Analogy to bi-elliptic transfers incorporating high- and low-thrust

This note introduces an orbit transfer enabled through the use of high and low thrust propulsion technologies. To date, research in the area of high and low-thrust hybrid propulsion transfers has focused on the use of such systems for sequential orbit raising maneuvers, where the high-thrust system delivers the spacecraft to an intermediate orbit between the initial and final orbit [1–3] and the low-thrust system then completes the orbit raising manoeuver. The orbit transfer introduced here, named a Hohmann-Spiral Transfer (HST), is fundamentally different to this and analogous to the high-thrust bi-elliptic transfer [4]. The HST initially uses two high-thrust impulses, firstly to reach an apoapsis beyond the target via an elliptical orbit and then secondly to circularize at this apoapsis radius. Hence, rather than following an elliptical trajectory towards the target circular orbit from the apoapsis, as in a bi-elliptic transfer, the low-thrust propulsion system propels the spacecraft along a spiral trajectory to the final orbit.
A generalized form of the critical specific impulse ratio that takes into consideration both the high and low specific impulse systems to determine the point at which an HST consumes the same amount of fuel as either a Hohmann or bi-elliptic transfer is derived. Additionally, the scenario where the transfer starts in an elliptical orbit, with apoapsis at an altitude coinciding with the target circular orbit is considered, such a scenario is equivalent to a Geostationary Transfer Orbit; the circular and elliptical initial condition cases are shown in Fig. 1. The generalized form is subsequently applied to these different scenarios. The following assumptions are applied throughout this analysis; orbits are co-planar, finite burn losses are ignored and only the gravitational force of the Earth is considered.