# Energy Transition Domain and Its Application in Constructing Gravity-Assist Escape Trajectories

## TL;DR

This paper introduces the energy transition domain (ETD) concept based on mechanical energy in the Earth-Moon PCR3BP, and proposes a method for constructing gravity-assist escape trajectories using ETD analysis.

## Contribution

It defines the ETD using mechanical energy in the PCR3BP and develops a new approach for constructing gravity-assist escape trajectories based on this concept.

## Key findings

- ETD depends on Jacobi energy, aiding trajectory selection.
- Constructed escape trajectories from low Earth orbit and geosynchronous orbit.
- Analyzed the properties of the obtained trajectories.

## Abstract

This Note proposes the concept and theory of energy transition domain (ETD) defined by the mechanical energy of spacecraft in the Earth-Moon planar circular restricted three-body problem (PCR3BP) inspired by the pioneering work from Ano{\`e} et al. (2024) on the ETD defined by the two-body energy with respect to the secordary body in the PCR3BP. An effective construction method of gravity-assist escape trajectories is then proposed. Firstly, the concept of the ETD defined by the mechanical energy is presented, and its dependency on the Jacobi energy is analyzed. This dependency may provide prior knowledge about selecting the range of the Jacobi energy in the construction of escape trajectories. Then, gravity-assist escape trajectories departing from the 167 km low Earth orbit and 36000 km geosynchronous Earth orbit are constructed based on the ETD. The initial states are selected in the sphere of influence of the Moon, and the trajectories are searched from the forward and backward integration. Finally, the obtained solutions are presented and analyzed.