Quick guide
How to use this calculator
- Choose the astronomical relationship and solve direction first, then keep angles, distances, wavelengths, magnitudes, fluxes, and motion units explicit.
- Use exact geometry where supplied and compare it with the small-angle or classical approximation rather than assuming every astronomical scale uses the same model.
- Use the companion outputs to reconcile the result, then retain the stated observational and model limits before interpreting a theoretical value as a measured physical property.
Calculation method
How the proper motion and tangential velocity calculator works
Keep angular motion, transverse speed, component magnitude, and distance in one explicit relationship without implying radial or full three-dimensional velocity.
Total proper motion μ = hypot(μᵅ*, μδ). Tangential velocity vₜ = 4.740470446 × μ(arcsec/year) × distance(pc). Reverse modes solve μ or distance from the same relationship.
Worked example
Proper Motion and Tangential Velocity example
Components +120 and −160 mas/year give total motion 200 mas/year; at 50 pc the tangential velocity is about 47.4047 km/s.
Total proper motion μ = hypot(μᵅ*, μδ). Tangential velocity vₜ = 4.740470446 × μ(arcsec/year) × distance(pc). Reverse modes solve μ or distance from the same relationship.
Supported inputs
Precision and limits
Astronomy and model boundary
The RA component must already include the conventional cos(declination) factor when applicable. Tangential velocity excludes radial velocity, perspective effects, reference-frame transformations, covariance, epoch propagation, and Solar or Galactic motion corrections.
Precision and reporting
Calculations retain working precision and round only for display. Very small and large nonzero values use scientific notation; displayed digits cannot create accuracy, traceability, or observational certainty absent from the entered data.
Category ownership
This collection owns unit-aware astronomy and extreme-scale measurement relationships. Calendar astronomy, orbital dynamics, cosmology, telescope equipment selection, and professional astrometric reduction require separate models and tools.
Privacy
Entered values and results stay in this browser and are not sent to analytics or third parties.
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