Satellite Engineering Research Corporation

Precise Time SynchronizationThroughout the Solar System

Robert A. Nelson

Satellite Engineering Research Corporation7701 Woodmont Avenue, Ste. 208

Bethesda, MD 20814301-657-9641

RobtNelson@aol.comwww.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

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

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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

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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

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6 planes, 4 satellites per planeAltitude: 20,184 kmVelocity: 3.874 km/s

Principal relativistic effects

Time dilation: − 7.1 s per dayGravitational redshift: + 45.7 s per dayNet secular effect: + 38.6 s per day

Residual periodic effect: 46 ns maximumSagnac effect: 133 ns maximum

GPS has served as a laboratory for relativity and has provided a model for theoretical algorithms

Global Positioning System

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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

Lagrange point Distance from Earth Distance 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

Earth radius = 6378 km

Moon radius = 1738 km

Orbit radius = 384 405 km

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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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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.

Communicationsatellites provide GPS-like signals

Space navigation using proven GPS technology

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12 satellites, 3 orbital planes, 4 satellites per plane, 2.5 Mars radii

12 satellite constellation about Mars

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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 = 88,643 s

Mars radius = 3330 km

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(0.1071)(398 600.5 km / s )(88 643 s) 20 406 km

4 4Ek GM

r P

20 406 km6.128

3330 km

r

R

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.

altitude 17 076 kmh r R

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• Transformation between Mars Time (MT) and Barycentric Coordinate Time (TCB)

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1 1 1TCB TT ( ) ( )

2E ext E E G E EU v dt L Dc c

r v r r

• Atomic clock (e.g., rubidium) on Mars

• Potential applications of Earth-Mars synchronization– VLBI – Interplanetary radionavigation references– Refined tests of general relativity

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1 1 1TCB MT ( ) ( )

2M ext M M M M MU v dt L Dc c

r v r r

• Transformation between Terrestrial Time (TT) and Barycentric Coordinate Time (TCB)

• Gravitational propagation time delay

Orbital semimajor axis1.524 AU = 2.280 108 km

Maximum light time21.0 min

Minimum light time4.4 min

Relativistic corrections to a clock on Mars

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• 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