Monitoring of Earth Orientation Variables
Jim Ray
Earth Orientation Department
U.S. Naval Observatory
What are Earth Orientation Parameters?
- The time-varying angles which describe the rotation and wobble
of the Earth as it spins in inertial space
- EPOs provide the link between:
- terrestrial reference frame - fixed to Earth
non-inertial (rotating, etc.)
- celestial reference frame - fixed to quasars
inertial (non-rotating)
- TRF <-- EOPs --> CRF
- Treated as 5 time--varying angles:
- polar motion - x,y coordinates of instantaneous pole location on
Earth's surface (in TRF)
- Universal time - UT1 or, equivalently, excess length of day; angle
about rotation (z) axis
- nutation - position of pole in celestial frame
Why do EOPs Matter?
- Nearly all observations of space objects or from space platforms
must be related to Earth points
- Could use dense, global tracking networks to continuously locate satellites
in TRF by geometric triangulation from the ground
- generally not practical (except for geostationary satellites)
- Instead, Newton's laws of motion give accurate description of satellite
dynamics using sparse observations
- But physical laws only usable (simple) in inertial (non-rotating) frame
- otherwise, must introduce complex pseudo-forces
How are EOPs Used?
- Method to analyze Earth-based observations:
- apply transform: TRF --> (EOPs) --> CRF
- compute orbit in inertial frame using laws of motion
- transform back: CRF --> (EOPs) --> TRF
- Simple rotation matrix relation used:
CRF = P * N(t) * R(t) * W(t) * TRF
where
- CRF = celestial (x,y,z) coordinates
- TRF = terrestrial (x,y,z) coordinates
- P = precession matrix
- N(t) = nutation matrix
- R(t) = rotation (UT1) matrix
- W(t) = wobble (polar motion) matrix
and the terms N(t), R(t), and W(t) are EOPs.
How Big are EOP Variations?
- variations on all time scales, from hours upward
- generally, larger changes over longer time scales
- Polar motion changes
- large annual periods (modulated)
- +/-600 mas range
--> nearly 20 meters of equatorial motion
- Length of Day changes
- large annual periods (plus known tides)
- +/-1 millisecond (ms) range for length of day over a year
--> nearly 0.5 meter of equatorial motion
- UT1 changes
- integral of length of day changes
- small errors in length of day can accumulate to very large UT1 errors
What is the Effect of EOP Errors?
- Method to generate orbit predictions (for real-time use, e.g.,
broadcast GPS orbits):
- transform past tracking data (collected in TRF):
TRF --> (EOPs) --> CRF
- compute orbit for observed period (in inertial frame)
- use laws of motion to predict future orbit (in inertial frame)
- transform back to TRF:
CRF --> (predicted EOPs) --> TRF
- EOP prediction errors contribute directly to orbit rotation errors
- 1 milliarcsecond (mas) = 13 cm equatorial rotation @ GPS altitude
- GPS orbits show rotations up to +/-20 mas
- equivalent to 2.6 meters equatorial variation
What Causes EOP Variations?
- Nutation - motion of celestial pole in CRF
- due to gravitational forces of Sun, Moon, and planets acting on non-spherical Earth
- accurately predicted by models
- prediction error <0.3 mas (<4cm @ GPS altitude)
- Polar motion - motion of pole in TRF
- due to exchange of angular momentum:
Earth's crust <--> atmosphere <--> oceans
- crudely predictable
- prediction error ~0.4 mas/day (~5 cm/day @ GPS altitude)
- UT1 - rotation rate
- due to exchange of angular momentum:
Earth's crust <--> atmosphere <--> core
- very poorly predictable
- prediction error ~0.1 ms/day = ~1.5 mas/day (~20 cm/day @ GPS altitude)
How are EOP Variations Measured?
- Very long baseline interferometry (VLBI) - applied to multi-station radio astronomy of quasars
- measure all 5 EOP angles
- weekly EOPs (5 times per week UT1)
- very expensive
- multi-agency, multi-national effort
- International VLBI Service (IVS)
- Satellite laser ranging (SLR) - round-trip timing of laser pulses to satellites
- measures polar motion and length of day
- daily to few-day EOPs
- very expensive
- multi-agency, multi-national effort
- International Laser Ranging Service (ILRS)
- Global Positioning System (GPS) - radiometric timing using global tracking network
- measures polar motion and length of day
- daily EOPs; most accurate polar motion
- inexpensive network and analysis
- International GPS Service (IGS)
Where to Get Latest EOPs?
- International Earth Rotation Service (IERS)
- exists to provide EOP service to user community
- ensures consistent, high-accuracy results
- USNO serves as Rapid Service & Prediction Center
- IERS Bulletin A (Rapid Service & Predictions)
- prepared at USNO
- publication of recent past EOPs
- plus predictions up to 1 year in future
- based on multi-technique combination (VLBI, SLR, GPS)
- Access EOP products at