# Presentation: 486726

## 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
- 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

## GPS works by triangulationusing signals referenced to onboard atomic clocks

**Satellite Engineering Research Corporation**

## 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

- 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**

## 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

**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**

## Global Positioning System

- 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**

## 8 satellite polar constellation about the Moon

**8 satellite polar constellation about the Moon**

- 8 satellites, 2 orbital planes, 4 satellites per plane, 3 lunar radii

## Level of coverage

## 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

## Relay between Moon and Earth via L4 spacecraft

## Coverage of back side of Moon from L4 and L5

## Space navigation using proven GPS technology

- 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**

## 12 satellite constellation about Mars

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

**12 satellite constellation about Mars**

## Level of coverage

## 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.

## Relativistic corrections to a clock on Mars

-   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  108 km
- Maximum light time
- 21.0 min
- Minimum light time
- 4.4 min

**Relativistic corrections to a clock on Mars**

## 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.

- 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**