StarNAV: Autonomous Optical Navigation of a Spacecraft by the Relativistic Perturbation of Starlight

Abstract

Future space exploration missions require increased autonomy. This is especially true for navigation, where continued reliance on Earth-based resources is often a limiting factor in mission design and selection. In response to the need for autonomous navigation, this work introduces the StarNAV framework that may allow a spacecraft to autonomously navigate anywhere in the Solar System (or beyond) using only passive observations of naturally occurring starlight. Relativistic perturbations in the wavelength and direction of observed stars may be used to infer spacecraft velocity which, in turn, may be used for navigation. This work develops the mathematics governing such an approach and explores its efficacy for autonomous navigation. Measurement of stellar spectral shift due to the relativistic Doppler effect is found to be ineffective in practice. Instead, measurement of the change in inter-star angle due to stellar aberration appears to be the most promising technique for navigation by the relativistic perturbation of starlight.

Integrated celestial navigation for spacecraft using interferometer and Earth sensor

“…The gravitational deflection of the starlight is a consequence of the General Theory of Relativity. It is formulated as 21 where uIik is the line-of-sight (LOS) unit vector describing the direction to the i th star in the absence of the gravitating bodies, and uIik ' is the one in the presence of the gravitating bodies as seen by a stationary observer, δuIik is the gravitational deflection of the starlight. Supposing that the direction measurement accuracy is on the order of 1 mas, and the spacecraft is known to be in Earth orbit, only the gravitational deflection induced from Earth is taken into account, which is given by where μE is the gravitational constant of Earth, c is the speed of light, rk is the position vector of the spacecraft relative to the Earth center in the Earth-centered inertial (ECI) frame.…”

“…The stellar aberration is the change in the apparent direction of a star due to the motion of the spacecraft. According to the Special Theory of Relativity, the mathematical description of the stellar aberration is written as 21 where uIik ″ is the LOS unit vector of the i th star measured by the moving spacecraft, v obs, k is the velocity of the spacecraft relative to the SSB, which can be computed as where vk is the velocity of the spacecraft relative to the Earth center, vE,k is the velocity of Earth relative to the SSB. o(c-3) denotes high order terms.…”

“…The objective of this paper is to present a novel navigation scheme, such that the autonomy of spacecrafts is guaranteed, and the positioning accuracy is improved. Motivated by the encouraging results in literature, 18–21 this paper focuses on the navigation approach based on the measurement related to the stellar aberration, which is independent of ground systems and artificial beacons.…”

Star Identification and Attitude Determination With Projective Cameras

“…where α i is the right ascension and δ i is the declination. Effects such as stellar aberration, parallax, and proper motion [23], [24] are neglected for simplicity of the present discussion, though they may be added without any effect on the subsequent discussions. Note that the unit vector e i represents a direction (a line) passing through the origin and, therefore, is described by a point in P 2 .…”

Mars's Moons-Induced Time Dispersion Analysis for Solar TDOA Navigation

“…Because they are not limited by ground stations, the celestial autonomous navigation methods are particularly important in the approach phase of deep space exploration (Yan et al, 2016). Traditional celestial autonomous navigation methods include angle measurement (Konopliv et al, 2011;Yu et al, 2014;Wang et al, 2017), speed measurement (Long et al, 2000;Chen et al, 2019;Christian, 2019), and distance measurement (Sheikh et al, 2006;Liu et al, 2015a;Sun et al, 2016;Zhang et al, 2019). But these methods fail to provide the radial navigation information (such as distance and velocity) between the spacecraft and the target celestial body in the approach phase of deep space exploration.…”