# 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.