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Consider we want to build a long term LEO station which serves as an intermediate stop for flights to the Moon and back (possibly with aerobrake). Refueling, docking, crew transfers etc. Several flights a year, for a couple of decades.

What would be the optimal orbital inclination for such a station? Given the Moon's inclination is non constant. And assuming we can select any place on Earth for a lunch site.

Optimal in mean launch costs. So that we could use smaller rockets, fewer launches and spend less fuel.

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  • $\begingroup$ What are you optimizing for? $\endgroup$ Sep 30 at 23:40
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    $\begingroup$ @OrganicMarble I'd say a mean lunch cost. Assuming we perform several flight per year. I have updated the question $\endgroup$
    – horsh
    Sep 30 at 23:58
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    $\begingroup$ If you're only going several times a year, you can schedule your departure so that the Moon is passing through the line of intersection between your station's orbital plane and its orbital plane at your arrival, and tuck the plane change into the margins of your Lunar capture burn. $\endgroup$
    – notovny
    Oct 1 at 4:07
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The latitude of your launch site would be the optimal inclination, as the relative inclination between the LEO orbit and Moon's orbit matters very little for delta-v cost.

A lunar transfer orbit is very long and skinny, so at lunar encounter, the spacecraft's velocity (< 200m/s) is much less than the Moon's velocity (> 1km/s), which means that its relative direction is not overly important. The capture cost of about 140 m/s thus only grows by 20 m/s even at a with a 45 degree inclination difference. This is far less than the losses one deals with for orbital launches.

All such LEO orbits give a fortnightly launch window for a lunar transfer, which should be often enough for your use case.

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Long term, and it must be in LEO?

There are many things to consider:

  • any LEO orbit's plane will drift, due to the shape of the Earth, so no orbit will stay aligned with the Moon's inclination.
  • You likely want a somewhat high-inclination orbit, so that your normal trajectory to the Moon arcs far north or south, thus avoiding the worst of the Van Allen belts.
  • You likely want a low launch site latitude, as a more equatorial site eases the job of reaching orbit by better using the Earth's rotation.
  • You want an inclination that is at least close to your launch site's latitude, to avoid planechange losses when launching from the surface.

Note that all of these things work against each other in some way!

If the final optimization is launch cost, then:
Figure out what angle of transfer will give you a sufficiently safe passage through/past the Van Allen belts. Now build your launch center on this same latitude.
This will give you a ground-to-waystation launch window once per day, or possibly a bit less if the LEO orbit is high enough to not present a suitably close ground track on each closest pass over the launch site.
And it will give you a (mostly) optimal waystation-to-Moon transfer window twice per Month.

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