moonLibration

Moon librations

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Syntax

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

Description

Implement Moon Libration Angles

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

Implement Moon Libration Angles and Rates

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

example

Examples

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Open Live Script

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 = 1×3
103 ×

    0.0001    0.0004    1.8010
Open Live Script

Specify the ephemerides (DE421) and use the Julian date 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 = 1×3
103 ×

   -0.0001    0.0004    2.5643


rates = 1×3

   -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 function 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 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, 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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Moon libration angles, returned 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, returned 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.

Version History

Introduced in R2013a

See Also

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