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.

Description

Reciprocal parallax gives a simple positive-distance estimate, but inversion turns a symmetric parallax interval into asymmetric distance bounds.

Reciprocal parallax gives a simple positive-distance estimate, but inversion turns a symmetric parallax interval into asymmetric distance bounds. Those bounds are not automatically posterior credible intervals.^[1]

Compare first-order distance uncertainty with the asymmetric inversion of a supplied ±1-error positive-parallax interval; neither is a posterior credible interval.

When to use Positive Parallax Distance Uncertainty

Use this tool to compare first-order distance uncertainty with the asymmetric inversion of a supplied ±1-error positive-parallax interval; neither is a posterior credible interval.

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 Positive Parallax Distance Uncertainty 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 parallaxMas, standardErrorMas using the field table and calculation rules, then run the tool.
Read distanceParsecs, linearStandardErrorParsecs, invertedLowerParsecs, invertedUpperParsecs. 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
parallaxMas	Parallax mas	number	Required
standardErrorMas	Standard error mas	number	Required

Enter positive parallax in mas and nonnegative standard error strictly smaller than parallax. Return distance parsecs, first-order standard error and reversed reciprocal endpoints: the larger parallax gives the lower distance. Zero error makes both bounds equal to the estimate.

distance=1000/parallaxMas; linearError=1000 error/parallax²; bounds=1000/(parallax±error)

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

Output field	Meaning	Value type
distanceParsecs	Distance parsecs	number
linearStandardErrorParsecs	Linear standard error parsecs	number
invertedLowerParsecs	Inverted lower parsecs	number
invertedUpperParsecs	Inverted upper parsecs	number

json

{
  "input": {
    "parallaxMas": 10,
    "standardErrorMas": 1
  },
  "output": {
    "distanceParsecs": 100,
    "linearStandardErrorParsecs": 10,
    "invertedLowerParsecs": 90.9090909090909,
    "invertedUpperParsecs": 111.11111111111111
  }
}

Limitations and assumptions

Nonpositive parallax intervals are rejected and no Bayesian prior or distance inference is provided. Large fractional errors weaken the linear approximation, and systematic zero-point correction is a separate step.

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 Parallax Zero Point Correction: Subtract caller-provided source-specific astrometric parallax zero points, preserving nonpositive results rather than inverting them to distances. For a complementary task, use Rectilinear Astrometric Epoch Propagation: Propagate a Cartesian constant-space-velocity astrometric state using RA* proper motion and Julian years; light-time, gravity and reference-frame precession are excluded.

References

Positive Parallax Distance Uncertainty — tool.io

Similar or alternative tools

Parallax Zero Point Correction
Subtract caller-provided source-specific astrometric parallax zero points, preserving nonpositive results rather than inverting them to distances.
Rectilinear Astrometric Epoch Propagation
Propagate a Cartesian constant-space-velocity astrometric state using RA* proper motion and Julian years; light-time, gravity and reference-frame precession are excluded.