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# earthNutation

Implement Earth nutation

## Syntax

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

## Description

example

angles= earthNutation(ephemerisTime) implements the International Astronomical Union (IAU) 1980 nutation series for ephemerisTime, expressed in Julian days. It returns angles.

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

angles= earthNutation(ephemerisTime,ephemerisModel) uses the ephemerisModel coefficients to implement these values.

angles= earthNutation(ephemerisTime,ephemerisModel,action) uses action to determine error reporting.

example

[angles,rates] = earthNutation(___) implements the International Astronomical Union (IAU) 1980 nutation series using any combination of the input arguments in the previous syntaxes. It returns angles and angular rates.

## Examples

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### Implement Earth Nutation Angles

Implement Earth nutation angles for December 1, 1990. Because no ephemerides model is specified, the default, DE405, is used. Use the juliandate function to specify the Julian date.

`angles = earthNutation(juliandate(1990,12,1))`
```angles =
1.0e-04 *
0.6448    0.2083```

### Implement Earth Nutation Angles and Angular Rates

Implement Earth nutation angles and angular rates for noon on January 1, 2000 using DE421:

`[angles,rates] = earthNutation([2451544.5 0.5],'421')`
```angles =
1.0e-04 *
-0.6750   -0.2799

rates =
1.0e-07 *
0.3687   -0.9937```

## Input Arguments

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### ephemerisTime — Julian datescalar | 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 fixed 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' | '430'

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 block implements 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 one of these 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 — Earth nutation anglesM-by-2 vector

Earth nutation angles, returned as an M-by-2 vector, where M is the number of Julian dates. The 2 vector contains the d(psi) and d(epsilon) angles, in radians. The input arguments include multiple Julian dates or epochs. The vector has the same number of rows as the ephemerisTime input.

### rates — Earth nutation angular ratesM-by-2 vector

Earth nutation angular rates, returned as an M-by-2 vector, where M is the number of Julian dates. The 2 vector contains the d(psi) and d(epsilon) angular rate, in radians/day. The input arguments include multiple Julian dates or epochs. The vector has the same number of rows as the ephemerisTime input.