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Precise Time Synchronization Throughout the Solar System

Precise Time Synchronization Throughout the Solar System. Robert A. Nelson Satellite Engineering Research Corporation 7701 Woodmont Avenue, Ste. 208 Bethesda, MD 20814 301-657-9641 RobtNelson@aol.com www.satellitecorp.com. Introduction. Extend GPS model for navigation to the solar system

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Precise Time Synchronization Throughout the Solar System

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  1. Precise Time SynchronizationThroughout the Solar System Robert A. Nelson Satellite Engineering Research Corporation 7701 Woodmont Avenue, Ste. 208 Bethesda, MD 20814 301-657-9641 RobtNelson@aol.com www.satellitecorp.com

  2. Introduction • Extend GPS model for navigation to the solar system • Use communications links for time synchronization • Notional concepts • NASA committee exploring alternative architectures for communication, navigation, • and time • Paper to be presented at EFTF in UK April 5 - 7 2

  3. To triangulate, GPS measures distance using the travel time of a radio signal. To measure travel time, GPS needs very accurate clocks. In addition to knowing the distance to a satellite. a user needs to know the satellite’s location. As the GPS signal travels through the ionosphere and troposphere, it gets delayed. Triangulation from satellites is the basis of the system. GPS works by triangulationusing signals referenced to onboard atomic clocks 3 Satellite Engineering Research Corporation

  4. Proper time vs. coordinate time • Proper time • The reading of a clock in its own rest frame • Different for clocks in different states of motion and in different gravitational potentials • Coordinate time • The time coordinate in the given space-time coordinate system • A global coordinate • Has same value everywhere for a given event 4

  5. Relativistic effects • Three effects contribute to the net relativistic effect on a transported clock • Velocity (time dilation) • Makes transported clock run slow relative to a clock on the geoid • Function of speed only • Gravitational potential (red shift) • Makes transported clock run fast relative to a clock on the geoid • Function of altitude only • Sagnac effect (rotating frame of reference) • Makes transported clock run fast or slow relative to a clock on the geoid • Depends on direction and path traveled 5

  6. Global Positioning System Principal relativistic effects Time dilation: − 7.1 s per day Gravitational redshift: + 45.7 s per day Net secular effect: + 38.6 s per day Residual periodic effect: 46 ns maximum Sagnac effect: 133 ns maximum 6 planes, 4 satellites per plane Altitude: 20,184 km Velocity: 3.874 km/s GPS has served as a laboratory for relativity and has provided a model for theoretical algorithms 6

  7. 8 satellite polar constellation about the Moon 8 satellites, 2 orbital planes, 4 satellites per plane, 3 lunar radii 7

  8. Level of coverage 8

  9. Earth-Moon system Lagrange points Earth radius = 6378 km Moon radius = 1738 km Orbit radius = 384 405 km Lagrange pointDistance from EarthDistance from Moon Lunar orbit radius km Lunar orbit radius km L1 0.849 066 326 385 0.150 934 58 020 L2 1.167 833 448 921 0.167 833 64 516 L3 0.992 912 381 680 1.992 912 766 085 L4 1.000 000 384 405 1.000 000 384 405 L5 1.000 000 384 405 1.000 000 384 405 9

  10. Relay between Moon and Earth via L4 spacecraft 10

  11. Coverage of back side of Moon from L4 and L5 11

  12. Space navigation using proven GPS technology Lunar S/C (polar orbit) Communication satellites provide GPS-like signals Lunar pseudolites Lunar rover L5 S/C L4 S/C Earth Good GDOP provided by L4, L5, and polar satellites, augmented by lunar pseudolites. 12

  13. 12 satellite constellation about Mars 12 satellites, 3 orbital planes, 4 satellites per plane, 2.5 Mars radii 13

  14. Level of coverage 14

  15. Mars-stationary orbit Mars mass / Earth mass = k = 0.1071 Mars period of rotation = 24 h 37 m 23 s = 88,643 s Mars radius = 3330 km According to Kepler’s third law, the radius of a Mars-stationary orbit is By comparison, for a geostationary orbit r = 42 164 km, r / R = 6.618, and h = 35 786 km. 15

  16. Relativistic corrections to a clock on Mars • Atomic clock (e.g., rubidium) on Mars • Potential applications of Earth-Mars synchronization • VLBI • Interplanetary radionavigation references • Refined tests of general relativity • Transformation between Terrestrial Time (TT) • and Barycentric Coordinate Time (TCB) Orbital semimajor axis 1.524 AU = 2.280  108 km Maximum light time 21.0 min Minimum light time 4.4 min • Transformation between Mars Time (MT) and • Barycentric Coordinate Time (TCB) • Gravitational propagation time delay 16

  17. Conclusion • Communication link provide clock synchronization • The GPS provides a proven technology for time synchronization and navigation that may be extended to space applications • Relativity has become an important practical engineering consideration for modern precise timekeeping systems. • These relativistic effects are well understood and have been applied successfully in the GPS. • Similar corrections need to be applied in precise timekeeping systems for clocks distributed throughout the solar system. 17

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