Online ECEF to ECI Calculator (ECEF2ECI)
Precise transformation between ECEF and ECI coordinate systems. This tool allows you to precisely convert ECEF cartesian coordinates to ECI cartesian coordinates based on IERS Earth rotation parameters.
Results:
| # | ECEF Coordinates | ECI Coordinates |
|---|---|---|
| X (m) | 0.0000 | 0.0000 |
| Y (m) | 0.0000 | 0.0000 |
| Z (m) | 0.0000 | 0.0000 |
| VX (m) | 0.0000 | 0.0000 |
| VY (m) | 0.0000 | 0.0000 |
| VZ (m) | 0.0000 | 0.0000 |
Notes:
For the transformation from International Celestial Reference System (ICRS) to International Terrestrial Reference System (ITRS) following models are considered:
- IAU 1976 Precession
- IAU 1980 Nutation
- Earth rotation
- Polar motion
Earth Oriantation Parameters (EOP) are extracted from EOP (IERS) 14 C04 TIME SERIES.
The conversion accuracy for the position is around cm level per vector component depending on the fractional part of the given seconds. Time precision can be given up to a millisecond.
ECEF and ECI coordinate systems:
ECEF (Earth-Centered Earth-Fixed) and ECI (Earth-Centered Inertial) are two coordinate systems commonly used in satellite navigation, tracking, and orbit analysis.
ECEF is a cartesian coordinate system with the origin at the center of the Earth, and the x-axis pointing towards the intersection of the equator and the prime meridian, the y-axis pointing towards 90 degrees east longitude and the z-axis pointing towards the North Pole. ECEF coordinates are often used to describe the position of a satellite or a receiver on or above the Earth's surface.
ECI, on the other hand, is an inertial coordinate system with the origin at the center of the Earth, and the x-axis pointing towards the vernal equinox (the point at which the celestial equator intersects the ecliptic plane), the y-axis pointing towards the direction of Earth's rotation, and the z-axis pointing towards the North Pole. ECI coordinates are often used to describe the position and motion of objects in space.
How to transform?
To transform coordinates from ECEF to ECI, we need to take into account the rotation of the Earth. This is done by using a rotation matrix that takes into account the angle of the Earth's rotation at a given time. The transformation matrix depends on the Julian Date (JD) of the time for which the transformation is being done. The transformation can be done as follows:
- Calculate the Greenwich Mean Sidereal Time (GMST) for the given JD.
- Calculate the rotation angle based on the GMST.
- Use the rotation matrix to transform the ECEF coordinates to ECI coordinates.