Angular Projected Binary Separation
Convert angular binary separation and distance to a tangent-plane projected separation in AU; this is not a deprojected semimajor axis.
Description
Angular binary separation at a supplied distance gives a projected tangent-plane physical separation.
Angular binary separation at a supplied distance gives a projected tangent-plane physical separation. It does not determine the true three-dimensional separation or an orbital semimajor axis.1
Convert angular binary separation and distance to a tangent-plane projected separation in AU; this is not a deprojected semimajor axis.
When to use Angular Projected Binary Separation
Use this tool to convert angular binary separation and distance to a tangent-plane projected separation in AU; this is not a deprojected semimajor axis.
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 Angular Projected Binary Separation 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 separationArcseconds, distanceParsecs using the field table and calculation rules, then run the tool.
- Read projectedSeparationAu. 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 |
|---|---|---|---|
| separationArcseconds | Separation arcseconds | number | Required |
| distanceParsecs | Distance parsecs | number | Required |
Enter nonnegative separation arcseconds strictly below 90 degrees and positive distance parsecs. The tool uses tangent geometry and converts parsecs to AU through the angular unit relation. Zero angle yields zero projected separation.
projectedAU=tan(separationArcsec/3600 in radians) × distancePc × 648000/π Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| projectedSeparationAu | Projected separation au | number |
{
"input": {
"separationArcseconds": 0.01,
"distanceParsecs": 10
},
"output": {
"projectedSeparationAu": 0.10000000000000009
}
}Limitations and assumptions
Projection, orbital phase and distance uncertainty are not removed. This is a separation scale rather than a deprojected orbit or mass estimate; wide-angle perspective may be unsuitable for a binary interpretation.
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 Occultation Stellar Angular Diameter: Estimate diameter from a central occultation-edge crossing and shadow speed, then angular size; diffraction, integration smearing and noncentral chords are excluded. For a complementary task, use Positive Parallax Distance Uncertainty: Compare first-order distance uncertainty with the asymmetric inversion of a supplied ±1-error positive-parallax interval; neither is a posterior credible interval.
References
-
Angular Projected Binary Separation — tool.io
Similar or alternative tools
- Occultation Stellar Angular Diameter
Estimate diameter from a central occultation-edge crossing and shadow speed, then angular size; diffraction, integration smearing and noncentral chords are excluded.
- Positive Parallax Distance Uncertainty
Compare first-order distance uncertainty with the asymmetric inversion of a supplied ±1-error positive-parallax interval; neither is a posterior credible interval.