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# earthNutation

Implement Earth nutation

## Syntax

``angles = earthNutation(ephemerisTime)``
``angles = earthNutation(ephemerisTime,ephemerisModel)``
``angles = earthNutation(ephemerisTime,ephemerisModel,action)``
``````[angles,rates] = earthNutation(___)``````

## Description

### Implement Earth Nutation Angles

example

````angles = earthNutation(ephemerisTime)` implements the International Astronomical Union (IAU) 1980 nutation series for `ephemerisTime`, expressed in Julian days. The function returns angles.The function uses the Chebyshev coefficients that the NASA Jet Propulsion Laboratory provides. This function requires that you download ephemeris data with the Add-On Explorer. For more information, see `aeroDataPackage`.`angles = earthNutation(ephemerisTime,ephemerisModel)` uses the `ephemerisModel` coefficients to implement these values.`angles = earthNutation(ephemerisTime,ephemerisModel,action)` uses `action` to determine error reporting.```

### Implement Earth Nutation Angles and Rates

example

``````[angles,rates] = earthNutation(___)``` implements the International Astronomical Union (IAU) 1980 nutation series using any combination of the input arguments in the previous syntaxes. The function returns angles and angular rates. ```

## Examples

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Implement Earth nutation angles for December 1, 1990. Because no ephemerides model is specified, the default, DE405, is used. Use the `juliandate` function to specify the Julian date.

`angles = earthNutation(juliandate(1990,12,1))`
```angles = 1.0e-04 * 0.6448 0.2083```

Implement Earth nutation angles and angular rates for noon on January 1, 2000 using DE421.

`[angles,rates] = earthNutation([2451544.5 0.5],'421')`
```angles = 1.0e-04 * -0.6750 -0.2799 rates = 1.0e-07 * 0.3687 -0.9937```

## Input Arguments

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Julian dates for which positions are calculated, specified as these values:

• Scalar — Specify one fixed Julian date.

• 2-element vector — Specify the Julian date in multiple parts. The first element is the Julian date for a specific epoch that is the most recent midnight at or before the interpolation epoch. The second element is the fractional part of a day elapsed between the first element and epoch. The second element must be positive. The value of the first element plus the second element cannot exceed the maximum Julian date.

• Column vector — Specify a column vector with M elements, where M is the number of fixed Julian dates.

• M-by-2 matrix — Specify a matrix, where M is the number of Julian dates and the second column contains the elapsed days (Julian epoch date/elapsed day pairs).

Data Types: `double`

Ephemerides coefficients, specified as one of these ephemerides defined by the Jet Propulsion Laboratory:

• `'405'` — Released in 1998. This ephemerides takes into account the Julian date range 2305424.50 (December 9, 1599 ) to 2525008.50 (February 20, 2201).

This function calculates these ephemerides with respect to the International Celestial Reference Frame version 1.0, adopted in 1998.

• `'421'` — Released in 2008. This ephemerides takes into account the Julian date range 2414992.5 (December 4, 1899) to 2469808.5 (January 2, 2050).

This function calculates these ephemerides with respect to the International Celestial Reference Frame version 1.0, adopted in 1998.

• `'423'` — Released in 2010. This ephemerides takes into account the Julian date range 2378480.5 (December 16, 1799) to 2524624.5 (February 1, 2200).

This function calculates these ephemerides with respect to the International Celestial Reference Frame version 2.0, adopted in 2010.

• `'430'` — Released in 2013. This ephemerides takes into account the Julian date range 2287184.5 (December 21, 1549) to 2688976.5 (January 25, 2650).

This function implements these ephemerides with respect to the International Celestial Reference Frame version 2.0, adopted in 2010.

Data Types: `double`

Function behavior when inputs are out of range, specified as one of these values:

ValueDescription
`'None'`No action.
`'Warning'`Warning in the MATLAB® Command Window and model simulation continues.
`'Error'`MATLAB returns an exception and model simulation stops.

Data Types: `char` | `string`

## Output Arguments

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Earth nutation angles, returned as an M-by-2 vector, where M is the number of Julian dates. The 2 vector contains the d(psi) and d(epsilon) angles, in radians. The input arguments include multiple Julian dates or epochs. The vector has the same number of rows as the `ephemerisTime` input.

Earth nutation angular rates, returned as an M-by-2 vector, where M is the number of Julian dates. The 2 vector contains the d(psi) and d(epsilon) angular rate, in radians/day. The input arguments include multiple Julian dates or epochs. The vector has the same number of rows as the `ephemerisTime` input.

## References

[1] Folkner, W. M., J. G. Williams, and D. H. Boggs. "The Planetary and Lunar Ephemeris DE 421." JPL Interplanetary Network Progress Report 24-178, 2009.

[2] Vallado, David A. Fundamentals of Astrodynamics and Applications. McGraw-Hill, 1997.

## Version History

Introduced in R2013a