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# moonLibration

Moon librations

## Syntax

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

## Description

example

````angles= moonLibration(ephemerisTime)` implements the Moon libration angles for `ephemerisTime`, expressed in Julian days. 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= moonLibration(ephemerisTime,ephemerisModel)` uses the `ephemerisModel` coefficients to implement these values. `angles= moonLibration(ephemerisTime,ephemerisModel,action)` uses `action` to determine error reporting.```

example

``````[angles,rates] = earthNutation(___)``` implements the Moon libration angles and rates using any combination of the input arguments in the previous syntaxes.```

## Examples

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Implement libration angles of the Moon for December 1, 1990 with DE405. Use the juliandate function to calculate the input Julian date value.

`angles = moonLibration(juliandate(1990,12,1))`
```angles = 1.0e+03 * 0.0001 0.0004 1.8010```

Specify the ephemerides (DE421) and use the juliandate function for the date (January 1, 2000) to calculate both the Moon libration angles and rates.

`[angles,rates] = moonLibration([2451544.5 0.5],'421')`
```angles = 1.0e+03 * -0.0001 0.0004 2.5643 rates = -0.0001 0.0000 0.2301```

## Input Arguments

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Julian dates for which the positions are calculated, specified as one of the following:

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

• `'432t'`

Released in April 2014. This ephemerides takes into account the Julian date range 2287184.5, (December 21, 1549 ) to 2688976.5, (January 25, 2650).

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

Data Types: `char`

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, model simulation continues.
`'Error'`MATLAB returns an exception, model simulation stops.

Data Types: `char`

## Output Arguments

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Moon libration angles, specified as an M-by-3 numeric array. M is the number of Julian dates, in rows. The columns contain the Euler angles (φ θ ψ) for Moon attitude, in radians.

If the input arguments include multiple Julian dates or epochs, this array has the same number of rows as the `ephemerisTime` input.

Moon libration angular rates, specified as an M-by-3 numeric array. M is the number of Julian dates, in rows. The columns contain the Moon libration Euler angular rates (ω), in radians/day.

If the input arguments include multiple Julian dates or epochs, this array has the same number of rows as the `ephemerisTime` input.

## References

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

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