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.

Description

Equatorial and ecliptic coordinates use differently tilted axes.

Equatorial and ecliptic coordinates use differently tilted axes. A supplied obliquity rotates between the two systems when both refer to the same epoch.^[1]

Rotate a sky direction between equatorial and ecliptic axes using supplied obliquity; the same epoch must be used for both frames.

When to use Equatorial Ecliptic Axis Rotation

Use this tool to rotate a sky direction between equatorial and ecliptic axes using supplied obliquity; the same epoch must be used for both frames.

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 Equatorial Ecliptic Axis Rotation 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 longitudeDegrees, latitudeDegrees, obliquityDegrees, direction using the field table and calculation rules, then run the tool.
Read transformedLongitudeDegrees, transformedLatitudeDegrees. 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
longitudeDegrees	Longitude degrees	number	Required
latitudeDegrees	Latitude degrees	number	Required
obliquityDegrees	Obliquity degrees	number	Required
direction	Direction	string	Required

Enter longitude/latitude degrees with latitude within ±90, obliquity 0–90 degrees and one exact supported direction. The tool converts to a unit vector, applies the signed x-axis rotation and returns wrapped longitude and latitude degrees. Zero obliquity leaves the direction unchanged within roundoff.

equatorial→ecliptic uses x-axis rotation −obliquity; reverse uses +obliquity

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

Output field	Meaning	Value type
transformedLongitudeDegrees	Transformed longitude degrees	number
transformedLatitudeDegrees	Transformed latitude degrees	number

json

{
  "input": {
    "longitudeDegrees": 90,
    "latitudeDegrees": 0,
    "obliquityDegrees": 30,
    "direction": "equatorial-to-ecliptic"
  },
  "output": {
    "transformedLongitudeDegrees": 90,
    "transformedLatitudeDegrees": -29.999999999999993
  }
}

Limitations and assumptions

It does not select an obliquity model, precess epochs or add nutation. Longitude/latitude field names must be interpreted in the selected input frame.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Extremely large text inputs are rejected. 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 Icrs To Galactic Coordinates: Apply the fixed ICRS/J2000 Galactic rotation to a sky direction; this is not an epoch propagation.

References

Equatorial Ecliptic Axis Rotation — 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.
Icrs To Galactic Coordinates
Apply the fixed ICRS/J2000 Galactic rotation to a sky direction; this is not an epoch propagation.