Optimal gateway trajectory design for Earth-to-Mars missions

Abstract

Half a decade after the original Space Age, we are at the dawn of another exciting period in spaceflight, already dubbed ’The New Space Age’. Fuelled by commercial interest and rapid technological improvements, the coming two decades are expected to have humans return to the Lunar surface and possibly set foot on Mars for the very first time. The gateway concept is likely to play a significant role in these missions. A gateway is a man-made structure in space that functions as an intermediate station in an interplanetary transfer. NASA’s Artemis program relies on a gateway in an Halo orbit around the Earth-Moon L2 Lagrange point to facilitate sustainable Moon missions. This thesis will contain an extensive feasibility study into the application of the gateway concept to Earth-to-Mars travel. At the end of this work, an optimal trajectory design for a gateway concept that supports efficient and practical (crew) transportation from Earth to Mars will be presented.

The research will regard three distinct gateway trajectory design aspects: The gateway location, the gateway orbit and the transfers supported by the gateway. These three aspects can be combined to form a large number of different gateway trajectory designs. A total of three analyses were performed. In these analyses, the performance of the different gateway designs was researched. The goal of the first two analyses, Analysis A and Analysis B, was to investigate a specific set of design aspects, evaluate and compare the designs’ performance and select a subset of design options to further investigate in the next analysis. As a result, Analysis C was able to perform a detailed study into a small number of designs and select a single optimal design.

Two types of gateway locations were identified: gateways orbiting a central celestial body and gateways in the vicinity of a Lagrange point. Analysis A focused on the Lagrange-point gateways only, so that the stationary-gateway assumption could be made. It was concluded that the equilateral Lagrange points are not suitable gateway locations. Additionally, it was determined that the remaining two analyses should focus on impulsive thrust transfers rather than their continuous thrust equivalent.
As a result, Analysis B could focus on a set of specific transfer trajectories and a selection of only seven gateway locations (both central-body and Lagrange-point locations). By modelling the gateway orbits and optimizing for Delta V requirements, it was found that the gateway orbit has a significant effect on the performance of the gateway concept. Both Halo orbits and vertical-Lyapunov orbits proved suitable gateway orbits for gateways stationed at the Lagrange points. Although central-body gateways significantly underperformed Lagrange-point gateways, a gateway orbiting the Moon at a high altitude was selected together with four Lagrange-point gateway designs.
Analysis C evaluated the consistency of the remaining five designs and investigated the TOF characteristics of the transfers supported by these gateways. By splitting a synodic year into ten separate launch windows and optimizing transfer trajectories for each, it was found that the Lagrange-point gateway designs allowed for more frequent travel from Earth to Mars than the gateway in Lunar orbit. Subsequently, it was found that a gateway at the Earth-Moon L1 location supports a better trade-off between TOF and Delta V compared to one at the Sun-Earth L2 point.

Through these three analysis, it was found that a gateway placed in a large Halo orbit at the Earth-Moon L1 point is the optimal gateway trajectory design for future Earth-to-Mars gateway missions. This design is capable of supporting multiple suitable transfer trajectories, of which the EdG1 x G1mEM is most efficient. The minimum Delta V transfer solution between Earth and Mars orbit in the synodic period starting January 1st 2033 is 5.99 km/s, but this would require a long TOF of 386 days. A TOF of 300 days is possible for a Delta V of 6.41 km/s, 250 days for a ¢V of 6.82 km/s and 200 days for a Delta V of 7.26 km/s. This gateway trajectory design scored good on consistency; allowing a transfer below a Delta V of 7km/s in five of the ten launch windows in which the synodic period was split.

A mission using this optimal gateway design was compared to a direct transfer between Earth and Mars (EM) and a flyby mission (EmEM), both traditional missions without gateway concepts. It was found that the inclusion of an intermediate gateway in the mission design both adds to the Delta V requirements and to the flight duration. The difference is a little over 1 km/s in Delta V for TOFs under 200 days and less than 0.2 km/s for a TOF of roughly a year. Mission planners will have to decide whether these differences are justified by the gateway concept’s benefits, such as its function as a logistics hub in space and its ability to
facilitate transfers between spacecraft.