Convert ICRS to ECI: Engineer's Guide

[kmg5246]

May be a simple question, but I am an Engineer so I am not as familiar with astronomy:

I am developing some orbital simulation software, and need to know how to convert ICRS (barycentric) coordinates to ECI. My program accesses the JPL Solar and Planetary Ephemeris (405) for data, and I need to translate it into Earth-centered.

Thanks

 

[LowlyPion]

You might start here if you haven't already:
http://lheawww.gsfc.nasa.gov/users/craigm/bary/

Good Luck.

 

[D H]

The DE405 time frame is Terrestrial Time (TAI + 32.184 seconds); positions are in ICRS coordinates.

If you are using the DE405 for gravitational effects, do not make a time-of-travel adjustment. Just do the dumb thing and pretend gravity propagates at an infinite speed.

To convert to ECI coordinates, all you need to do is calculate the position of the Earth. The DE405 has the location of the Earth-Moon barycenter wrt the solar system barycenter, the location of the Moon wrt the Earth, and the masses of the Earth and the Moon. Deriving the Earth's position wrt the solar system barycenter based on the above is simple algebra.

To convert to ECEF coordinates you will need a model of time and a model of the Earth's rotation, both of which you can obtain from http://www.iers.org. You might want to read D. Vallado, Fundamentals of Astrodynamics and Applications, Third Edition, before you jump into the time and Earth rotation models.

You will need to convert to and from ECEF coordinates if you want an accurate model of vehicles orbiting the Earth because you will need to model Earth as a non-spherical body to have any hopes of accuracy.

 

[kmg5246]

Once again forgive me for my inexperience with the subject:

When I use the Moon position data from DE405, the coordinates do not match an ephemeris produced by STK (in J2000 ECI). I have added corrections for nutation and precession, but neither reduce the difference by any significant amount. It appears to require some sort of rotation transformation, but I am unsure of the angles between ICRF and ECI.

 

[D H]

STK uses the DE405 for ephemeris, so something is amiss somewhere. I suspect it one of two things.

Number one suspect: What do you mean by ECI? ECI is a rather vague term. It might mean Mean of Date, True of Date, J2000 (FK5 catalog), GCRF (ICRF axes, Earth-centered origin), or who knows what. If you are using Mean of Date coordinates you will need to correct for Earth precession. If you are using True of Date, you will need to correct for Earth precession and nutation. There is a very small rotation between J2000 and GCRF. If you are using GCRF, this is just the ICRF shifted to the center of the Earth.

Number two suspect: How are you representing time? There are a *lot* of time references: TT, BCT, TAI, UTC, UT1, ... Which ones are you using for state propagation, ephemeris calculations, data logging, etc?

Number three suspect: Are you using STK and DE405 consistently? For example, the position of the moon at some time is not the same as the position of the Moon as seen by an Earth-based observer at that same time.

 

[kmg5246]

The data I have currently for LRO and the STK file is in Earth Mean Equator of J2000. I am taking ephemeris files for various s/c and simulating them visually (3D/2D). I don't see why there would be multiple time references, but I could be wrong.

 

[D H]

The issue of reference frames
If you are using the data from http://lroc.sese.asu.edu/downloads.html" , the Earth-based ephemerides are in EME J2000, aka Earth Mean Equator/Mean Equinox (J2000), aka Mean of Date (J2000). The x-axis points in the direction of the mean vernal equinox, the x and y-axis together define the Earth's mean equator, and the z axis complete the RHS. The DE405 are in ICRF coordinates. You will need to convert between frames.

• ICRS to ecliptic J2000. There is a very slight difference between the new ICRS frame and the ecliptic J2000 frame. The difference between the two is on the order of milliarcseconds. For starters, you can treat the transformation as an identity. If you want to get very precise, go to the IERS (http://www.iers.org" ) to get the transformation.
• Ecliptic J2000 to EME J2000. This is the Earth's precession, FK5 catalogue. You do not want to add in nutation, because that takes you to true-of-date (J2000).

The issue of time
The FK5 Earth precession model is expressed in terms of Greenwich Mean Sidereal Time (GMST), which in turn is expressed in terms of Universal Time (UT1). The DE405 is expressed in terms of Terrestrial Time (TT), which is more-or-less a fixed offset from Atomic Time (TAI). The clock on your cell phone shows Coordinated Universal Time (UTC). One UTC second is equal to one TAI second. However, UTC is always kept within a second of UT1 by adding leap seconds. So you will need models of

• TAI. This is the time frame in which you should be propagating states.
• TT. This one is easy: TT = TAI + 32.184 seconds.
• UTC. This is completely ad-hoc. Use the leap second tables maintained by the IERS.
• UT1. Also is completely ad-hoc. Use the delta-UT (DUT1) tables maintained by the IERS.
• GMST. This is a quadratic in UT1.

Don't shoot me, I'm only the messenger.

 

[sla29970]

ICRS is a BCRS. ECI is a GCRS. The conversion between them is a full 4-transformation. For a look at the vocabulary see the IAU Working Group on Nomenclature for Fundamental Astronomy.
http://syrte.obspm.fr/iauWGnfa/
and also USNO Circular 179
http://www.usno.navy.mil/USNO/astronomical-applications/publications/circ-179

the IAUWGNFA has the algorithm spelled out, and IAU Standards of Fundamental Astronomy
http://www.iausofa.org/
has software that implements the transformations. Or, if an unencumbered version is needed, see USNO NOVAS
http://www.usno.navy.mil/USNO/astronomical-applications/software-products/novas
and USNO circulars 180 and 181.

 

[Chronos]

Reference coordinates are complicated. They are mostly used by agreement in the scientific community [decades past, to be precise].

 

[D H]

ICRS is a BCRS. ECI is a GCRS. The conversion between them is a full 4-transformation.

True, but for the most part that is an angels dancing on a pin kind of technical detail. Even in the GPS world that is a small effect. DeSitter precession is an order of magnitude smaller than Schwarzschild effect for GPS.

If you were truly concerned about time you would see that this thread is two years old.