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.

Description

Constant space velocity propagates a three-dimensional astrometric position rather than adding angular proper motion alone.

Constant space velocity propagates a three-dimensional astrometric position rather than adding angular proper motion alone. Radial motion can change distance and apparent angular motion through perspective.^[1]

Propagate a Cartesian constant-space-velocity astrometric state using RA* proper motion and Julian years; light-time, gravity and reference-frame precession are excluded.

When to use Rectilinear Astrometric Epoch Propagation

Use this tool to propagate a Cartesian constant-space-velocity astrometric state using RA* proper motion and Julian years; light-time, gravity and reference-frame precession are excluded.

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 Rectilinear Astrometric Epoch Propagation 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 raDegrees, decDegrees, distanceParsecs, raStarMotionMasPerYear, decMotionMasPerYear, radialKmPerSecond, elapsedJulianYears using the field table and calculation rules, then run the tool.
Read propagatedRaDegrees, propagatedDecDegrees, propagatedDistanceParsecs. 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
raDegrees	Ra degrees	number	Required
decDegrees	Dec degrees	number	Required
distanceParsecs	Distance parsecs	number	Required
raStarMotionMasPerYear	RA proper motion multiplied by cos(declination), not the unscaled RA angular derivative.	number	Required
decMotionMasPerYear	Dec motion mas per year	number	Required
radialKmPerSecond	Radial km per second	number	Required
elapsedJulianYears	Elapsed julian years	number	Required

Enter RA/Dec degrees, positive distance parsecs, RA* and Dec proper motions in mas/year, signed radial velocity km/s and elapsed Julian years. RA* means RA motion already multiplied by cos Dec. The tool combines radial/east/north velocity, converts radial units using a 365.25-day year, advances the Cartesian position and recovers wrapped RA, Dec and distance. A zero resulting position is an error.

positionNext=distance × lineOfSight + CartesianVelocity × elapsedJulianYears

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

Output field	Meaning	Value type
propagatedRaDegrees	Propagated ra degrees	number
propagatedDecDegrees	Propagated dec degrees	number
propagatedDistanceParsecs	Propagated distance parsecs	number

json

{
  "input": {
    "raDegrees": 0,
    "decDegrees": 0,
    "distanceParsecs": 1,
    "raStarMotionMasPerYear": 1000,
    "decMotionMasPerYear": 0,
    "radialKmPerSecond": 0,
    "elapsedJulianYears": 1
  },
  "output": {
    "propagatedRaDegrees": 0.00027777777779647295,
    "propagatedDecDegrees": 0,
    "propagatedDistanceParsecs": 1.0000000000117522
  }
}

Limitations and assumptions

Gravity, light-time, precession and frame bias are excluded. All inputs must share a reference frame and epoch; this is rectilinear propagation, not an ephemeris.

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 Galactic Space Velocity Uvw: Transform ICRS proper motion (RA*=RA·cos Dec), distance and radial velocity into heliocentric U toward Galactic center, V along rotation, W north; no solar-motion correction is applied. 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

Rectilinear Astrometric Epoch Propagation — tool.io

Similar or alternative tools

Galactic Space Velocity Uvw
Transform ICRS proper motion (RA*=RA·cos Dec), distance and radial velocity into heliocentric U toward Galactic center, V along rotation, W north; no solar-motion correction is applied.
Iau1976 Epoch Precession
Precess a mean equatorial direction with the bounded IAU 1976 approximation; proper motion, nutation and modern frame bias are not included.