earthNutation

Implement Earth nutation

Syntax

angles = earthNutation(ephemerisTime)

angles = earthNutation(ephemerisTime,ephemerisModel)

angles = earthNutation(ephemerisTime,ephemerisModel,action)

[angles,rates] = earthNutation(___)

Description

Implement Earth Nutation Angles

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

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

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

Implement Earth Nutation Angles and Rates

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

Examples

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 = 1×2
10-4 ×

    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 = 1×2
10-4 ×

   -0.6750   -0.2799

rates = 1×2
10-7 ×

    0.3687   -0.9937

Input Arguments

ephemerisTime — Julian date

scalar | 2-element vector | column vector | M-by-2 matrix

Julian dates for which positions are calculated, specified as these values:

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

Data Types: double

action — Function behavior

'Error' (default) | 'None' | 'Warning'

Function behavior when inputs are out of range, specified as one of these values:

Value	Description
'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

angles — Earth nutation angles

M-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 rates

M-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.

References

[1] Folkner, W. M., J. G. Williams, and D. H. Boggs. "The Planetary and Lunar Ephemeris DE 421." JPL Interplanetary Network Progress Report 24-178, 2009.

[2] Vallado, David A. Fundamentals of Astrodynamics and Applications. McGraw-Hill, 1997.

Version History

Introduced in R2013a