# Online ECI to ECEF Calculator **(ECI2ECEF)**

**Precise **transformation between ECI and ECEF coordinate systems. This tool allows you to precisely convert ECI cartesian coordinates to ECEF cartesian coordinates based on IERS Earth rotation parameters.

#### Results:

# | ECI Coordinates | ECEF 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.

#### ECI and ECEF coordinate systems:

ECI (Earth-Centered Inertial) and ECEF (Earth-Centered Earth-Fixed) coordinate systems are used for various applications in satellite navigation, tracking, and orbit analysis.

ECI coordinates are used to describe the position and motion of objects in space with respect to the Earth's center, which makes it a natural choice for orbit analysis, space mission planning, and satellite navigation. ECI coordinates are also used in spacecraft navigation, where accurate and precise positioning is critical for a successful mission.

ECEF coordinates, on the other hand, are used to describe the position and motion of objects on or near the Earth's surface. They are commonly used in GPS (Global Positioning System) navigation, where GPS receivers use ECEF coordinates to calculate their position by measuring the time delay of signals transmitted by GPS satellites.

In addition to satellite navigation and orbit analysis, ECI and ECEF coordinate systems are also used in other applications such as geodesy, geophysics, and surveying. For example, geophysicists use ECEF coordinates to map the Earth's magnetic field, and surveyors use ECEF coordinates to determine the position of landmarks and structures with respect to the Earth's surface.

#### How to transform?

To transform coordinates from ECI to ECEF, we need to use the inverse of the rotation matrix, which is calculated using the negative of the rotation angle. The transformation can be done as follows:

- Calculate the Greenwich Mean Sidereal Time (GMST) for the given JD.
- Calculate the negative of the rotation angle based on the GMST.
- Use the inverse of the rotation matrix to transform the ECI coordinates to ECEF coordinates.