Autonomous Navigation of Relativistic Spacecraft in Interstellar Space
Abstract
This paper introduces a general autonomous navigation method for any spacecraft for which relativistic effects are significant. It builds on a relativistic observation model and represents the foundational step in the development of interstellar navigation. By comparing astrometric and spectrometric measurements obtained in two different reference frames, the method estimates instantaneous spacecraft position and velocity, and distances to observed stars. The paper first derives relativistic autonomous observation equations, which are more general than those provided in the existing literature. It then presents an autonomous navigation algorithm that compares favorably to a nonrelativistic approach. A case study investigates the method in the context of technological details of a mission, including certain sources of noise and disturbance in the interstellar medium. Specifically, a state-of-the-art spacecraft traveling to Proxima Centauri at can estimate its position and velocity with less than 0.001% error, and distances to stars it observes with less than 1% error. Measurement noise is the dominant source of this error; thus, the algorithm is highly sensitive to sensor performance. A simple running average reduces these errors by more than an order of magnitude, which suggests that this algorithm is suitable as a first step in a realistic, recursive navigation algorithm.
References
[1] “Voyager,” Jet Propulsion Lab., https://voyager.jpl.nasa.gov/ [retrieved 8 Sept. 2019].
[2] , “A Terrestrial Planet Candidate in a Temperate Orbit around Proxima Centauri,” Nature, Vol. 536, No. 7617, 2016, pp. 437–440. https://doi.org/10.1038/nature19106
[3] “Parker Solar Probe Becomes Fastest-Ever Spacecraft,” Parker Solar Probe, Johns Hopkins University Applied Physics Lab., http://parkersolarprobe.jhuapl.edu/News-Center/Show-Article.php?articleID=109 [retrieved 8 Sept. 2019].
[4] “Breakthrough Initiatives—Challenges,” Breakthrough Initiatives, https://breakthroughinitiatives.org/challenges/3 [retrieved 8 Sept. 2019].
[5] “Breakthrough Starshot,” Breakthrough Initiatives, https://breakthroughinitiatives.org/initiative/3 [retrieved 13 Aug. 2019].
[6] , “Directed Energy for Relativistic Propulsion and Interstellar Communications,” Journal of the British Interplanetary Society, Vol. 68, Nos. 5/6, 2015, pp. 172–182.
[7] , “Relativistic Propulsion Using Directed Energy,” Nanophotonics and Macrophotonics for Space Environments VII, No. 8876, International Soc. for Optics and Photonics (SPIE), 2013, Paper 887605.
[8] , “KickSat: A Crowd-Funded Mission to Demonstrate the World’s Smallest Spacecraft,” Proceedings of the AIAA/USU Conference on Small Satellites, Paper SSC13-IX–5, 2013, pp. 1–9, https://digitalcommons.usu.edu/smallsat/2013/all2013/111.
[9] , “A Probabilistic Network Formulation for Satellite Swarm Communications,” Presented at the 2018 AIAA Information Systems, AIAA Infotech @ Aerospace, AIAA SciTech Forum, AIAA Paper 2018-1802, 2018. https://doi.org/10.2514/6.2018-1802
[10] , “R-Selected Spacecraft,” engrXiv Preprints, 2019, pp. 1–23. https://doi.org/10.31224/osf.io/wxhpt
[11] , “A Roadmap to Interstellar Flight,” 2016, https://www.nasa.gov/sites/default/files/atoms/files/roadmap_to_interstellar_flight_tagged.pdf.
[12] , “State of the Art of Small Spacecraft Technology,” NASA TP-2018-220027, 2018.
[13] , Radiometric Tracking Techniques for Deep Space Navigation, Wiley, Hoboken, NJ, 2003, Chaps. 2–4.
[14] , “Onboard Image-Processing Algorithm for a Spacecraft Optical Navigation Sensor System,” Journal of Spacecraft and Rockets, Vol. 49, No. 2, 2012, pp. 337–352. https://doi.org/10.2514/1.A32065
[15] , “Initial Orbit Determination Using Doppler Shift of Fraunhofer Lines,” Celestial Mechanics and Dynamical Astronomy, Vol. 130, No. 80, 2018, pp. 1–26. https://doi.org/10.1007/s10569-018-9878-9
[16] , “Spacecraft Navigation Using X-Ray Pulsars,” Journal of Guidance, Control, and Dynamics, Vol. 29, No. 1, 2006, pp. 49–63. https://doi.org/10.2514/1.13331
[17] , “SEXTANT X-Ray Pulsar Navigation Demonstration: Flight System and Test Results,” Presented at the 2016 IEEE Aerospace Conference, IEEE, New York, 2016, pp. 1–11. https://doi.org/10.1109/AERO.2016.7500838
[18] , “Geometry of GPS Dilution of Precision: Revisited,” GPS Solutions, Vol. 21, No. 4, 2017, pp. 1747–1763.
[19] , “The Formation and Extent of the Solar System Comet Cloud,” Astronomical Journal, Vol. 94, No. 5, 1987, p. 1330. https://doi.org/10.1086/114571
[20] , “Zur Elektrodynamik Bewegter Körper,” Annalen der Physik, Vol. 322, No. 10, 1905, pp. 891–921. https://doi.org/10.1002/andp.19053221004
[21] , Physics of the Interstellar and Intergalactic Medium, Princeton Univ. Press, Princeton, NJ, 2011, Chaps. 12–14, 23–26.
[22] , “Relativistic Astronomy,” Astrophysical Journal, Vol. 854, No. 2, 2018, p. 123. https://doi.org/10.3847/1538-4357/aaa9b7
[23] , “Relativistic Astronomy. II. In-Flight Solution of Motion and Test of Special Relativity Light Aberration,” Astrophysical Journal, Vol. 877, No. 1, 2019, p. 14. https://doi.org/10.3847/1538-4357/ab1650
[24] , “StarNAV: Autonomous Optical Navigation of a Spacecraft by the Relativistic Perturbation of Starlight,” Sensors, Vol. 19, No. 19, 2019, p. 4064. https://doi.org/10.3390/s19194064
[25] , “The View from the Starship Bridge and Other Observations,” IEEE Spectrum, Vol. 1, No. 1, 1964, pp. 86–92. https://doi.org/10.1109/MSPEC.1964.5531934
[26] , “A Static Estimation Method for Autonomous Navigation of Relativistic Spacecraft,” Presented at the 2019 IEEE Aerospace Conference, IEEE, New York, 2019, pp. 1–10. https://doi.org/10.1109/AERO.2019.8741804
[27] , Modern Astrometry, Springer, Berlin, 2002, p. 338.
[28] “Star Sensor ASTRO 15 Datasheet—Attitude and Orbit Control Systems,” Jena Optronik, https://jena-optronik.de/en/aocs/astro15.html [retrieved 8 Sept. 2019].
[29] “Compact Reconnaissance Imaging Spectrometer for Mars (CRISM),” Johns Hopkins Univ. Applied Physics Lab., http://crism.jhuapl.edu/instrument/design/overview.php [retrieved 8 Sept. 2019].
[30] , “Die Grundlage Der Allgemeinen Relativitätstheorie,” Annalen der Physik, Vol. 354, No. 7, 1916, pp. 769–822. https://doi.org/10.1002/andp.19163540702
[31] , Spacetime and Geometry, An Introduction to General Relativity, Addison-Wesley, San Fransisco, CA, 2004, Chaps. 1, 2.
[32] , “Is the Speed of Light Independent of the Velocity of the Source,” Physical Review Letters, Vol. 39, Oct. 1977, pp. 1051–1054. https://doi.org/10.1103/PhysRevLett.39.1051
[33] “International Celestial Reference System (ICRS),” U.S. Naval Observatory, https://www.usno.navy.mil/USNO/astronomical-applications/data-services/icrs-links [retrieved 15 Aug. 2020].
[34] , “How I Created the Theory of Relativity,” Physics Today, Aug. 1982.
[35] , Generalized Inverses: Theory and Applications, Springer-Verlag, New York, 2003, Chap. 2.
[36] “List of Star-Catalog Catalogs,” NASA Goddard Space Flight Center, High Energy Astrophysics Science Archive Research Center (HEASARC), https://heasarc.gsfc.nasa.gov/docs/cgro/db-perl/W3Browse/w3table.pl?MissionHelp=star_catalog [retrieved 23 Sept. 2019].
[37] “Gaia Data Release 2. Summary of the Contents and Survey Properties,” European Space Agency Gaia Collaboration, Astronomy and Astrophysics, Vol. 616, 2018, p. A1. https://doi.org/10.1051/0004-6361/201833051
[38] “2019 Nautical Almanac,” TheNauticalAlmanac.com, https://www.thenauticalalmanac.com/ [retrieved 23 Sept. 2019].
[39] “Gaia Data Release 2 Documentation Release 1.2,” European Space Agency (ESA), and Gaia Data Processing and Analysis Consortium (DPAC), https://gea.esac.esa.int/archive/documentation/GDR2/ [retrieved 23 Sept. 2019].
[40] “European Southern Observatory (ESO)—The Very Large Telescope Interferometer (VLTI),” European Southern Observatory, http://www.eso.org/sci/facilities/paranal/telescopes/vlti.html [retrieved 21 Nov. 2019].
[41] , CRC Handbook of Chemistry and Physics, 101st ed., Internet Version 2020, CRC Press/Taylor & Francis, Boca Raton, FL, Chapter: Ionization Energies of Atoms and Atomic Ions.
