Laskar Mean Obliquity
Evaluate the Laskar long-term mean-obliquity polynomial within ±10000 years of J2000; nutation and reference-frame realization are separate.
Description
Mean obliquity is the angle between equatorial and ecliptic planes without short-period nutation.
Mean obliquity is the angle between equatorial and ecliptic planes without short-period nutation. A long-term polynomial can supply a model angle when its epoch and bounded range are explicit.1
Evaluate the Laskar long-term mean-obliquity polynomial within ±10000 years of J2000; nutation and reference-frame realization are separate.
When to use Laskar Mean Obliquity
Use this tool to evaluate the Laskar long-term mean-obliquity polynomial within ±10000 years of J2000; nutation and reference-frame realization are separate.
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 Laskar Mean Obliquity 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 julianCenturiesFromJ2000 using the field table and calculation rules, then run the tool.
- Read meanObliquityArcseconds, meanObliquityDegrees. 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 |
|---|---|---|---|
| julianCenturiesFromJ2000 | Julian centuries from j 2000 | number | Required |
Enter finite Julian centuries from J2000 within ±100, corresponding to ±10,000 years. The tool evaluates the eleven-coefficient Laskar polynomial by Horner's method and returns arcseconds and degrees. At zero it uses the model's 84381.448-arcsecond constant.
obliquityArcseconds=HornerPolynomial(julianCenturiesFromJ2000/100) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| meanObliquityArcseconds | Mean obliquity arcseconds | number |
| meanObliquityDegrees | Mean obliquity degrees | number |
{
"input": {
"julianCenturiesFromJ2000": 0
},
"output": {
"meanObliquityArcseconds": 84381.448,
"meanObliquityDegrees": 23.439291111111114
}
}Limitations and assumptions
This is a mean-angle approximation, without nutation, modern frame realization or uncertainty. It does not convert a calendar date to an epoch or rotate coordinates by itself.
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 Four Term Nutation Components: Evaluate a four-term low-precision nutation approximation from supplied mean angles; not an IAU 2000/2006 implementation. For a complementary task, use Equatorial Ecliptic Axis Rotation: Rotate a sky direction between equatorial and ecliptic axes using supplied obliquity; the same epoch must be used for both frames.
References
-
Laskar Mean Obliquity — tool.io
Similar or alternative tools
- Four Term Nutation Components
Evaluate a four-term low-precision nutation approximation from supplied mean angles; not an IAU 2000/2006 implementation.
- Equatorial Ecliptic Axis Rotation
Rotate a sky direction between equatorial and ecliptic axes using supplied obliquity; the same epoch must be used for both frames.