= Earth To Orbit =

A table of launch information.

|| Destination            || Launch V || 2000km || 2000km || 10 gee  || 10 gee || transit || Arrival || altitude || radius ||
||                        || V m/s    || gees   || time s || dist km || time s || hrs     || ∆V m/s  || km       || km     ||
|| LEO                    || 7451     || 1.41   || 537    || 283     || 76     || 0.74    || 65      || 300      || 6678   ||
|| m288                   || 8586     || 1.88   || 466    || 376     || 88     || 1.30    || 1009    || 6411     || 12789  ||
|| GEO                    || 9875     || 2.49   || 405    || 497     || 101    || 5.24    || 1490    || 35786    || 42164  ||
|| Moon                   || 10547    || 2.84   || 379    || 567     || 108    || 119.42  || 833     || 378022   || 384400 ||
|| Slingshot Moon to m288 || 10547    || 2.84   || 379    || 567     || 108    || 241.74  || -2184   || 6411     || 12789  ||
|| Slingshot Moon to GEO  || 10547    || 2.84   || 379    || 567     || 108    || 255.56  || -1053   || 35786    || 42164  ||

Note that the slingshot orbits show negative arrival ∆V.  With some kind of rotating or linear tether system at the arrival orbit, the positive ∆V from ground launch payloads and the negative ∆V from a slingshot payloads can be averaged.  This greatly reduces the size of the orbital insertion kick motors needed to inject payloads into these orbits.  By sending 30% of m288 payloads the long way around the moon, for example, the cost of delivering payloads to m288 could be halved. 

=== Rotating Tether orbits ===

Apogee can be circularized without big rocket motors by using rotating tethers.  Assume 3 gees centifugal force on the tether ends, 5 ton payloads (150kN), with some sort of magic that briefly reduces the attach shock. The tether rotates with end speeds of 0.5*∆V, and is that much slower than the circular orbit it injects into.  The mass is that needed for the tether, using Kevlar with a design support length of 60km-gee or a characteristic velocity of 770m/s, or a "space elevator strength" of 0.6 MegaYuri.  Taper is not needed for any of the destination orbits, and in fact some extra end mass may be added to increase stored angular momentum.
            
||<-3> Payload                        ||<-4> Tether Orbit                        ||<-3> Tether Properties    ||       ||
|| Destination || Circular || Delta V || Perigee  || Perigee || Apogee || Apogee || Length || Period || Mass || notes ||
||             ||  m/s     || m/s     || V m/s    || R km    || V m/s  || R km   || km     || sec    ||  kg  ||       ||
|| LEO         ||  7726    ||   65    ||  7825    ||   6566  ||  7693  ||   6678 ||  0.07  ||   3.4  ||   18 || orbit too crowded for tether ||
|| m288        ||  5583    || 1009    ||  7206    ||   9006  ||  5078  ||  12780 || 17.97  ||  52.8  || 4546 ||       ||
|| GEO         ||  3075    || 1490    ||  5788    ||  16966  ||  2330  ||  42146 || 37.00  ||  78.0  || 9361 || may need taper ||
|| Moon        ||  1018    ||  833    ||  2662    ||  90975  ||   603  || 384394 || 11.56  ||  43.6  || 2924 ||       ||

There will probably be a fairly large counterweight in the middle. Alternately, the tether will be much more massive than needed for  supporting one payload.   This means its orbit shifts less when capturing one payload.   The restoring velocity may come from returning payloads, or from loop-launched mass passing tangentially by the rotating tether in a fast orbit from above or below, possibly with lunar slingshot assist.  Mad handwaving here.

The initial tether will probably be injected from a slingshot orbit around the moon, and deployed vertically.  Additional launches directly from the loop on the ground will add mass and lower the perigee.  There may be some rocket thrust required initially to get the first tether set up, but after that, mass can be added with properly timed loop-launched payloads.  More mad handwaving!