Lunar Base Power from L1 SSPS

L1SSPS

Baseline: Power a lunar base with a surface power plant

Delivering a power plant to Luna's surface requires a high speed launch into a Hohmann to Luna, plus extra velocity to match Luna's 1.022 km/s (average) orbit velocity, plus lunar escape velocity, 2.38 km/s .

Luna's semimajor axis is 384,400 km - let's use that for the "average" radius. Luna's equatorial radius is 1738 km, so a direct Hohmann to the nearside surface has an apogee of 384,400 - 1738 = 382,662 km .

Lunar L1 is 326,390 km from Earth's center.

We can calculate total delta V, launching from the launch loop:

The travel time to a direct Lunar landing is 5 days, while the travel time to L1 is one day less. That means slightly less cryo-propellant boiloff during the journey.

L1 requires the least total ΔV. "Landing" (= apogee insertion) is by far the lowest for L1, a quarter of the lunar landing delta V. While the launch ΔV to L1 is higher than launch to GEO, a launch loop produces launch velocity very cheaply. L1 "landing" ΔV may be slightly high - L1 is near the Hill sphere, where lunar and Earth gravity are about the same, so we can expect the energy arriving at L1 will be slightly lower.

L1 is metastable - continual delta V tweaks will be required to "orbit" that position. The optimum orbit will be a tradeoff between SSPS tracking and ΔV. Ultra-high-ISP electric thrust, plus light pressure, might minimize the propellant cost, but a continuous trickle of propellant must be supplied for long-term stability. The same is true for a fixed GEO-"stationary" satellite, which requires about 50m/s/year of station-keeping ΔV.

SSPS from L1 to the Moon

The transmit distance from a GEO SSPS to a rectenna on Earth 45° latitude and 45° longitude from the equatorial nadir is:

\sqrt{ \left( R_{GEO} ~-~ \sqrt{ 3 \over 4 } R_E ~ \right)^2 ~ + \left( { 1 \over 2 } R_E \right)^2 } ~ = ~ 36779 km

The distance from L1 SSPS to a rectenna on Luna (again, 45° latitude and 45° longitude from the equatorial nadir) is 56512 km. That is a factor of 2.36 more distance attenuation.

But all is NOT equal. GEO-to-Earth SSPS typically assumes 2.45 GHz ISM band microwaves ... wiping out WIFI and Bluetooth and trillions of dollars of other uses, but hey, it's space!

The L1 to Luna path is vacuum, and there are no pre-existing uses of the spectrum on Luna. The power beam points 180 degrees away from Earth. Besides some diffuse reflection off the Moon's surface, a high intensity beam (anywhere in the spectrum) is unlikely to cause interference to Earth or to satellites and spaceprobes. The beam may briefly shine in the same direction as the Webb Space Telescope and at Earth/Sun L2, or the ACE Solar Observation Probe at Earth/Sun L1, but we can avoid those wavelengths or interrupt the power beam when this is likely to happen.

From Earth-Luna L1, the angular size of the Earth is 2*atan( 6371 / 326390 ) = 2.24 degrees; perhaps twice a year, the Earth will block sunlight to the SSPS for three or four hours, a little longer than a lunar eclipse. The lunar base should have enough local energy storage ride out this eclipse, shutting down high-power-usage processes. A good time for maintenance.

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