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# moonLibration

Moon librations

## Syntax

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

## Description

example

angles= moonLibration(ephemerisTime) implements the Moon libration angles for ephemerisTime.

The function uses the Chebyshev coefficients that the NASA Jet Propulsion Laboratory provides.

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 Moon

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```

### Implement Libration Angles and Rates for Moon

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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### ephemerisTime — Julian datesscalar | 2-element vector | column vector | M-by-2 matrix

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

### ephemerisModel — Ephemerides coefficients‘405' (default) | '421'|'423'

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.

Data Types: char

### action — Function behavior'Error' (default) | 'None' | 'Warning'

Function behavior when inputs are out of range, specified as a string as one of these string 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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### angles — Moon libration anglesM-by-3 numeric array

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.

### rates — Moon libration angular ratesM-by-3 numeric array

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.