1. RELATIVISTIC POSITIONING AND NAVIGATION
Angelo Tartaglia
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2. How could the Enterprise starship find her way in the universe?
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3. How to use a pulsar to find Starbucks
More practical…
How to use a pulsar to find Starbucks
Cosmic GPS would employ pulsing stars, not satellites, as celestial beacons
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4. Coordinates and positioning
Space-time is a 4-dimensional generally curved metric manifold
Gaussian coordinates may be used to localize events.
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5. Emission coordinates time Signals Light cone Clocks 2011 March 03
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6. Null or light coordinates
Cartesian grid
Light rays grid
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7. Null vectors and waves The wave vector:  is a null vector
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8. The null basis
time
space
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9. Positioning in space-time
event
light coordinates r
space
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10. Wave fronts
hyperplane
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11. time a b a b
space
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12. Uncertainty volume Tb Td
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13. Locally uniform motion
Proper time t
time Tb Ta
space
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14. Light coordinates of an event
integer
From simple linear equations
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16. Uncertainty depends on clock
As big as allowed by the linearity of the worldline
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17. Accelerated motion Four-velocity Four-acceleration
Maximum integration time
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18. A gravitational field The gravitational field shows up when:
Gravitational potential
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19. Pulsars as clocks
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20. Two options X-ray pulsars Radio-pulsars Our choice is radio-pulsars
~ 1800 “clocks”
“Fixed” positions in the sky
Very stable clocks
Periods ≥ 1 ms
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22. Parkes observatory (Australia)
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23. Four real pulsars
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24. Static observer
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25. Uncertainties
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26. Eppur si muove
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27. Extension to moving sources
The method can be extended to nearby moving sources as clocks on satellites or on celestial bodies of the Solar system, provided one has the time dependence of the direction cosines of the null basis vectors
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28. Conclusion
The problem of obtaining the local coordinates from the arrival times of pulses from remote sources has been solved
The method naturally includes all relativistic effects
The method can be applied both to pulsars and to clocks onboard satellites or celestial bodies
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29. ML. Ruggiero, E. Capolongo, A
ML. Ruggiero, E. Capolongo, A. Tartaglia, Pulsars as celestial beacons to detect the motion of the Earth, IJMPD, in stampa (2011).
A. Tartaglia, ML. Ruggiero, E. Capolongo A null frame for spacetime positioning by means of pulsating sources, Advances in Space Research, 47, , 2011.
A. Tartaglia , Emission Coordinates for the Navigation in Space, Acta Astronautica, 67, , 2010
D. Bini, A. Geralico, ML. Ruggiero, A. Tartaglia, Emission vs Fermi coordinates: applications to relativistic positioning systems, Classical and Quantum Gravity, 25, 1-11, 2008.
ML. Ruggiero, A. Tartaglia, Mapping Cartesian Coordinates into Emission Coordinates: some Toy Models, IJMPD, 17, , 2008.
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