Sidereal Orbits
Launch loop vehicle mass is limited; however, with high precision launch it is relatively easy to rendezvous vehicles to connect into larger assemblies; for example, launching rocket/heatshield packages with later cargo packages to complete a vehicle for apogee plane change and subsequent aerobraking-assisted orbit changes.
The launch loop will rotate under the perigee of a previous launch once per sidereal day, every 86164.089 seconds, about 4 minutes shorter than a solar day.
The actual rendezvous time will be modified by the nonlinear gravity field of the Earth due to the equatorial bulge, and the gravity of the Sun, Moon, and Jupiter. These perturbations are not included here, but for a real system they can be predicted and computed to millimeter accuracy. There will also be less-predictable perturbations due to residual atmosphereic gas drag (a function of solar UV activity), spacecraft outgassing, light pressure, and other small effects.