight is that amplitude squared, multiplied by 2π sinθ (the circumference in the unit sphere) and the cos0 vector component along the thrust axis. So, "the scattered thrust" is

substituting ~ ~ x = 1-cos²θ ~ and ~ dx = - cos0 sinθ d0 ~ ~ this simplifies to ~ \int^1_1 x² dx ~~ = 0 . The scattering is symmetrical along the axis, so this is not surprising.

So, the light pressure on the molecule, atom, or ion is proportional to the scattering cross section, not where the scattered light goes.

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Interstellar Photodissociation and Photoionization Rates . . . Roberge, Lepp, Dalgarno 1991 Astrophysical Journal . . . Roberge1991.pdf

Water In Space . . . Ewine F. van Dishoeck

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