Position and velocity vectors in Earth-centered inertial mean-equator mean-equinox
calculates the position vector in the Earth-centered inertial (ECI) coordinate system for a
given position vector in the Earth-centered Earth-fixed (ECEF) coordinate system at a
specific Coordinated Universal Time (UTC). For more information on the Earth-centered
Earth-fixed coordinate system, see Algorithms.
r_eci] = ecef2eci(
calculates the position, velocity, and acceleration vectors at a higher precision using
Earth orientation parameters. If Earth orientation parameters are not specified, the
function sets them to
a_eci] = ecef2eci(___,
Convert ECEF Position and Velocity to ECI
Convert the ECEF position and velocity to ECI at 12:00 on January 4, 2019.
r_ecef = [-5762640 -1682738 3156028]; v_ecef = [3832 -4024 4837]; utc = [2019 1 4 12 0 0]; [r_eci, v_eci] = ecef2eci(utc, r_ecef, v_ecef);
r_eci = 1.0e+06 * -2.9818 5.2070 3.1616 v_eci = 1.0e+03 * -3.3837 -4.8870 4.8430
Convert ECEF Position to ECI Including Polar Motion Effects
Convert the ECEF position to ECI at 12:00 on January 4, 2019, including the effects of polar motion.
r_ecef = [-5762640 -1682738 3156028]; utc = [2019 1 4 12 0 0]; mjd = mjuliandate(utc); pm = polarMotion(mjd, 'action', 'none')*180/pi; r_eci = ecef2eci(utc, r_ecef, 'pm', pm);
r_eci = 1.0e+06 * -2.9818 5.2070 3.1616
Convert ECEF Position to ECI Using
Convert ECEF position and velocity to ECI at 12:00 on January 4, 2019
r_ecef = [-5762640 -1682738 3156028]; v_ecef = [3832 -4024 4837]; utcDT = datetime(2019, 1, 4, 12, 0, 0) [r_eci, v_eci] = ecef2eci(utcDT, r_ecef, v_ecef)
utcDT = datetime 04-Jan-2019 12:00:00 r_eci = 1.0e+06 * -2.9818 5.2070 3.1616 v_eci = 1.0e+03 * -3.3837 -4.8870 4.8430
utc — Coordinated Universal Time
1-by-6 array | 1-by-6 matrix | scalar
Coordinated Universal Time (UTC) specified as one of these:
1-by-6 array of UTC values in the order year, month, day, hour, minutes, and seconds:
Time Value Enter Year Double value that is a whole number greater than 1, such as
Month Double value that is a whole number greater than 0, within the range
Day Double value that is a whole number greater than 0, within the range
Hour Double value that is a whole number greater than 0, within the range
Minute and second Double value that is a whole number greater than 0, within the range
datetimearray. To create the array, use the
[2000 1 12 4 52 12.4]
r_ecef — Position components
Array of ECEF position components, specified as a 3-by-1 array.
v_ecef — Velocity components
ECEF velocity components, specified as a 3-by-1 array.
a_ecef — Acceleration components
ECEF acceleration components, specified as a 3-by-1 array.
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
dAT — Difference between TAI and UTC
0 (default) | scalar
Difference between International Atomic Time (TAI) and UTC, specified as a scalar, in seconds.
dUT1 — Difference between UTC and Universal Time
0 (default) | scalar
Difference between UTC and Universal Time (UT1), specified as a scalar, in seconds.
pm — Polar displacement
array of zeroes (default) | 1-by-2 array
Polar displacements due to the motion of Earth crust along the x- and y-axis, in degrees.
To calculate the displacement, use the
pm = polarMotion(mjd, 'action', 'none')*180/pi;
dCIP — Adjustment to the CIP location
Adjustment to the location of the Celestial Intermediate Pole (CIP), in degrees,
specified as a comma-separated pair consisting of
dCIP and an
M-by-2 array. This location (dDeltaX,
dDeltaY) is along the x- and
y- axes. By default, this function assumes a 1-by-2 array of
For historical values, see the International Earth Rotation and Reference Systems
Service Web site (
https://www.iers.org) and navigate to the Earth
orientation data Data/Products page.
Specify an M-by-2 array of location adjustment values, where M is the number of direction cosine or transformation matrices to be converted. Each row corresponds to one set of dDeltaX and dDeltaY values.
lod — Excess length of day
0 (default) | scalar
Excess length of day (difference between astronomically determined duration of day and 86400 SI seconds), specified as a scalar, in seconds.
r_eci — Position components
ECI position components, specified as a 3-by-1 array.
v_eci — Velocity components
ECI velocity components, specified as a 3-by-1 array.
a_eci — Acceleration components
ECI acceleration components, specified as a 3-by-1 array.
ecef2eci function uses these Earth-centric coordinate
Earth Centered Inertial Frame (ECI) — The inertial frame used is the International Celestial Reference Frame (ICRF). This frame can be treated as equal to the ECI coordinate system realized at J2000 (Jan 1 2000 12:00:00 TT). For more information, see ECI Coordinates.
Earth-centered Earth-fixed Frame (ECEF) — The fixed-frame used is the International Terrestrial Reference Frame (ITRF). This reference frame is realized by the IAU2000/2006 reduction from the ICRF coordinate system. For more information, see ECEF Coordinates.
 Vallado, D. A. Fundamentals of Astrodynamics and Applications. alg. 4. New York: McGraw-Hill, 1997.
 Gottlieb, R. G., "Fast Gravity, Gravity Partials, Normalized Gravity, Gravity Gradient Torque and Magnetic Field: Derivation, Code and Data," Technical Report NASA Contractor Report 188243, NASA Lyndon B. Johnson Space Center, Houston, Texas, February 1993.
 Konopliv, A. S., S. W. Asmar, E. Carranza, W. L. Sjogen, D. N. Yuan., "Recent Gravity Models as a Result of the Lunar Prospector Mission, Icarus", Vol. 150, no. 1, pp 1–18, 2001.
 Lemoine, F. G., D. E. Smith, D.D. Rowlands, M.T. Zuber, G. A. Neumann, and D. S. Chinn, "An improved solution of the gravity field of Mars (GMM-2B) from Mars Global Surveyor", Journal Of Geophysical Research, Vol. 106, No. E10, pp 23359-23376, October 25, 2001.
 Seidelmann, P.K., Archinal, B.A., A’hearn, M.F. et al. "Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006." Celestial Mech Dyn Astr 98, 155–180 (2007).
Introduced in R2019a