= Delta V to Circular orbits from the Launch Loop and the Space Elevator =

For destination orbits below GEO, the space elevator releases transfer vehicles from some altitude above the target orbit into an ellipse with apogee at the tether and perigee at the destination orbit.  Thrust is applied to slow the orbit at the destination perigee until the orbit is circular.  To reach low orbits, much delta V is required.

The launch loop throws transfer vehicles into elliptical transfer orbits with an apogee at the destination circular orbit.  Forwards delta V must be added at apogee for circularization.  Note that with transfer orbit perigee in the upper atmosphere, at least some of this delta V must be applied at the '''first''' apogee or the vehicle will re-enter.  This is a feature - if the thrust engine fails, this returns the transfer vehicle to Earth for another try.

Assuming a single impulse delta V, the launch loop is a lower delta V method to reach orbits below 13682 kilometers radius.

||<-2> destination  || Space || Launch || Space ||
||<-2> circular orbit || Elevator || Loop || Elevator ||
||  radius || velocity ||<-2> delta V      || Release ||
||      km ||  km/s ||  km/s  ||   km/s ||  km   ||
||    6378 || 7.905 || -2.241 || -0.031 || 29790 || Earth equator ||
||    6780 || 7.668 || -2.131 ||  0.088 || 30184 || ISS ||
||    8000 || 7.059 || -1.849 ||  0.381 || 31261 ||
||   10000 || 6.313 || -1.501 ||  0.715 || 32736 ||
||   12789 || 5.583 || -1.158 ||  1.005 || 34383 || Server Sky M288, 5 orbits per day    ||
||   13000 || 5.537 || -1.136 ||  1.021 || 34493 || radii where launch loop is less delta V    ||
||   13682 || 5.398 || -1.071 ||  1.071 || 34836 || radius where SE and LL delta V match ||
||   14000 || 5.336 || -1.041 ||  1.092 || 34991 || radii where space elevator is less delta V ||
||   20000 || 4.464 || -0.632 ||  1.341 || 37385 ||
||   26550 || 3.875 || -0.358 ||  1.448 || 39255 || GPS ||
||   30000 || 3.645 || -0.253 ||  1.473 || 40044 ||
||   40000 || 3.157 || -0.035 ||  1.490 || 41845 ||
||   42164 || 3.075 ||  0.000 ||  1.488 || 42164 || GEO ||
||   50000 || 2.823 ||  0.105 ||  1.471 || 43170 ||
||  100000 || 1.996 ||  0.403 ||  1.300 || 46748 ||
||  200000 || 1.412 ||  0.523 ||  1.058 || 49358 ||
||  300000 || 1.153 ||  0.534 ||  0.916 || 50442 ||
||  384399 || 1.018 ||  0.526 ||  0.833 || 50964 || Moon ||
||  400000 || 0.998 ||  0.523 ||  0.820 || 51039 ||
|| 1491553 || 0.517 ||  0.382 ||  0.469 || 52514 || Earth-Sun L1:  maximum stable Earth orbit ||

[[attachment:LOOPvsSEdV.ods | LibreOffice spreadsheet ]]