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Earth Nutation

Implement Earth nutation

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  • Earth Nutation block

Libraries:
Aerospace Blockset / Environment / Celestial Phenomena

Description

The Earth Nutation block implements the International Astronomical Union (IAU) 1980 nutation series for a given Julian date The block uses the Chebyshev coefficients that the NASA Jet Propulsion Laboratory provides.

The Epoch parameter controls the number of block inputs. If you select Julian date, the block has one input port, if you select T0 and elapsed Julian time, the block has two input ports.

Tip

For TJD, Julian date input for the block:

Ports

Input

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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

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 T0JD and ΔTJD 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

Elapsed Julian time between the fixed Julian date and the ephemeris time, specified as a positive scalar. The sum of T0JD and ΔTJD 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

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Earth nutation, output as a vector of longitude (Δψ) and obliquity (Δε), in rad.

Data Types: double

Earth nutation angular rate for the longitude (Δψ dot ) and obliquity (Δε dot ), specified as a scalar in rad/day.

Dependencies

This port displays if the Calculate rates parameter is selected.

Data Types: double

Parameters

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Epoch, specified as:

  • Julian date

    Julian date to calculate the Earth nutation. When this option is selected, the block has one input port, TJD.

  • T0 and elapsed Julian time

    Julian date, specified by two block inputs:

    • Fixed Julian date representing a starting epoch.

    • Elapsed Julian time between the T0JD and the desired model simulation time. The sum of T0JD and ΔTJD 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'

Select an Ephemeris model from the list 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.

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.

Programmatic Use

Block Parameter: de
Type: character vector
Values: DE405 | DE421 | DE423 | DE430
Default: 'DE405'

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

ActionDescription

None

No action.

Warning

Warning in the Diagnostic Viewer, model simulation continues.

Error (default)

Error in the Diagnostic Viewer, model simulation stops.

Programmatic Use

Block Parameter: errorflag
Type: character vector
Values: 'None' | 'Warning' | 'Error'
Default: 'Error'

Calculate the rate of the Earth nutation by selecting this check box.

Dependencies

Select this check box to display the Δψ dot Δεdot 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, McGraw-Hill, New York, 1997.

Extended Capabilities

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

Version History

Introduced in R2013a

See Also

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