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Moon Libration

Implement Moon librations

Library

Environment/Celestial Phenomena

Description

For a given Julian date, the Moon Libration block implements the Moon librations using Chebyshev coefficients. The block uses the Chebyshev coefficients that the NASA Jet Propulsion Laboratory provides.

    Tip   As Julian date input for the block, you can use the Julian Date Conversion block or the Aerospace Toolbox juliandate function to calculate the Julian date. You can also calculate your own Julian date and input it using the Constant block.

Dialog Box

Epoch

Select one of the following:

  • Julian date

    Julian date to calculate the Moon libration. When you select this option, the block has one input port.

  • T0 and elapsed Julian time

    Julian date, specified by two block inputs:

    • A fixed starting epoch (T0).

    • Variable elapsed time between T0 and the desired model simulation time.

    T0 plus the variable elapsed time cannot exceed the maximum Julian date for the specified Ephemerides.

Ephemeris model

Select one of the following ephemerides models defined by the Jet Propulsion Laboratory.

Ephemerides ModelDescription
DE405

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

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

DE421

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

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

DE423

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

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

    Note:   This block requires that you download ephemeris data with the Support Package Installer. Click the Get data button to start the installer. For more information, see aeroDataPackage.

Action for out of range input

Specify the block behavior when the block inputs are out of range.

ActionDescription
NoneNo action.
WarningWarning in the MATLAB® Command Window, model simulation continues.
Error (default)MATLAB returns an exception, model simulation stops.

Calculate rates

Select this check box to calculate the rate of the Moon libration and add a second block output.

Inputs and Outputs

InputDimension TypeDescription

First

Scalar

  • Julian date (TJD) (default) — One input. Specify a date between the minimum and maximum Julian date.

  • Fixed Julian date (T0JD) plus the elapsed Julian time (ΔTJD) between the fixed date and the ephemeris time. — Two inputs, where the first input is T0JD and the second input is ΔTJD. ΔTJD must be a positive number. The sum of T0JD and ΔTJD must fall between the minimum and maximum Julian date.

The block Epoch parameter controls the number of block inputs.

See the Ephemerides parameter for the minimum and maximum Julian dates.

Second (Optional)

Scalar

ΔTJD — Elapsed Julian time (ΔTJD) between the fixed date and the ephemeris time. The sum of T0JD and ΔTJD must fall between the minimum and maximum Julian date.

See the Ephemerides parameter for the minimum and maximum Julian date.

OutputDimension TypeDescription
FirstVectorEuler angles (φ θ ψ) for Moon attitude. Units are radians.
Second (Optional)VectorMoon libration Euler angular rates (ω). Units are radians/day.

References

Folkner, W. M., J. G. Williams, D. H. Boggs, "The Planetary and Lunar Ephemeris DE 421," IPN Progress Report 42-178, 2009.

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

See Also

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External Web Sites

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