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$ \sqrt{ ( R_{GEO} ~-~ \sqrt{ 3 \over 4 } R_E ) )^2 ~ + ( { 1 \over 2 } R_E )^2 } } ~ = ~ $ $ \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:

Earth + 80km to:

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 } ~ = ~

MoreLater

L1SSPS (last edited 2021-04-08 01:43:46 by KeithLofstrom)