1. Satellite Engineering Research Corporation 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

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

3. Satellite Engineering Research Corporation 3 GPS works by triangulation using signals referenced to onboard atomic clocks Triangulation from satellites is the basis of the system. 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. Satellite Engineering Research Corporation

4. 4 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 Proper time vs. coordinate time

5. Satellite Engineering Research Corporation 5 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 Relativistic effects

6. Satellite Engineering Research Corporation 6 6 planes, 4 satellites per plane Altitude: 20,184 km Velocity: 3.874 km/s 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 GPS has served as a laboratory for relativity and has provided a model for theoretical algorithms Global Positioning System

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

8. Satellite Engineering Research Corporation 8 Level of coverage

9. Satellite Engineering Research Corporation 9 Earth-Moon system Lagrange points Lagrange point Distance from Earth Distance from Moon Lunar orbit radius km Lunar orbit radius km L1 0.849 066326 385 0.150 934 58 020 L2 1.167 833448 921 0.167 833 64 516 L3 0.992 912381 680 1.992 912766 085 L4 1.000 000384 405 1.000 000384 405 L5 1.000 000384 405 1.000 000384 405 Earth radius = 6378 km Moon radius = 1738 km Orbit radius = 384 405 km

10. Satellite Engineering Research Corporation 10 Relay between Moon and Earth via L4 spacecraft

11. Satellite Engineering Research Corporation 11 Coverage of back side of Moon from L4 and L5

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

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

14. Satellite Engineering Research Corporation 14 Level of coverage

15. Satellite Engineering Research Corporation 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.

16. Satellite Engineering Research Corporation 16 Transformation between Mars Time (MT) and Barycentric Coordinate Time (TCB) 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) Gravitational propagation time delay Orbital semimajor axis 1.524 AU = 2.280  10 8 km Maximum light time 21.0 min Minimum light time 4.4 min Relativistic corrections to a clock on Mars

17. Satellite Engineering Research Corporation 17 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. Conclusion