Moon Libration

Implement Moon librations

• Library:

• Aerospace Blockset / Environment / Celestial Phenomena

• 

Description

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

Tip

For TJD, Julian date input for the block:

• Calculate the date using the Julian Date Conversion block or the Aerospace Toolbox juliandate function.

• Calculate the Julian date using some other means and input it using the Constant block.

Ports

Input

TJD — Julian date

scalar | positive | between minimum and maximum Julian dates

Julian date, specified as a positive scalar between minimum and maximum Julian dates.

See the Ephemeris model parameter for the minimum and maximum Julian dates.

Dependencies

This port displays if the Epoch parameter is set to Julian date.

Data Types: double

T0JD — Fixed Julian date

scalar | positive

Fixed Julian date for a specific epoch that is the most recent midnight at or before the interpolation epoch, specified as a positive scalar. The sum of T0_JD and ΔT_JD must fall between the minimum and maximum Julian dates.

See the Ephemeris model parameter for the minimum and maximum Julian dates.

Dependencies

This port displays if the Epoch parameter is set to T0 and elapsed Julian time.

Data Types: double

ΔTJD — Elapsed Julian time

scalar | positive

Elapsed Julian time between the fixed Julian date and the ephemeris time, specified as a positive scalar. The sum of T0_JD and ΔT_JD must fall between the minimum and maximum Julian date.

See the Ephemeris model parameter for the minimum and maximum Julian dates.

Dependencies

This port displays if the Epoch parameter is set to T0 and elapsed Julian time.

Data Types: double

Output

φ θ ψ (rad) — Euler angles

vector

Euler angles (φ θ ψ) for Moon attitude, in rad.

Data Types: double

ω (rad/day) — Moon libration Euler angular rate

vector

Moon libration Euler angular rates (ω), in rad/day.

Data Types: double

Parameters

Epoch — Epoch

Julian date (default) | T0 and elapsed Julian time

Epoch, specified as:

• Julian date

  Julian date to calculate the Moon libration. When this option is selected, the block has one input port, T_JD.

• T0 and elapsed Julian time

  Julian date, specified by two block inputs:

  • Fixed Julian date representing a starting epoch.

  • Elapsed Julian time between the fixed Julian date (T0_JD) and the desired model simulation time. The sum of T0_JD and ΔT_JD must fall between the minimum and maximum Julian dates.

Programmatic Use

Block Parameter: epochflag

Type: character vector

Values: Julian date | T0 and elapsed Julian time

Default: 'Julian date'

Ephemeris model — Ephemeris model

DE405 (default) | DE421 | DE423 | DE430 | DE432t

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

Ephemeris Model	Description
DE405	Released in 1998. This ephemeris 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 ephemeris 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 ephemeris 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.
DE430	Released in 2013. This ephemeris 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.
DE432t	Released in April 2014. This ephemeris 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.

Note

This block requires that you download ephemeris data using the Add-On Explorer. To start the Add-On Explorer, in the MATLAB^® Command Window, type aeroDataPackage. on the MATLAB desktop toolstrip, click the Add-Ons button.

Programmatic Use

Block Parameter: de

Type: character vector

Values: DE405 | DE421 | DE423 | DE430

Default: 'DE405'

Action for out-of-range input — Out-of-range block behavior

None (default) | Warning | Error

Out-of-range block behavior, specified as follows.

Action	Description
None	No action.
Warning	Warning in the MATLAB Command Window, model simulation continues.
Error (default)	MATLAB returns an exception, model simulation stops.

Programmatic Use

Block Parameter: errorflag

Type: character vector

Values: 'None' | 'Warning' | 'Error'

Default: 'Error'

Calculate rates — Calculate rate of Moon libration

on (default) | off

Select to calculate the rate of the Moon libration.

Dependencies

Select this check box to display the ω port.

Programmatic Use

Block Parameter: velflag

Type: character vector

Values: 'off' | 'on' |

Default: 'on'

References

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

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.