I need to transform ECI to ECEF coordinate. Here, I need the formula in math and algorithm. I have looking for the formula in the internet, but I can find one. I have x, y, z cartesian coord in ECI. And want to transform it to ECEF coord. Anybody knows the formula and algorithm?


The Explanatory Supplement to the Astronomical Almanac has all the equations you need. Take a look at chapters 3 and 4.

Keep in mind you need some clear definitions of what you mean by ECEF and ECI. Most people utilize WGS84 for ECEF, but that is not a requirement. Similarly ECI could be J2000 or ICRF

In general you will need 4 steps to convert from ECI to ECEF:

  1. Calculate earth's precession
  2. Calculate earth's nutation
  3. Account for earth's rotation including UTC-UT1 offset
  4. Account for polar motion
  5. Convert to lan/lon if desired

The first two transformations are purely analytical, and can be obtained from books like the Explanatory Supplement. The third and fourth transformation rely on irregularly varying parameters that have to be updated for a specific date.

The help system for the Systems ToolKit (STK) has some excellent descriptions on various frames and transformation process, but not actual equations.

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  • $\begingroup$ Thank you, its solved. I just count precesison effect and Account for earth's rotation. $\endgroup$ – Elisa Fitri Nov 1 '19 at 0:28

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