Relativistic Localization for Solar System Navigation

As we prepare to set foot on the Moon and subsequently turn our attention to Mars and the outer solar system, it becomes necessary to consider the entire mission environment as one unified system. One reason for this is a challenge that all space missions face: relativity. Not only will communications between a deep space vehicle and mission control be delayed, but the actual position of the Earth (and other objects) from the vehicle's point of view will begin to differ from the non-relativistic case. As it flies further and further away, this relativistic aberration will affect on-board devices that depend on precise spatial targeting, induce a drift in on-board clocks (causing them to run slower than Earth-based clocks), and even shift the apparent positions of the stars. For simulations, a particular concern is the time history of a simulated object. Under relativity, time slows down in the presence of mass (or gravity), but it also slows down for moving observers, resulting in discrepancies between observed positions, velocities, accelerations, and clocks of objects relative to each other. Overall, this implies the need for a simulation that accurately tracks these relativistic states. Presently, a relativistic simulation can be constructed for one observer using a combination of open-source tools. However, in this paper, we present an approach to simulating any number of simultaneous observers in a relativistic solar-system-scale space environment using the Space Teams simulation platform. We begin by delineating the method of simulating this type of relativistic universe, wherein each observer sees the correct positions, orientations, and relativistic aberrations of all other objects and observers, while a global, non-relativistic frame captures the overall dynamics of the system. We then discuss the use of this environment in simulating a solar-system-scale localization system, based on the Global Positioning System (GPS). We show that by tracking time histories of the spatial and temporal states of each object in the simulation, we can display an accurate view of the system from any reference point, while simultaneously applying environmental effects (such as gravitational forces) to all objects in a manner consistent with a relativistic universe.