# eci2lla

Convert Earth-centered inertial (ECI) coordinates to latitude, longitude, altitude (LLA) geodetic coordinates

## Syntax

• `lla = eci2lla(position,utc)` example
• `lla = eci2lla(position,utc,reduction)` example
• `lla = eci2lla(position,utc,reduction,deltaAT)` example
• `lla = eci2lla(position,utc,reduction,deltaAT,deltaUT1)` example
• `lla = eci2lla(position,utc,reduction,deltaAT,deltaUT1,polarmotion)` example
• `lla = eci2lla(position,utc,reduction,deltaAT,deltaUT1,polarmotion,Name,Value)` example

## Description

example

````lla = eci2lla(position,utc)` converts Earth-centered inertial (ECI) coordinates, specified by position, to latitude, longitude, altitude (LLA) geodetic coordinates. The conversion is based on the Universal Coordinated Time (UTC) you specify.```

example

````lla = eci2lla(position,utc,reduction)` converts Earth-centered inertial (ECI) coordinates, specified by `position`, to latitude, longitude, altitude (LLA) geodetic coordinates. The conversion is based on the specified reduction method and the Universal Coordinated Time (UTC) you specify.`lla = eci2lla(position,utc,reduction,deltaAT)` uses the difference between International Atomic Time and UTC that you specify as `deltaAT` to calculate the ECI coordinates.`lla = eci2lla(position,utc,reduction,deltaAT,deltaUT1)` uses the difference between UTC and Universal Time (UT1), which you specify as `deltaUT1`, in the calculation.`lla = eci2lla(position,utc,reduction,deltaAT,deltaUT1,polarmotion)` uses the polar displacement, `polarmotion`, in the calculation.`lla = eci2lla(position,utc,reduction,deltaAT,deltaUT1,polarmotion,Name,Value)` uses additional options specified by one or more Name,Value pair arguments.```

## Examples

collapse all

### Convert Position to LLA Coordinates Using UTC

Convert the position to LLA coordinates from ECI coordinates [-6.07 -1.28 0.66]*1e6 at 01/17/2010 10:20:36 UTC.

`lla=eci2lla([-6.07 -1.28 0.66]*1e6,[2010 1 17 10 20 36])`
```lla = 1.0e+05 * 0.0001 -0.0008 -1.3940```

### Convert Position to LLA Coordinates Using UTC and Reduction Method IAU-76/FK5

Convert the position to LLA coordinates from ECI coordinates [-1.1 3.2 -4.9]*1e4 at 01/12/2000 4:52:12.4 UTC, with a difference of 32 seconds between TAI and UTC, and 0.234 seconds between UTC and UT1. For an ellipsoid with a flattening of 1/290 and an equatorial radius of 60000 meters, use the IAU-76/FK5 reduction, polar motion [-0.0682e-5 0.1616e-5] radians, and nutation angles [-0.2530e-6 -0.0188e-6].

```lla = eci2lla([-1.1 3.2 -4.9]*1e4,[2000 1 12 4 52 12.4],... 'IAU-76/FK5',32,0.234,[-0.0682e-5 0.1616e-5],'dNutation'... ,[-0.2530e-6 -0.0188e-6],... 'flattening',1/290,'RE',60000)```
```lla = -55.5592 -75.0892 -311.3709```

## Input Arguments

collapse all

### `position` — ECI coordinatesM-by-3 array

ECI coordinates in meters, specified as an M-by-3 array.

### `utc` — Universal Coordinated Time1-by-6 array | M-by-6 matrix

Universal Coordinated Time (UTC), in the order year, month, day, hour, minutes, and seconds, for which the function calculates the conversion, specified as one of the following:

• For the year value, enter a double value that is a whole number greater than 1, such as `2013`.

• For the month value, enter a double value that is a whole number greater than 0, within the range `1` to `12`.

• For the hour value, enter a double value that is a whole number greater than 0, within the range `1` to `24`.

• For the hour value, enter a double value that is a whole number greater than 0, within the range `1` to `60`.

• For the minute and second values, enter a double value that is a whole number greater than 0, within the range `1` to `60`.

Specify these values in one of the following formats:

• 1-by-6 array

Specify a 1-row-by-6-column array of UTC values.

• M-by-6 matrix

Specify an M-by-6 array of UTC values, where M is the number of transformation matrices to calculate. Each row corresponds to one set of UTC values.

This is a one row-by-6 column array of UTC values.

Example: `[2000 1 12 4 52 12.4]`

This is an M-by-6 array of UTC values, where M is 2.

Example: `[2000 1 12 4 52 12.4;2010 6 5 7 22 0]`

Data Types: `double`

### `reduction` — Reduction method`'IAU-2000/2006'` (default) | `'IAU-76/FK5'`

Reduction method to calculate the coordinate conversion, specified as one of the following:

• `'IAU-76/FK5'`

Reduce the calculation using the International Astronomical Union (IAU)-76/Fifth Fundamental Catalogue (FK5) (IAU-76/FK5) reference system. Choose this reduction method if the reference coordinate system for the conversion is FK5. You can use the `'dNutation'` Name,Value pair with this reduction.

 Note:   This method uses the IAU 1976 precession model and the IAU 1980 theory of nutation to reduce the calculation. This model and theory are no longer current, but the software provides this reduction method for existing implementations. Because of the polar motion approximation that this reduction method uses, `eci2lla` performs a coordinate conversion that is not orthogonal because of the polar motion approximation.
• `'IAU-2000/2006'`

Reduce the calculation using the International Astronomical Union (IAU)-2000/2005 reference system. Choose this reduction method if the reference coordinate system for the conversion is IAU-2000. This reduction method uses the P03 precession model to reduce the calculation. You can use the `'dCIP'` Name,Value pair with this reduction.

### `deltaAT` — Difference between International Atomic Time and UTCM-by-1 array of zeroes (default) | scalar | one-dimensional array

Difference between International Atomic Time (IAT) and UTC, in seconds, for which the function calculates the coordinate conversion.

• scalar

Specify difference-time value to calculate one direction cosine or transformation matrix.

• one-dimensional array

Specify a one-dimensional array with M elements, where M is the number of ECI coordinates. Each row corresponds to one set of ECI coordinates.

Specify `32` seconds as the difference between IAT and UTC.

Example: `32`

Data Types: `double`

### `deltaUT1` — Difference between UTC and Universal Time (UT1)M-by-1 array of zeroes (default) | scalar | one-dimensional array

Difference between UTC and Universal Time (UT1), in seconds, for which the function calculates the coordinate conversion.

• scalar

Specify difference-time value to calculate ECI coordinates.

• one-dimensional array

Specify a one-dimensional array with M elements of difference time values, where M is the number of ECI coordinates. Each row corresponds to one set of ECI coordinates.

Specify `0.234` seconds as the difference between UTC and UT1.

Example: `0.234`

Data Types: `double`

### `polarmotion` — Polar displacementM-by-2 array of zeroes (default) | 1-by-2 array | M-by-2 array

Polar displacement of the Earth, in radians, from the motion of the Earth crust, along the x- and y-axes.

• 1-by-2 array

Specify a 1-by-2 array of the polar displacement values to convert one ECI coordinate.

• M-by-2 array

Specify an M-by-2 array of polar displacement values, where M is the number of ECI coordinates to convert. Each row corresponds to one set of UTC values.

Example: `[-0.0682e-5 0.1616e-5]`

Data Types: `double`

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside single quotes (`' '`). You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: `'dNutation',[-0.2530e-6 -0.0188e-6]`

### `'dNutation'` — Adjustment to longitude (dDeltaPsi) and obliquity (dDeltaEpsilon)M-by-2 array of zeroes (default) | M-by-2 array

Adjustment to the longitude (dDeltaPsi) and obliquity (dDeltaEpsilon), in radians, specified as the comma-separated pair consisting of `dNutation` and an M-by-2 array. You can use this Name,Value pair with the IAU-76/FK5 reduction.

For historical values, see the International Earth Rotation and Reference Systems Service website (`http://www.iers.org`) and navigate to the Earth Orientation Data Data/Products page.

• M-by-2 array

Specify M-by-2 array of adjustment values, where M is the number of LLA coordinates to be converted. Each row corresponds to one set of longitude and obliquity values.

Data Types: `double`

### `'dCIP'` — Adjustment to the location of the celestial intermediate pole (CIP)M-by-2 array of zeroes (default)

Adjustment to the location of the celestial intermediate pole (CIP), in radians, specified as the comma-separated pair consisting of `dCIP` and an M-by-2 array. This location (dDeltaX, dDeltaY) is along the x- and y- axes. You can use this argument with the IAU-200/2006 reduction.

For historical values, see the International Earth Rotation and Reference Systems Service website (`http://www.iers.org`) and navigate to the Earth Orientation Data Data/Products page.

• M-by-2 array

Specify M-by-2 array of location adjustment values, where M is the number of LLA coordinates to convert. Each row corresponds to one set of dDeltaX and dDeltaY values.

Example: `'dcip',[-0.2530e-5 -0.0188e-4]`

Data Types: `double`

### `'flattening'` — Custom ellipsoid planet1-by-1 array

Custom ellipsoid planet defined by flattening.

Example: `1/290`

Data Types: `double`

### `'re'` — Custom planet ellipsoid radius1-by-1 array

Custom planet ellipsoid radius, in meters.

Example: `60000`

Data Types: `double`