Raymond Wright, Ball Aerospace; Luke Tafur, Ball Aerospace; Naomi Owens Fahrner, Ball Aerospace; Joshua Wysack, Ball Aerospace
Keywords: Space Domain Awareness, Space Situational Awareness, SDA, SSA, Imaging, Orbits, Manifolds
Abstract:
The cislunar region is becoming an active region of interest for the government, scientific research, and commercial use. With more entities entering the cislunar regime, Space Situational Awareness (SSA) of these highways enables Space Domain Awareness (SDA) to monitor incoming and outgoing threats, and Space Traffic Management (STM) to define safe access to and return from cislunar space. From the physics of the three-body problem, there exists natural bottlenecks which can be exploited by SDA missions, reducing search volume sizes.
In the circular restricted three-body problem (CR3BP), the Zero Velocity Surfaces (ZVS) represents a surface where a third body, the satellite, cannot cross. When the satellite reaches this surface, the satellite’s velocity in the direction of the surface becomes zero and the satellite “bounces” off the surface. The other unique feature of the ZVS is the Lagrange Points. Lagrange points are typically defined as points in space between two massive bodies where the gravitational attraction is equal and opposite on the third body. However, within the Zero Velocity surfaces, Lagrange Points 1, 2, and 3 (L1, L2, L3) can act as gateways between the two massive bodies. L1 is the gateway from Primary Body 1 (Earth) to Primary Body 2 (Moon), L2 is the gateway to “escape” the system into space from the Primary Body 2 (Moon) side, and L3 is the gateway to “escape” the system into space from the Primary Body 1 (Earth) side. These gateways also allow entry in the system. All CR3BP planetary systems have this relationship. This paper will focus on the Earth-Moon system relationship, but this can also be applied to systems such as Sun-Earth, Sun-Jupiter, and Pluto-Charon as well.
Gaining access to the cislunar regime requires opening the energy field that is defined by the Jacobi Integral. The Jacobi Integral relates a satellite’s position and velocity vectors to two extremely large masses. When the extremely large masses are defined in a coordinate system where they are stationary, this integral remains constant and is called the Jacobi Constant. If a satellite does not have enough energy leaving Earth, then the L1 gateway to the Moon will not be accessible.
In the 1890s, Henri Poincaré studied “paths” that connected the Lagrange points together1. This was further refined by Conley and McGehee in 19682. They were able to show there exist stable and unstable manifolds that create “superhighways” that connect the Lagrange Points. They also showed that once a satellite enters a manifold, it will use little to no energy to maintain its course on the manifold until its destination2. Entering and exiting a manifold requires sufficient fuel to provide the necessary change in velocity to:
Open the desired Lagrange Point
Enter the manifold with sufficient velocity
Exit the manifold into an orbit with sufficient velocity
Space missions are concerned about cost, with cost-driven factors such as mass, volume, power, and consumables. A major consumable is fuel needed for launch, orbit insertion, and attitude control. The driving factor of fuel costs are changes in velocity. The manifolds provide a low-cost delta-V solution on reaching cislunar space.
These manifolds can be exploited by adversaries as they provide a fuel-efficient way of reaching the cislunar regime. This paper will focus on categorizing the manifold space that adversaries could use by using typical delta-V’s for entering or returning from cislunar space. Entering cislunar space will be defined as either launching from Earth or exiting an Earth Orbit. Returning from cislunar space will be defined as returning from the Earth-Moon Lagrange Points or from a Lunar orbit. The manifold space will help define a surveillance volume to be used for STM to capture much of the traffic in the Earth-Moon transit corridor
Having these manifolds defined provides insight into the minimum volume to search/tripwire for cislunar access. This potentially reduces the size of the Cislunar volume search problem significantly. Work from Fahrner3 will be used to construct optimized Cislunar architectures for these reduced Cislunar volumes of interest. These architectures will be compared with optimized architectures for the entire Cislunar volume and the cost between these will be analyzed.
Date of Conference: September 19-22, 2023
Track: Cislunar SDA