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| $ \sqrt{ ( R_{GEO} ~-~ \sqrt{ 3 \over 4 } ~ R_E ~ ) )^2 ~ + ( { 1 \over 2 } R_E )^2 } ~ = ~ $ |
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:
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Earth + 80km to: |
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|
GEO |
Luna |
L1 |
|
perigee |
6458 |
6458 |
6458 |
km |
apogee |
42164 |
382662 |
326390 |
km |
Vperigee |
10.346 |
11.018 |
11.002 |
km/s |
Vapogee |
1.585 |
0.186 |
0.218 |
km/s |
ΔV launch |
9.881 |
10.553 |
10.537 |
km/s |
Varrive |
1.490 |
0.832 |
0.647 |
km/s |
ΔV landing |
1.490 |
2.521 |
0.647 |
km/s |
total ΔV |
11.371 |
13.074 |
11.184 |
km/s |
trip time |
5.24 |
118.62 |
93.84 |
hours |
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 delta V very cheaply.
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{ ( R_{GEO} ~-~ \sqrt{ 3 \over 4 } ~ R_E ~ ) )^2 ~ + ( { 1 \over 2 } R_E )^2 } ~ = ~