TerraFrame 0.2.0

A library for calculating the orientation of the earth relative to GCRS.

TerraFrame

TerraFrame is a library designed to provided key Earth related calculations and associated functionality to modeling & simulation software. Primarily, TerraFrame provides Earth orientation and gravity routines.

Earth Orientation

TerraFrame provides an implementation of the IAU 2006/2000A precession-nutation model which accounts for precession, nutation, and polar motion. Specifically, this implementation provides a transformation tensor between the Geocentric Celestial Reference System (GCRS) and the International Terrestrial Reference System (ITRS).

TerraFrame also provides routines for calculating the Earth's angular velocity tensor. The angular velocity tensor is based on the partial derivative of the numerous IAU 2006/2000A equations with respect to time (in seconds).

IERS precession and nutation model data files are shipped with TerraFrame. Utility code is also provided which automates the downloading of IERS data for polar motion, UTC, and UT1 offsets.

Gravity

Gravity calculations are provided by an implementation of the EGM2008. A double Clenshaw summation approach is used to evaluate the spherical harmonics which yields high numerical stability and computational efficiency. TerraFrame is numerically capable of evaluating EGM2008 to it’s complete degree and order: 2190.

By default, only data for degree and order 200 is shipped with TerraFrame for space efficiency. Most near earth modeling & simulation applications will not need to exceed degree and order 100 per WGS84 guidance.

Ancillary Functionality

Support is provided for converting from geodetic latitude, longitude, and height above ellipsoid to geocentric cartesian coordinates or vice versa. The WGS84 spheroid and a simple spherical earth are provided as built-in options.

TerraFrame also provides robust datetime and timescale conversion functionality that is fully leap second aware. Conversions between UTC, UT1, TT, and TAI are provided. The user is encouraged to not work in UTC directly to avoid leap second ambiguity. Conversion to UTC from TT or TAI can be safely done in post-processing.

License

This project - except for the IERS and WGS84 data files - is covered under the Mozilla Public License Version 2.0 (MPL2). See the LICENSE.txt file for more information.

Acknowledgements and References

This project uses data published by the International Earth Rotation and Reference Systems Service (IERS). The original data along with additional information can be found on the IERS website: here.

The Astropy, PyERFA, and GeographicLib libraries have been used as invaluable sources of truth for the testing of TerraFrame.

This project would not have been possible without the technical information provided by the following sources:

• Urban, S. E., & Seidelmann, P. K. (Eds.). Explanatory Supplement to the Astronomical Almanac (3rd ed.). University Science Books, 2013. ISBN: 978-1-891389-85-6.
• Gérard Petit and Brian Luzum (Eds.). IERS Conventions (2010), IERS Technical Note No. 36, Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2010. ISBN: 3-89888-989-6.
• Deakin, R.E., 1998, 'Derivatives of the earth’s potentials'. Geomatics Research Australasia, No.68, June, 1998, pp. 31-60.

Acronyms and Abbreviations

Term	Meaning
CIO	Celestial Intermediate Origin
CIP	Celestial Intermediate Pole
CIRS	Celestial Intermediate Reference System
CEO	Celestial Ephemeris Origin
EGM	Earth Gravitational Model
GCRS	Geocentric Celestial Reference System
IAU	International Astronomical Union
IERS	International Earth Rotation and Reference Systems Service
ITRF	International Terrestrial Reference Frame
ITRS	International Terrestrial Reference System
TAI	International Atomic Time
TIO	Terrestrial Intermediate Origin
TIRS	Terrestrial Intermediate Reference System
TT	Terrestrial Time
UT1	Universal Time
UTC	Coordinated Universal Time
WGS	World Geodetic System