The orbital mechanics of space elevator launch systems

The construction of a space elevator would be an inspiring feat of planetary engineering of immense cost and risk. But would the benefit outweigh the costs and risks? What, precisely, is the purpose for building such a structure? For example, what if the space elevator could provide propellant-free (free release) orbital transfer to every planet in the solar system and beyond on a daily basis? In our view, this benefit might outweigh the costs and risks. But can a space elevator provide such a service? In this manuscript, we examine 3 tiers of space elevator launch system design and provide a detailed mathematical analysis of the orbital mechanics of spacecraft utilizing such designs. We find the limiting factor in all designs is the problem of transition to the ecliptic plane. For Tiers 1 and 2, we find that free release transfers to all the outer planets is possible, achieving velocities far beyond the ability of current Earth-based rocket technology, but with significant gaps in coverage due to planetary alignment. For Tier 3 elevators, however, we find that fast free release transfers to all planets in the solar system are possible on a daily basis. Finally, we show that Tier 2 and 3 space elevators can potentially use counterweights to perform staged slingshot maneuvers, providing a velocity multiplier which could dramatically reduce transit times to outer planets and interstellar destinations.