Precise Time Synchronization Throughout the Solar System

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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_at_aol.com
• www.satellitecorp.com

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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

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GPS works by triangulationusing signals
referenced to onboard atomic clocks
Satellite Engineering Research Corporation
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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

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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

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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 Sagna
c 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
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8 satellite polar constellation about the Moon
8 satellites, 2 orbital planes, 4 satellites per
plane, 3 lunar radii
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Level of coverage
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Earth-Moon system Lagrange points
Earth radius 6378 km Moon radius 1738 km
Orbit radius 384 405 km
Lagrange point Distance from Earth
Distance from Moon Lunar orbit ra
dius 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 6
80 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
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Relay between Moon and Earth via L4 spacecraft
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Coverage of back side of Moon from L4 and L5
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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.
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12 satellite constellation about Mars
12 satellites, 3 orbital planes, 4 satellites per
plane, 2.5 Mars radii
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Level of coverage
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Mars-stationary orbit
Mars mass / Earth mass k 0.1071
Mars period of rotation 24 h 37 m 23 s 88,64
3 s
Mars radius 3330 km
According to Keplers 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.
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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

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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.