Four Term Nutation Components

Evaluate a four-term low-precision nutation approximation from supplied mean angles; not an IAU 2000/2006 implementation.

Description

Nutation adds short-period variations to longitude and obliquity.

Nutation adds short-period variations to longitude and obliquity. A four-term approximation gives a low-precision correction from supplied mean angular arguments rather than a full modern standard series.^[1]

Evaluate a four-term low-precision nutation approximation from supplied mean angles; not an IAU 2000/2006 implementation.

When to use Four Term Nutation Components

Use this tool to evaluate a four-term low-precision nutation approximation from supplied mean angles; not an IAU 2000/2006 implementation.

Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.

How to use Four Term Nutation Components and understand its results

Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
Enter nodeLongitudeDegrees, sunMeanLongitudeDegrees, moonMeanLongitudeDegrees using the field table and calculation rules, then run the tool.
Read longitudeNutationArcseconds, obliquityNutationArcseconds. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
nodeLongitudeDegrees	Node longitude degrees	number	Required
sunMeanLongitudeDegrees	Sun mean longitude degrees	number	Required
moonMeanLongitudeDegrees	Moon mean longitude degrees	number	Required

Enter finite node longitude and Sun/Moon mean longitudes in degrees. The tool converts them to radians, evaluates the sine/cosine sums and returns longitude and obliquity nutation in arcseconds.

Δψ=−17.2sinΩ−1.32sin2L−0.23sin2l+0.21sin2Ω; Δε=9.2cosΩ+0.57cos2L+0.1cos2l−0.09cos2Ω

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
longitudeNutationArcseconds	Longitude nutation arcseconds	number
obliquityNutationArcseconds	Obliquity nutation arcseconds	number

json

{
  "input": {
    "nodeLongitudeDegrees": 90,
    "sunMeanLongitudeDegrees": 0,
    "moonMeanLongitudeDegrees": 0
  },
  "output": {
    "longitudeNutationArcseconds": -17.2,
    "obliquityNutationArcseconds": 0.7600000000000005
  }
}

Limitations and assumptions

It does not calculate mean arguments from time or implement IAU 2000/2006 nutation. Frame bias, precession, apparent coordinate corrections and accuracy estimates are not included.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Laskar Mean Obliquity: Evaluate the Laskar long-term mean-obliquity polynomial within ±10000 years of J2000; nutation and reference-frame realization are separate. For a complementary task, use Iau1976 Epoch Precession: Precess a mean equatorial direction with the bounded IAU 1976 approximation; proper motion, nutation and modern frame bias are not included.

References

Four Term Nutation Components — tool.io

Similar or alternative tools

Laskar Mean Obliquity
Evaluate the Laskar long-term mean-obliquity polynomial within ±10000 years of J2000; nutation and reference-frame realization are separate.
Iau1976 Epoch Precession
Precess a mean equatorial direction with the bounded IAU 1976 approximation; proper motion, nutation and modern frame bias are not included.